Integration of fuzzy-weighted zero-inconsistency and fuzzy decision by opinion score methods under a q-rung orthopair environment: A distribution case study of COVID-19 vaccine doses

Abstract

Owing to the limitations of Pythagorean fuzzy and intuitionistic fuzzy sets, scientists have developed a distinct and successive fuzzy set called the q-rung orthopair fuzzy set (q-ROFS), which eliminates restrictions encountered by decision-makers in multicriteria decision making (MCDM) methods and facilitates the representation of complex uncertain information in real-world circumstances. Given its advantages and flexibility, this study has extended two considerable MCDM methods the fuzzy-weighted zero-inconsistency (FWZIC) method and fuzzy decision by opinion score method (FDOSM) under the fuzzy environment of q-ROFS. The extensions were called q-rung orthopair fuzzy-weighted zero-inconsistency (q-ROFWZIC) method and q-rung orthopair fuzzy decision by opinion score method (q-ROFDOSM). The methodology formulated had two phases. The first phase ‘development’ presented the sequential steps of each method thoroughly.The q-ROFWZIC method was formulated and used in determining the weights of evaluation criteria and then integrated into the q-ROFDOSM for the prioritisation of alternatives on the basis of the weighted criteria. In the second phase, a case study regarding the MCDM problem of coronavirus disease 2019 (COVID-19) vaccine distribution was performed. The purpose was to provide fair allocation of COVID-19 vaccine doses. A decision matrix based on an intersection of ‘recipients list’ and ‘COVID-19 distribution criteria’ was adopted. The proposed methods were evaluated according to systematic ranking assessment and sensitivity analysis, which revealed that the ranking was subject to a systematic ranking that is supported by high correlation results over different scenarios with variations in the weights of criteria.

1. Introduction

Decision-making techniques are gaining wide attention, of which the multicriteria decision-making (MCDM) is the most vital [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19]. MCDM is one of the most common real-life behaviours that can be represented as the outcomes of mental and reasoning processes for the identification of the most suitable alternatives concerning predefined attributes or criteria [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37], [38], [39], [40]. In several cases, decision makers (DMs) have difficulty in expressing a specific preference and precise evaluation values accurately when case studies rely on unreliable, ambiguous or incomplete information [41], [42], [43], [44], [45], [46], [47], [48], [49]. Presuming that the preferences of alternatives to qualities articulated by DMs or experts are precise is unrealistic because of the complications of objectivity and vagueness of human reasoning [50][94-101]. Hence, conducting an optimal decision process is an extremely difficult task for DMs. Hence, the principle of fuzzy sets is presented to address MCDM concerns in uncertainty and vagueness, utilising the membership degree to illustrate the level of an element involving a fuzzy set [51]. To improve accuracy in the information expression of evaluation criteria and reliability of decision-making results, researchers have developed tools using different generalisations of fuzzy sets for different application scenarios, including the intuitionistic fuzzy set (IFS) [52] and Pythagorean fuzzy set (PFS) [53]. In complex and varied practical decision-making, fuzzy sets and particular derived fuzzy numbers have potential defects[[51], [94], [95], [96], [97], [98], [99], [100], [101]].

The concept of IFSs takes into account the expression of membership (µ) and non-membership (υ) degrees, and thus the selection of support the MCDM problems are involved. However, this fuzzy set has disadvantages in the context of decision-making information description, and these disadvantages impose restrictions on the representation of membership and non-membership grades, making the sum of the two parameters lower than or equal to 1 [50]. Owing to the limitations of IFSs, researchers have developed a more comprehensive fuzzy set, called the PFS. Notably, the concept of PFSs is driven from IFSs, but more generalisation is involved [54]. PFSs are distinguished in the summation of squares of membership and non-membership grades, which are real numbers bounded by 1 (less than or equal to 1) [55]. The constraint of the PFSs is better than that of IFSs, as indicated in this example: 0.4² +  0.8² =  0.16 + 0.64 = 0.8  ≤ 1. PFSs have received considerable attraction from scientists because it can overcome higher degrees of ambiguously [56, 57]. In the reality, the DMs are obligated to the constraints of PFSs as they cannot provide values to the membership and non-membership grades clearly on the basis of their own preferences [55]. Owing to the limitations of PFSs, a distinct and successive fuzzy set is needed to address the restrictions encountered by DMs.

Yager [58] developed a novel fuzzy concept called the q-rung orthopair fuzzy set (q-ROFS) to solve the disadvantages of information expression in traditional fuzzy sets (i.e. IFSs and PFSs). In the q-ROFSs, the constraint of other fuzzy sets is removed, and the summation of the q powers of membership and non-membership grades are real numbers between the interval [0, 1]. Thus, the DMs are allowed to select any grades for µ and υ anywhere freely (µ ∈ [0, 1] and υ ∈ [0, 1]) [59]. For example, when DM is asked to give his or her preference about a specific case, he or she assigns a value of 0.9 for membership grade and a value of 0.8 for non-membership grade. In this case, the conditions of IFSs and PFSs cannot be achieved because of their constraints. However, the exampled membership and non-membership grades can be represented using a q-ROFS and raising the parameter of the q value to a value equal or greater than 4. When q = 1, the q-ROFS degrades to IFSs. When q = 2, the q-ROFS becomes PFSs (Fig. 1 concludes the relationship amongst IFSs, PFSs and q-ROFS).

Fig. 1.

Concept relationship between IFSs, PFSs and q-ROFS [50].

Owning to the structure representation, the constraint of q-ROFS is considered much better than the other constraints because it provides more space and flexibility under uncertain conditions and enables DMs to select the membership and non-membership degrees freely [60]. Since it was set up, many researchers have extensively studied and utilised it to solve ungainly and troublesome fuzzy cases from different perspectives. Some aggregation operators in the framework of q-ROFSs, such as q-rung orthopair fuzzy Einstein ordered weighted geometric, q-rung orthopair fuzzy Einstein weighted geometric, q-rung orthopair fuzzy Einstein weighted averaging and q-rung orthopair fuzzy Einstein ordered weighted averaging, were presented [41]. Another study [61] was evaluated site selection scheme of garbage disposal plant and support for garbage disposal site selection by illustrating a novel MCDM technique depending on interval q-rung orthopair fuzzy weighted power Muirhead mean operator. A study by [62] defined the conception, the operational laws, score function and accuracy function of Q-rung orthopair normal fuzzy (q-RONF) set. Furthermore, they introduced several novel aggregation operators to aggregate the q-RONF information, including the q-RONF weighted, the q-RONF hybrid operator and the q-RONF ordered weighted. Accordingly [63] measured the q-rung orthopair hesitant fuzzy sets)q-ROHFSs(and the properties related to the distance and similarity measures of q-ROHFSs, and the axiomatised definition and formula for the entropy of q-ROHFSs. Moreover, a q-rung orthopair shadowed set was suggested to represent attribute values and extends the vlsekriterijumska optimizcija i kaompromisno resenje (VIKOR) [50]. The authors in [64] introduced the hybrid concept of q-rung orthopair m-polar fuzzy set (qROmPFS) and developed a robust MCDM approach where several uncertainties are measured by the proposed concept. Additionally, a decision-making model has been developed and used for hybrid q-ROFSs with notions of covering rough sets and techniques for the order of preference by similarity to ideal solution (TOPSIS) [55]. In [56], the entropy measure and TOPSIS based on the correlation coefficient was investigated. Accordingly. the performance of green suppliers with experts’ subjective evaluations was measured with an effective and applicable MCGDM method and q-ROFSs-based TOPSIS method [65]. A systematic selection of a renewable energy source was presented using a q-ROFSs-based MCDM framework considering sustainability attributes [66].

From a different MCDM aspect, the fuzzy decision by opinion score method (FDOSM) was developed [67], which presented a comprehensive solution to resolve different challenges in MCDM. The development of the FDOSM considered the concept of an ideal solution, reduced the number of comparisons, defined fair and implicit understandable comparisons, prevented inconsistency, reduced vagueness and yielded a minimum number of mathematical operations. The first version of the FDOSM focuses exclusively on triangular fuzzy numbers (TFNs) and considers the arithmetic mean operator in the direct aggregation MCDM approach whilst neglecting the other operators. The FDOSM neglects the application of distance measurement and compromise rank MCDM approaches, presenting a serious issue that may lead to different ranking results. Consequently, the FDOSM is extended using same fuzzy set, but it focuses on other direct aggregation operators, which include geometric mean, harmonic mean and root mean square. In this version, distance measurement and compromise rank approaches are applied for the identification of the best alternative [45]. The last version of FDOSM is extended on the basis of interval type-2 trapezoidal membership [68]. However, the concept of FDOSM can assign weights for the criteria of each alternative in an implicit way. The FDOSM is limited when it explicitly computes weight for each criterion. To resolve this issue, a method explicitly assigning weights to criteria without pairwise comparison among the sets of criteria is needed. According to the literature review, the latest method was proposed in [69], namely, fuzzy-weighted zero-inconsistency (FWZIC) method, which can provide weights for criteria with zero inconstancy. The FWZIC method solves the following limitations of the best worst method and analytic hierarchy process: (i) the inability of the procedure to offer decision maker instant feedback on the consistency of pairwise comparisons, (ii) absence of accounting for ordinary consistency and (iii) shortage of consistency threshold value for evaluating the reliability of results [69]. However, FWZIC was developed according to TFNs. However, it is limited when used in solving uncertainty and vagueness issues. Owing to the advantages of the interval type-2 trapezoidal membership in the definition of the exact membership function, a new version of FWZIC was developed [70].

In summary, taking the advantages of q-ROFS in dealing with the uncertain conditions by providing a more space in the data representation and structuring effectively, the authors of this study extended the FWZIC and FDOSM under the fuzzy environment of q-ROFS. The extensions were called q-rung orthopair fuzzy-weighted zero-inconsistency (q-ROFWZIC) method and q-rung orthopair fuzzy decision by opinion score method (q-ROFDOSM). The detailed description and steps of each and corresponding case studies are illustrated in the following section.

2. Methodology

Two sequential phases are presented in the proposed methodology, which are development and case study phases. In the development phase, the proposed MCDM methods are formulated and integrated. The first method (q-ROFWZIC) is developed and used in determining the weights of the evaluation criteria, and the second method (q-ROFDOSM) is developed for the prioritisation of the alternatives on the basis of the weighted criteria. The second phase presents the description of a distribution case study of coronavirus disease 2019 (COVID-19) vaccine doses as a proof of concept. The summarised methodology is illustrated in Fig. 2 .

Fig. 2.

Methodology flowchart.

2.1. Phase I: Development of MCDM Methods

In this methodology phase, the mechanism of two MCDM methods based on the q-ROFSs environment was developed. The weighting process for the evaluation criteria is achieved by using q-ROFWZIC, while q-ROFDOSM is used for the ranking of alternatives. The q-ROFWZIC method has five steps, and the q-ROFDOSM is formulated on the basis of two stages: data transformation and data processing as seen (Fig. 2). The following subsections describe each method separately and provide relevant mathematical expressions.

2.1.1. Formulation of q-ROFWZIC method

In this section, the details of the five steps of q-ROFWZIC method are explained for the purpose of weight determination for the evaluation criteria used.

Step 1: Definition of the set of evaluation criteria

This step has two processes. The first process is the exploration and presentation of a predefined set of evaluation criteria, and the second process is the classification and categorisation of all the collected criteria. The defined and selected criteria must be evaluated by a panel of experts, as explained in the next step.

Step 2: Structured expert judgement

To evaluate and define the level of importance for the evaluation criteria, a panel of three experts must be identified and utilised. After exploration and identification of the list of prospective experts, selection and nomination commence, and the structured expert judgement (SEJ) panel is established. Lastly, an evaluation form is developed and used in obtaining the consensus of all the SEJ panelists for each criterion, the linguistic scale is converted into its equivalent numerical scale.

• a)Identify experts: Anyone who has knowledge about a subject cannot be considered an expert. Instead, an ‘expert for a given subject’ is used here to designate a person whose present or past field involves the subject in question and who is regarded by others as knowledgeable about the subject. Such individual is occasionally designated in the literature as a ‘domain’ or ‘substantive’ expert. This process distinguishes the individual from ‘normative experts’, that is, experts in statistics and subjective probability.
• b)Select experts: After the identification of the set of experts, the experts who will be involved in the study must be selected. In general, the largest number of experts consistent with the level of resources should be used. All potential experts named during expert identification can be contacted through email, and whether they are interested and whether they consider themselves potential experts for the panel are determined.
• c)Develop the evaluation form: The development of an evaluation form is a crucial step because this instrument is used in obtaining expert consensus. Before the finalisation of the evaluation form, the questionnaire undergoes reliability and validity testing, and the potential experts can review it.
• d)Define the level of importance scale: In this step, the selected group of experts can define the level of importance or significance of each criterion with a five-point Likert scale. No theoretical reason exists to rule out different lengths of a response scale [69]. The options reflect an underlying continuum rather than a finite number of possible attitudes. Various lengths ranging from 2 points to 11 points or higher are used in surveys. Five has become the norm in Likert scales probably because it strikes a balance between the conflicting goals of offering sufficient choices (because providing only two or three options means measuring only the direction rather than the strength of opinion) and makes things manageable for respondents (few people have a clear idea of the difference between the 8th and 9th points in an 11‐point agree–disagree scale). Research confirms that data from Likert items (and those from similar rating scales) becomes significantly less accurate when the number of scale points decreases to values below five or increases to values above seven. However, these studies provide no reasons for preferring five-point scales to seven‐point scales.
• e)Convert linguistic scale to equivalent numerical scale: As mentioned, all preference values are identified in a subjective form, which cannot be used for further analysis unless the values are converted into numerical values. Thus, in this step, the level of importance or significance of each criterion recorded by each expert on the linguistic Likert scale is converted into an equivalent numerical scale, as shown in Table 1 .

Table 1.

Five-point Likert scale and equivalent numerical scale.

Numerical scoring scale	Linguistic scoring scale
1	Not important
2	Moderately Slight important
3	Moderately important
4	Important
5	Very important

A Likert scale assumes that the evaluation criteria have different important levels that should be assigned by an expert. The importance level is assigned with a linguistic scale that facilitates the process of the evaluation criteria. The importance levels range from ‘not important’ level to ‘very important’. However, when an additional analysis needs to be conducted on the scores obtained by experts, it is difficult to extract any useful information from linguistic scores unless it is converted into numerical values. Thus, an equivalent numerical value has been provided along with each linguistic term where measuring the importance level of the evaluation criteria.

Step 3: Building an expert decision matrix

The previous step clarifies how the experts can be selected and how their preferences must indicate. In this step, an expert decision matrix (EDM) is constructed. The main parts of the EDM are the evaluation criteria used and alternatives, as shown in Table 2 .

Table 2.

Expert decision matrix.

Criteria Experts	C1	C2	…	Cn
E1	Imp (E1/C1)	Imp (E1/C2)	…	Imp (E1/Cn)
E2	Imp (E2/C1)	Imp (E2/C2)	…	Imp (E2/Cn)
E3	Imp (E3/C1)	Imp (E3/C2)	…	Imp (E3/Cn)
...	…	…	…	…
Em	Imp (En/C1)	Imp (En/C2)	…	Imp (Em/Cn)

**Imp represents the importance level.

According to Table 2, a crossover is made between the evaluation criteria and the SEJ panel. Each criterion (Cj) in the attribute intersects with each selective expert (Ei), where the expert has scored the suitable level of importance for each criterion. The EDM is the base for further analysis steps in the proposed method, which are illustrated in the next steps.

Step 4: Application of q-ROFS membership function

In this step, the q-ROFS membership function and subsequent defuzzification process are applied to the EDM data, and the data are transformed to a q‐ROF-EDM to increase their precision and ease of use in further analysis. However, in MCDM, the problem is uncertain and imprecise because assigning a precise preference rate to any criterion is difficult. The advantage of using the fuzzy method is the use of vague numbers instead of crisp numbers in the determination of the relative values of attributes (criteria); this approach addresses the issue of imprecise and uncertain problems. The q-ROFS is an objective having the form of [71] and defined in Eqs. (1) and (2).

$$P=\{〈m,({\mu }_d\left(m\right),{\mathrm{v}}_d\left(m\right))〉|m\in m\},$$ (1)

where μ_d: M → [0, 1] is the membership function, while v_d: M → [0, 1] is non-membership function of element m ∈ M to p, and it must fulfil the restriction seen in Eq. (2).

$$0<{\left({\mu }_d\left(m\right)\right)}^q+{\left(v_d\left(m\right)\right)}^q\le 1,\text{where}\mathrm{q}\ge 1.$$ (2)

The degree of hesitancy is presented in Eq. (3) as following:

$${\pi }_m\left(m\right)=\sqrt[q]{{\left({\mu }_d\left(m\right)\right)}^q+{\left(v_d\left(m\right)\right)}^q-{\left({\mu }_d\left(m\right)\right)}^q.{\left(v_d\left(m\right)\right)}^q}.$$ (3)

The applied q-rung orthopair fuzzy arithmetic mean (q-ROFA) aggregation operation is shown in Eq. (4) as follows:

$$\mathrm{q}-\text{ROFA}\left({\tilde{a}}_1,{\tilde{a}}_2,\dots ,{\tilde{a}}_n\right)=〈{\left(1-\prod _{k=1}^n\left(1-{\mu }_k^q\right)\right)}^{\frac{1}{q}},\prod _{k=1}^n{v}_k〉$$ (4)

Eq. (5) shows the q-ROFS division operation as follows:

$${\mathit{p}}_1\oslash {\mathit{p}}_2=\left(\frac{{\mathit{\mu }}_1}{{\mathit{\mu }}_2},\sqrt{\frac{{\mathit{v}}_1^{\mathit{q}}-{\mathit{v}}_2^{\mathit{q}}}{1-{\mathit{v}}_2^{\mathit{q}}}}\right),\text{if}{\mathit{\mu }}_1\le \mathit{min}\left\{{\mathit{\mu }}_2,\frac{{\mathit{\mu }}_2{\mathit{\pi }}_1}{{\mathit{\pi }}_2}\right\},{\mathit{v}}_1\ge {\mathit{v}}_2.$$ (5)

Eq. (6) shows the equation of q-ROFS division on a crisp value. The value of each linguistic term with q-ROFS is shown in Table 3 .

$$\begin{array}{c}p/\lambda =\left(\sqrt[q]{1-{\left(1-{\left({\mu }_p\right)}^q\right)}^{\frac{1}{\lambda }}},{\left(v_p\right)}^{\frac{1}{\lambda }}\right),\lambda \hfill \\ >0.\hfill \end{array}$$ (6)

Table 3.

Linguistic terms and their equivalent q-ROFS.

Linguistic scale	q-ROFS
Not important	(0.20, 0.90)
Slight important	(0.40, 0.60)
Moderately important	(0.65, 0.50)
Important	(0.80, 0.45)
Very important	(0.90, 0.20)

Table 3 indicates that all linguistic variables are converted into q-ROFS. The fuzzy number is assumed to be the variable for each criterion for Expert K. In other words, Expert K must ask to identify the importance level of the evaluation criteria within variables measured using a linguistic scale.

Step 5: Computation of the final values of the weight coefficients of the evaluation criteria

Based on the fuzzification data for the criteria in the previous step, the final values of the weight coefficients of the evaluation criteria (w1, w2,  ..., wn)^T are calculated as follows:

• a)The ratio of fuzzification data is computed using Eqs. (3), (4) and (5). The preceding equations are used with q-ROFS, as shown in Table 4 .
• b)
  The mean values are computed for the identification of the fuzzy values of the weight coefficients of the evaluation criteria ${\left(\widetilde{w1},\widetilde{w2},...,\widetilde{wn}\right)}^T$. The q‐ROF-EDM is used in computing the weight value of each criterion with Eqs. (3)–(6), where Eq. (7) symbolises the process.

  $$\widetilde{w_j}=\left(\sum _{i=1}^m\frac{Imp\left(\widetilde{E_{ij}}/C_{ij}\right)}{{\sum }_{j=1}^{n}Imp\left(\widetilde{E_{ij}}/C_{ij}\right)}\right)/m),\text{for}i=1,2,3,..mandj=1,2,3,..n.$$ (7)
• c)
  Defuzzification is performed for the determination of the final weight. Eq. (8) is used as the defuzzification method for scoring each criterion. For the calculation of the final values of the weight coefficients, the weight for the importance of each criterion should be assigned given the sum of the weights of all the criteria for the rescaling purpose applied in this stage.

  $$S_k={{\mu }_{\mathrm{k}}}^q-{{\mathrm{v}}_{\mathrm{k}}}^q,\text{where}\mathrm{q}\ge 1.$$ (8)

Table 4.

q‐ROF-EDM.

Criteria/Experts	$\widetilde{\mathbf{C}1}$	$\widetilde{\mathbf{C}2}$	…	$\widetilde{\mathbf{Cn}}$
E1	$\frac{\widetilde{\text{Imp}\left(\mathrm{E}1/\mathrm{C}1\right)}}{{\sum }_{\mathrm{j}=1}^{\mathrm{n}}\widetilde{\text{Imp}(\mathrm{E}1/{\mathrm{C}}_{1\mathrm{j}})}}$	$\frac{\widetilde{\text{Imp}\left(\mathrm{E}1/\mathrm{C}1\right)}}{{\sum }_{\mathrm{j}=1}^{\mathrm{n}}\widetilde{\text{Imp}(\mathrm{E}1/{\mathrm{C}}_{1\mathrm{j}})}}$	…	$\frac{\widetilde{\text{Imp}\left(\mathrm{E}1/\mathrm{C}1\right)}}{{\sum }_{\mathrm{j}=1}^{\mathrm{n}}\widetilde{\text{Imp}(\mathrm{E}1/{\mathrm{C}}_{1\mathrm{j}})}}$
E2	$\frac{\widetilde{\text{Imp}\left(\mathrm{E}2/\mathrm{C}1\right)}}{{\sum }_{\mathrm{j}=1}^{\mathrm{n}}\widetilde{\text{Imp}(\mathrm{E}2/{\mathrm{C}}_{2\mathrm{j}})}}$	$\frac{\widetilde{\text{Imp}\left(\mathrm{E}2/\mathrm{C}2\right)}}{{\sum }_{\mathrm{j}=1}^{\mathrm{n}}\text{Imp}(\mathrm{E}2/{\mathrm{C}}_{2\mathrm{j}})}$	…	$\frac{\widetilde{\text{Imp}\left(\mathrm{E}2/\text{Cn}\right)}}{{\sum }_{\mathrm{j}=1}^{\mathrm{n}}\text{Imp}(\mathrm{E}2/{\mathrm{C}}_{2\mathrm{j}})}$
...	…	…	…	…
Em	$\frac{\widetilde{\text{Imp}\left(\text{Em}/\mathrm{C}1\right)}}{{\sum }_{\mathrm{j}=1}^{\mathrm{n}}\widetilde{\text{Imp}(\text{Em}/\mathrm{C}{\mathrm{m}}_{\mathrm{j}}})}$	$\frac{\widetilde{\text{Imp}\left(\text{Em}/\mathrm{C}2\right)}}{{\sum }_{\mathrm{j}=1}^{\mathrm{n}}\widetilde{\text{Imp}(\text{Em}/{\mathrm{C}}_{\text{mj}})}}$	…	$\frac{\widetilde{\text{Imp}\left(\text{Em}/\text{Cn}\right)}}{{\sum }_{\mathrm{j}=1}^{\mathrm{n}}\widetilde{\text{Imp}(\text{Em}/{\mathrm{C}}_{\text{mn}})}}$

where $\widetilde{\mathit{Imp}\left(\mathit{E}1/\mathit{C}1\right)}$ represent the fuzzy number of Imp (E1/C1).

2.1.2. Formulation of the q-ROFDOSM

The q-ROFDOSM is the extended version of different FDOSM versions [72], [73], [74]. The following description provides information about the first stage of the q-ROFDOSM, which is the data transformation unit. The second stage of the q-ROFDOSM is explained, which is data processing.

Stage One: Data transformation unit

According to [74], the transformation of the decision matrix into an opinion matrix is achieved with the following steps.

Step 1

The ideal solution of each sub evaluation criterion in the decision matrix used is selected. Therefore, the ideal solution is defined in Eq. (9).

$$A^{*}=\left\{\left[\left(\underset{i}{max}{v}_{ij}|j\in J\right),\left(\underset{i}{min}{v}_{ij}|j\in J\right),\left(O{p}_{ij}\in I.J\right)|i=1.2.3.\dots .m\right]\right\},$$ (9)

where max is the ideal value for benefit criteria, min is the ideal solution for cost criteria and Op_ijis the ideal value for critical criteria when the ideal value lies between the max and min. The critical value is determined by the decision maker.

Step 2

In this step, the ideal solution value must be selected for each evaluation criterion. Then, a five-point Likert scale is used to perform the reference comparison between the selected ideal solution of each evaluation criterion and other values within same criterion, as shown in Eq. (10).

$$O{p}_{Lang}=\left\{\left(\left(\underset{ij}{\tilde{v}}\otimes v_{ij}|j\in J\right).|i=1.2.3.\dots .m\right)\right\},$$ (10)

where ⊗ represents the reference comparison between the ideal solution and value of alternatives in the same criterion. The final output of this block indicating the linguistic term is the opinion matrix that is ready to be transformed into a fuzzy opinion matrix by using q-ROFSs, as expressed in Eq. (11).

$$O{p}_{Lang}=\begin{array}{c}{A}_1\\ ⋮\\ A_m\end{array}\left[\begin{array}{ccc}o{p}_{11}& \cdots & o{p}_{1n}\\ ⋮& \ddots & ⋮\\ o{p}_{m1}& \cdots & o{p}_{mn}\end{array}\right].$$ (11)

Stage Two: Data-processing unit

The opinion matrix of each Likert scale refers to the output of the transformation unit. The final block begins by transferring the opinion matrix into a q‐ROF opinion matrix by converting the linguistic terms of the opinion matrix into q-ROFSs using Table 5 .

Table 5.

q‐ROF opinion matrix.

Linguistic scale	q-ROFSs
No Difference	(0.90, 0.20)
Slight Difference	(0.80, 0.45)
Difference	(0.65, 0.50)
Big Difference	(0.40, 0.60)
Huge Difference	(0.20, 0.90)

In the q-ROFDOSM, two different contexts of can be used for ranking the alternatives, which are individual and group decision making (GDM).

2.1.2.1. Individual q-ROFDOSM

q-ROFS is applied with the proposed method in this stage. The obtained explicit weights of each criterion are introduced to q-ROFDOSM for the prioritisation of the alternatives. The fuzzy opinion matrices resulting from the previous stage are aggregated using the equation of the q-rung orthopair fuzzy weighted arithmetic mean (q-ROFWA) aggregation operation (12).

$$\mathrm{q}-\text{ROFWA}\left({\tilde{a}}_1,{\tilde{a}}_2,\dots ,{\tilde{a}}_n\right)=〈{\left(1-{\prod }_{k=1}^n{\left(1-{\mu }_k^q\right)}^{wk}\right)}^{1/q},{\prod }_{k=1}^n{v}_k^{w_k}〉$$ (12)

Then, the defuzzification process of each alternative is computed using Eq. (8). After the calculations are performed with the mentioned equations in the individual context of q-ROFDOSM, alternatives can be ranked and prioritised. A value will be assigned to each alternative will be assigned a value, and they will be ordered based on the best value. The vaccine recipient with the highest score will have the highest priority.

2.1.2.2. Group q-ROFDOSM

Owing to the variations that might be found in the ranking of alternatives among decision makers, aggregated decisions obtained from various evaluators are necessary to unify alternative ranking. Thus, this study utilises a GDM with q-ROFDOSM to unify all the variations in the ranking of the decision makers. Furthermore, arithmetic mean is used, and a final score of GDM is obtained. The highest score value is the best alternative. In this case, the decision makers’ opinions are combined after the final alternatives ranking.

2.2. Phase II: MCDM case study

The current phase discusses a case study of COVID-19 vaccine distribution. Countries worldwide faced the greatest challenge last year brought by the coronavirus disease 2019 (COVID-19) pandemic, and the need for a vaccine has become more important than ever [75], [76], [77], [78], [79], [80], [81], [82]. The fair allocation of COVID-19 vaccine distribution is encouraged by the World Health Organisation, and public health benefits must be maximized in order that health products are available and accessible to those in need [83]. However, the distribution mechanism of COVID-19 vaccine doses considered a MCDM problem because of the following issues: required inclusion of different distribution criteria, criteria that are different in significance and increase in problem complexity because of data variation amongst the included criteria. To end this problem complexity, an MCDM-based solution must be used. A comprehensive decision matrix of COVID-19 vaccine distribution is constructed on the basis of the intersection of vaccine recipients (VRs) and distribution criteria, as presented in Table 6 [84].

Table 6.

Constructed decision matrix.

VR	C1	C2	C3	C4	C5	VR	C1	C2	C3	C4	C5
1	Pharmacist	Hypertension, diabetes	31	Green	NA	151	-	NA	53	Green	NA
2	Pharmacist	NA	59	Yellow	Hearing difficulty	152	-	NA	59	Red	Epilepsy
3	Doctor	Diabetes	37	Green	NA	153	-	Cardiovascular	83	Orange	Hearing difficulty
4	Pharmacist	Obesity	47	yellow	NA	154	Health worker	Respiratory	59	Yellow	NA
5	Health Worker	NA	29	Green	Vision impairment	155	Health worker	NA	59	Red	NA
6	Electricity supplier	NA	29	Red	Hearing difficulty	156	Doctor	NA	41	Green	NA
7	Teacher	NA	31	Green	NA	157	Nurse	NA	29	Green	NA
8	Teacher	NA	31	Yellow	NA	158	Doctor	Diabetes	43	Red	NA
9	Police officer	NA	47	Red	NA	159	Medical goods seller	Diabetes	43	Green	NA
10	Teacher	NA	37	Green	NA	160	Medical goods seller	Obesity	37	Orange	NA
11	-	Respiratory	59	Red	NA	161	Medical goods seller	Diabetes	37	Green	NA
12	-	Cardiovascular	7	Red	NA	162	Fire service employee	NA	41	Orange	Epilepsy
13	-	Diabetes	3	Orange	NA	163	-	NA	17	Yellow	NA
14	-	Diabetes	43	Yellow	NA	164	-	NA	23	Green	NA
15	-	Respiratory	37	Yellow	NA	165	-	Hypertension	59	Yellow	NA
16	Pharmacist	NA	43	Green	NA	166	-	NA	43	Green	NA
17	Pharmacist	NA	41	Yellow	NA	167	-	NA	19	Orange	NA
18	Doctor	Respiratory	41	Green	NA	168	Medical goods seller	NA	41	Yellow	Epilepsy
19	Nurse	NA	29	Orange	NA	169	Fire service employee	Diabetes	47	Yellow	NA
20	Pharmacist	Cardiovascular	37	Red	NA	170	Fire service employee	NA	59	Orange	NA
21	-	Cardiovascular	41	Orange	NA	171	Fire service employee	Respiratory	61	Orange	Vision impairment
22	-	NA	13	Green	NA	172	Doctor	NA	59	Green	NA
23	-	NA	11	Green	NA	173	Health worker	Cardiovascular	61	Orange	NA
24	-	Respiratory	89	Yellow	Vision impairment	174	Midwife	NA	23	Red	NA
25	-	NA	61	Green	NA	175	Nurse	Hypertension	43	Red	NA
26	Medical goods seller	Hypertension	43	Orange	Hearing difficulty	176	Health worker	Respiratory	43	Red	NA
27	Medical goods seller	Diabetes	47	Green	NA	177	Health worker	Diabetes	41	Red	NA
28	Teacher	Respiratory	59	Yellow	NA	178	Doctor	NA	41	Yellow	NA
29	Police officer	NA	47	Yellow	NA	179	Doctor	Hypertension	29	Yellow	NA
30	police officer	NA	53	Green	NA	180	Postal employee	NA	29	Red	NA
31	midwife	Diabetes	31	Orange	NA	181	Medical goods seller	Cardiovascular	43	Yellow	Vision impairment
32	Health Worker	NA	47	Red	Hearing difficulty	182	Religious staff	Respiratory	59	Red	NA
33	Nurse	Hypertension, cardiovascular	43	Yellow	NA	183	Journalist	Hypertension	53	Red	NA
34	Midwife	Obesity	23	Orange	NA	184	Electricity supplier	NA	53	Red	NA
35	Doctor	Obesity, hypertension	61	Yellow	NA	185	Education specialist	NA	23	Red	NA
36	Pharmacist	NA	59	Green	NA	186	Medical goods seller	NA	23	Red	NA
37	Specialist education professional	Cardiovascular, hypertension	59	Orange	NA	187	-	NA	1	Yellow	NA
38	Electricity supplier	NA	41	Orange	NA	188	-	NA	29	Orange	NA
39	Police officer	NA	31	Yellow	NA	189	-	Diabetes	59	Red	Epilepsy
40	Religious staff	Cardiovascular	59	Yellow	Hearing difficulty	190	-	NA	7	Green	NA
41	Teacher	Hypertension	47	Orange	NA	191	-	NA	41	Orange	NA
42	Health Worker	NA	37	Orange	NA	192	-	NA	31	Green	NA
43	Doctor	NA	37	Green	NA	193	Midwife	NA	31	Yellow	NA
44	Nurse	Diabetes	41	Green	Hearing difficulty	194	Midwife	Hypertension	53	Yellow	NA
45	Pharmacist	Diabetes	53	Red	NA	195	Health worker	NA	43	Green	NA
46	Doctor	Obesity	41	Green	NA	196	Health worker	NA	61	Red	Vision impairment
47	-	Cardiovascular	97	Red	Vision impairment	197	Nurse	Respiratory	23	Yellow	NA
48	-	NA	31	Orange	NA	198	Delivery worker	NA	31	Green	NA
49	-	NA	29	Orange	NA	199	Medical goods seller	NA	47	Orange	NA
50	-	NA	53	Red	NA	200	Medical goods seller	Cardiovascular, Hypertension	61	Orange	NA
51	-	Obesity	53	Orange	NA	201	Medical goods sales	NA	37	Green	Epilepsy
52	-	NA	47	Orange	NA	202	Education specialist	Respiratory	23	Red	NA
53	Journalist	NA	31	Yellow	NA	203	Police officer	NA	43	Yellow	NA
54	Journalist	NA	31	Orange	NA	204	-	NA	2	Red	NA
55	Journalist	Diabetes	59	Green	NA	205	-	NA	2	Green	NA
56	Teacher	NA	41	Yellow	NA	206	-	Diabetes	67	Red	Epilepsy
57	Probation staff	NA	31	Green	Hearing difficulty	207	-	NA	2	Orange	NA
58	Pharmacist	NA	43	Yellow	NA	208	-	NA	2	Yellow	NA
59	Pharmacist	NA	53	Yellow	NA	209	-	NA	5	Green	NA
60	Nurse	NA	59	Green	NA	210	Medical goods seller	NA	29	Green	NA
61	Midwife	NA	23	Yellow	NA	211	Fire service employee	NA	29	Yellow	NA
62	Health Worker	NA	61	Green	Hearing difficulty	212	Medical goods seller	NA	41	Red	NA
63	-	NA	47	Red	NA	213	Midwife	NA	23	Orange	NA
64	-	NA	19	Orange	NA	214	Health worker	NA	61	Orange	NA
65	-	Hypertension	83	Yellow	Vision impairment	215	Doctor	NA	61	Red	NA
66	-	NA	5	Orange	NA	216	Doctor	NA	59	Yellow	NA
67	Doctor	NA	29	Orange	NA	217	Health worker	Obesity	59	Green	Epilepsy
68	Nurse	NA	31	Yellow	NA	218	Midwife	Diabetes	41	Red	NA
69	Fire service Employee	NA	29	Yellow	NA	219	-	Respiratory	89	Green	Hearing difficulty
70	Postal employee	Respiratory	53	Green	NA	220	-	NA	7	Orange	NA
71	Journalist	Hypertension	61	Red	NA	221	-	Cardiovascular	83	Orange	Epilepsy
72	-	NA	19	Orange	NA	222	Medical goods seller	NA	47	Yellow	NA
73	-	NA	61	Orange	NA	223	Education specialist	NA	41	Red	Epilepsy
74	-	NA	61	Green	NA	224	Medical goods seller	Respiratory	61	Green	NA
75	Pharmacist	Obesity	41	Orange	NA	225	-	NA	43	Orange	NA
76	Midwife	Respiratory	37	Yellow	NA	226	-	Obesity	59	Orange	NA
77	Doctor	NA	23	Orange	NA	227	-	NA	3	Green	NA
78	Midwife	Respiratory	59	Red	NA	228	-	Hypertension	89	Orange	Hearing difficulty
79	Health worker	Hypertension	41	Yellow	Epilepsy	229	-	NA	17	Green	NA
80	Doctor	NA	59	Yellow	NA	230	Doctor	Hypertension	41	Yellow	NA
81	Nurse	NA	37	Red	NA	231	Health worker	NA	61	Red	NA
82	Religious staff	Hypertension	53	Green	NA	232	Nurse	Respiratory	61	Orange	NA
83	Delivery worker	NA	23	Yellow	NA	233	Health worker	NA	47	Green	NA
84	Postal employee	NA	23	Green	NA	234	Midwife	NA	61	Orange	NA
85	Specialist education professional	Obesity, diabetes	61	Yellow	Vision impairment	235	-	Hypertension	89	Red	Hearing difficulty
86	Fire service employee	Respiratory	59	Orange	NA	236	-	NA	1	Orange	NA
87	Pharmacist	Obesity	23	Red	NA	237	-	Hypertension	79	Green	NA
88	Doctor	NA	41	Orange	NA	238	Probation staff	NA	23	Yellow	NA
89	Health worker	NA	47	Red	NA	239	Religious staff	Diabetes	53	Orange	NA
90	-	NA	13	Orange	NA	240	Electricity supplier	NA	41	Orange	NA
91	-	NA	7	Green	NA	241	Religious staff	Hypertension	59	Red	NA
92	-	NA	11	Orange	NA	242	-	Hypertension	71	Red	NA
93	-	Diabetes, hypertension	97	Yellow	Epilepsy	243	-	NA	2	Yellow	NA
94	-	NA	89	Yellow	Epilepsy	244	-	Cardiovascular	47	Orange	NA
95	Probation staff	NA	41	Red	NA	245	Doctor	NA	43	Red	NA
96	Journalist	Cardiovascular, hypertension	61	Red	NA	246	Midwife	Respiratory	61	Red	NA
97	Medical goods seller	Obesity	59	Yellow	NA	247	Pharmacist	NA	53	Green	Hearing difficulty
98	Charity staff	NA	59	Orange	NA	248	Midwife	Diabetes, hypertension	31	Yellow	NA
99	Doctor	NA	53	Yellow	NA	249	Midwife	NA	59	Yellow	NA
100	Doctor	NA	53	Red	NA	250	Midwife	NA	47	Orange	NA
101	Pharmacist	NA	37	Orange	NA	251	Probation staff	Cardiovascular, hypertension	61	Red	NA
102	-	NA	47	Green	NA	252	Postal employee	NA	41	Green	NA
103	-	NA	47	Green	NA	253	Education specialist	NA	43	Green	NA
104	-	NA	61	Orange	NA	254	Delivery worker	Hypertension	59	Orange	NA
105	-	NA	71	Yellow	NA	255	Journalist	Respiratory	61	Red	Vision impairment
106	Electricity supplier	NA	43	Red	NA	256	-	NA	1	Red	NA
107	Charity staff	NA	37	Red	Hearing difficulty	257	-	NA	1	Red	NA
108	Religious staff	NA	47	Orange	NA	258	-	Obesity	31	Yellow	NA
109	Pharmacist	NA	43	Red	NA	259	-	NA	11	Green	NA
110	Doctor	Cardiovascular, hypertension	47	Yellow	NA	260	Nurse	NA	23	Red	NA
111	-	Obesity	29	Green	NA	261	Pharmacist	NA	47	Orange	NA
112	-	NA	5	Red	NA	262	Pharmacist	Hypertension	53	Yellow	NA
113	-	NA	41	Red	NA	263	Fire service employee	NA	23	Green	NA
114	-	NA	59	Orange	NA	264	Religious staff	NA	23	Red	NA
115	-	NA	3	Green	NA	265	Electricity supplier	Cardiovascular	53	Orange	Hearing difficulty
116	Midwife	NA	29	Red	NA	266	Religious staff	Respiratory	53	Orange	NA
117	Nurse	Obesity, diabetes	29	Yellow	NA	267	Teacher	NA	31	Yellow	NA
118	Midwife	Diabetes	58	Green	Hearing difficulty	268	Education specialist	Hypertension	41	Yellow	NA
119	Health worker	NA	53	Orange	NA	269	-	NA	5	Green	NA
120	Electricity supplier	Cardiovascular	61	Red	NA	270	-	NA	2	Red	NA
121	Postal employee	Respiratory	31	Orange	NA	271	-	NA	59	Green	NA
122	Journalist	Obesity	53	Orange	NA	272	-	NA	37	Red	NA
123	Teacher	NA	37	Green	NA	273	-	Obesity	61	Green	NA
124	-	Diabetes	61	Green	NA	274	-	Hypertension	97	Red	Hearing difficulty
125	-	Respiratory	97	Yellow	Hearing difficulty	275	Health worker	Diabetes	41	Orange	NA
126	-	Respiratory	79	Green	NA	276	Nurse	Respiratory	31	Yellow	NA
127	Religious staff	Respiratory	43	Red	NA	277	Nurse	NA	59	Orange	NA
128	Religious staff	Obesity, diabetes	43	Green	Hearing difficulty	278	-	Hypertension	37	Yellow	NA
129	Religious staff	NA	29	Green	NA	279	-	NA	1	Green	NA
130	Nurse	Respiratory	29	Green	NA	280	-	Cardiovascular	61	Orange	NA
131	Health worker	NA	53	Green	NA	281	-	Diabetes	83	Red	Epilepsy
132	Midwife	Obesity, diabetes	29	Orange	NA	282	-	Obesity	73	Red	NA
133	Health worker	NA	37	Orange	NA	283	Teacher	Cardiovascular, hypertension	61	Red	NA
134	Health worker	NA	47	Orange	NA	284	Education specialist	Obesity, diabetes	61	Red	NA
135	-	Obesity	73	Red	NA	285	-	NA	5	Green	NA
136	-	NA	13	Yellow	NA	286	-	NA	97	Orange	NA
137	-	NA	59	Yellow	NA	287	Religious staff	NA	29	Red	NA
138	-	NA	2	Yellow	NA	288	Police officer	Diabetes	61	Red	NA
139	Charity staff	NA	37	Yellow	NA	289	Journalist	NA	47	Yellow	Vision impairment
140	Charity staff	NA	53	Orange	NA	290	Medical goods seller	NA	47	Green	NA
141	Delivery worker	Diabetes	59	Orange	Epilepsy	291	Midwife	NA	31	Yellow	NA
142	Electricity supplier	Obesity	43	Orange	NA	292	Doctor	Hypertension	37	Orange	NA
143	Nurse	Respiratory	29	Orange	NA	293	Health worker	NA	41	Green	NA
144	Doctor	NA	53	Orange	NA	294	Health worker	NA	37	Yellow	NA
145	Pharmacist	Obesity	53	Yellow	NA	295	-	NA	5	Green	NA
146	Teacher	NA	37	Green	NA	296	-	NA	19	Orange	NA
147	Fire service employee	NA	43	Green	NA	297	-	Hypertension	73	Orange	NA
148	Teacher	NA	47	Yellow	NA	298	-	NA	7	Orange	NA
149	Education specialist	NA	31	Orange	NA	299	Medical goods seller	NA	47	Red	NA
150	-	NA	37	Yellow	NA	300	Religious staff	NA	31	Red	NA

This adopted decision matrix feeds by a dataset who represent the alternatives considering five criteria: C₁=vaccine recipient memberships, C₂=chronic disease conditions, C₃=age, C₄=geographic locations severity; and, C₅=disabilities [84]. In this adopted dataset, 300 cases of vaccine recipients were created. Although the generalisation and inclusion of more than 300 cases are possible, the insights from the generated cases usually can satisfy the concepts of the presented work, from which the results can then meet the desired goals. A coding scheme using the exception-handling model was developed in Python to generate the augmented dataset of the 300 cases based on the five discussed criteria [84]. The most suitable probabilities and certain assumptions about COVID-19 vaccine alternatives were generated. In that date set, the rule-based control scheme was based on expert opinions with precise descriptions for the criteria. After generating the dataset, a panel of three experts subjectively validated it to increase the veracity of the data to the best extent possible and cover most recipients’ situations. The three expert panellists were identified and selected from related study areas (i.e. molecular biology, immunology, biomedical engineering, medical biotechnology and clinical microbiology). Finally, according to the same expert panel, C3 and C4 have ranges of measures and are considered benefit criteria (that is, a larger value is more important), whereas other criteria are fitted to categorical data, which can be considered critical criteria [84]. Lastly, this decision matrix is introduced to start with the distribution process.Thus, a COVID-19 vaccine distribution can be achieved accordingly

3. Discussion results

This section presents the result to the aforementioned case study, which is the vaccine distribution mechanism achieved after prioritising the COVID-19 vaccine recipients. In this regard, Section 3.1 provides the results of the q-ROFWZIC method and the constructed criteria weights. In particular, the judgement of the three experts is converted using mathematical calculations. The purpose is to show the overall weights within this section. Section 3.2 displays the distribution results of the COVID-19 recipients. The distribution is based on the individual decision-making and GDM contexts of q-ROFDOSM.

3.1. Criteria weighting results

This section provides the weight determination results of the COVID-19 vaccine distribution criteria with the q-ROFWZIC method developed in Section 2.2.1. After the involved steps, the distribution criteria are weighted according to the three experts’ preferences without any inconsistency after the method philosophy. Based on q values (i.e. q = 1, 3, 5, 7, 10) used in q-ROFS, the final weight results of the five criteria for vaccine distribution are obtained (Table 7 ).

Table 7.

Weight determination.

Criteria/q	C1	C2	C3	C4	C5
q = 1	0.202	0.202	0.236	0.194	0.164
q = 3	0.203	0.202	0.220	0.183	0.190
q = 5	0.206	0.197	0.241	0.160	0.194
q = 7	0.211	0.187	0.261	0.136	0.203
q = 10	0.221	0.169	0.287	0.103	0.217

According to step 4, the process of q-ROFS membership function is used in transforming crisp values to equivalent fuzzy numbers. The process of transformation and the fuzzification of the experts’ opinions on the significance of the five criteria are achieved. The ratio values of the criteria are computed according to Eqs. (3), (4) and (5), then the mean of the experts’ preference for each criterion is calculated and used in determining the fuzzy weight. Then, Eqs. (7) and (8) are used in determining the final weight for each of the five criteria, as explained in step 5. For all q-ROFWZIC values of 1, 3, 5, 7 and 10, age (C3) received the highest weight as the first important criterion, followed by vaccine recipient memberships (C1). For q-ROFWZIC values (q = 1, 3, 5), Chronic Disease Conditions (C2) received the third important criteria. For q-ROFWZIC values of 7 and 10, Disabilities (C5) received the third important criteria. For q-ROFWZIC value of 1, Geographic Locations Severity (C4) received the fourth important criteria. For q-ROFWZIC values of 3 and 5, Disabilities (C5) received the fourth important criteria. For q-ROFWZIC values of 7 and 10, Chronic Disease Conditions (C2) received the fourth important criteria. Finally, for q-ROFWZIC values of 3, 5, 7 and 10, Geographic Locations Severity (C4) received the lowest weight as the fifth important criteria. For q-ROFWZIC value of 1, Disabilities (C5) received the lowest weight as the fifth important criteria. Practically, these calculated weight values are integrated to the q-ROFDOSM for the computation of the distribution results of the 300 vaccine recipients.

3.2. Distribution results

The results and discussions presented in this section pertain to the distribution of the COVID-19 vaccine and are based on individual and GDM contexts. The opinion matrix and fuzzy opinion matrix used in the distribution of the COVID-19 vaccine are processed. By using the five scales, the three decision makers provided their opinions on the conversion of the decision matrix into the opinion matrix. According to Eq. (9), the decision makers determined the ideal solution value according to the COVID-19 vaccine distribution criteria. The opinion matrix was created by comparing the ideal solution with other values per criterion or each alternative with the linguistic terms and converted into a fuzzy opinion matrix. The q-ROFDOSM method was applied on the resulting fuzzy opinion matrices for determination of the COVID-19 vaccine distribition. At q values of 1, 3, 5, 7 and 10, the results of the COVID-19 vaccine distribution based on the individual decision-making context of q-ROFDOSM are presented in Table 8 along with a sample of 10 vaccine recipients. The remaining is presented in Table A1 in the Appendix.

Table 8.

Vaccine distribution results based on individual q-ROFDOSM (first 10 alternatives).

q = 1
Alternatives	Expert 1		Expert 2		Expert 3
	Score	Final rank	Score	Final rank	Score	Final rank
VR1	-0.190854	218	-0.378625	248	-0.294512	241
VR2	0.241797	54	0.133978	60	0.182772	56
VR3	-0.021543	144	-0.110281	145	-0.110281	171
VR4	-0.115005	190	-0.289401	209	-0.212635	209
VR5	-0.13084	204	-0.31839	244	-0.15489	196
VR6	0.078329	114	-0.001965	106	-0.001965	135
VR7	-0.269037	235	-0.48015	269	-0.294512	241
VR8	-0.186338	208	-0.382637	250	-0.212635	209
VR9	0.035383	128	0.012109	96	0.153367	61
VR10	-0.363175	263	-0.48015	269	-0.294512	241
q = 3
Alternatives	Expert 1		Expert 2		Expert 3
	score	final rank	score	final rank	score	final rank
VR1	-0.130612	205	-0.327956	248	-0.231083	233
VR2	0.27259	69	0.159673	71	0.222882	71
VR3	0.078316	131	0.014126	118	0.014126	157
VR4	-0.064433	189	-0.247035	214	-0.155851	209
VR5	-0.079331	204	-0.239367	213	-0.073248	185
VR6	0.145141	111	0.094111	93	0.094111	122
VR7	-0.22061	234	-0.425087	269	-0.231083	233
VR8	-0.149352	219	-0.33734	250	-0.155851	209
VR9	0.105552	123	0.114789	86	0.272782	47
VR10	-0.305836	262	-0.425087	269	-0.231083	233
q = 5
Alternatives	Expert 1		Expert 2		Expert 3
	score	final rank	score	final rank	score	final rank
VR1	-0.045117	205	-0.205559	248	-0.128103	233
VR2	0.18326	86	0.104189	91	0.155117	81
VR3	0.116648	117	0.079693	100	0.079693	132
VR4	-0.011278	189	-0.156481	214	-0.083244	210
VR5	-0.028273	202	-0.13111	213	-0.015679	179
VR6	0.117504	116	0.090003	97	0.090003	129
VR7	-0.113159	234	-0.276722	269	-0.128103	233
VR8	-0.076365	220	-0.220682	250	-0.083244	210
VR9	0.098267	127	0.115263	80	0.242009	33
VR10	-0.165607	262	-0.276722	269	-0.128103	233
q = 7
Alternatives	Expert 1		Expert 2		Expert 3
	score	final rank	score	final rank	score	final rank
VR1	-0.006175	194	-0.12517	248	-0.067522	233
VR2	0.110879	108	0.060162	101	0.097272	101
VR3	0.112545	103	0.093842	79	0.093842	103
VR4	0.008955	189	-0.096914	217	-0.042656	210
VR5	-0.006762	196	-0.066428	208	0.008087	177
VR6	0.082033	117	0.067481	94	0.067481	126
VR7	-0.053512	234	-0.177565	269	-0.067522	233
VR8	-0.036637	222	-0.142507	250	-0.042656	210
VR9	0.072285	120	0.088602	82	0.190354	27
VR10	-0.083814	250	-0.177565	269	-0.067522	233
q = 10
Alternatives	Expert 1		Expert 2		Expert 3
	score	final rank	score	final rank	score	final rank
VR1	0.00956	189	-0.059204	248	-0.024363	216
VR2	0.050663	113	0.02489	113	0.046543	113
VR3	0.088206	84	0.082568	49	0.082568	71
VR4	0.013559	174	-0.047112	217	-0.014532	207
VR5	0.000597	198	-0.022901	206	0.01409	166
VR6	0.043713	117	0.037974	93	0.037974	124
VR7	-0.016359	234	-0.093189	269	-0.024363	216
VR8	-0.011633	222	-0.075758	250	-0.014532	207
VR9	0.040108	118	0.051437	80	0.127586	24
VR10	0.43889	269	0.454543	274	0.493271	227

As mentioned in Section 2.1.2, the highest alternative must have the highest score, and the lowest alternative must have the lowest score value. However, for the analysis of the q-ROFDOSM final rank results, Table 9 shows the best four alternatives (VR) obtained from the three experts for all q values.

Table 9.

Individual ranking results of the best four alternatives for various values of q.

Experts\q	Expert 1	Expert 2	Expert 3
q = 1	VR281>VR221> VR274>VR93	VR281>VR221>VR125>VR274	VR221>VR281>VR274>VR47
q = 3	VR281>VR221>VR47>VR274	VR281>VR221>VR232>VR206	VR221>VR281>VR274>VR189
q = 5	VR281>VR221>VR93>VR274	VR281>VR221>VR232>VR206	VR221>VR281>VR93>VR49
q = 7	VR281>VR221>VR93>VR274	VR281>VR221>VR93>VR232	VR281>VR221>VR94>VR93
q = 10	VR281>VR221>VR93>VR94	VR281>VR221>VR93>VR94	VR281>VR221>VR94>VR93

As shown in Table 9, we aimed to analyse the effect of variation in q value on the individual q-ROFDOSM ranking results. For this purpose, we presented the best four alternatives (VR) for various values of q, and the ranking results were provided the three experts. Variation in q values has an effect on ranking for the best four alternatives of each expert. For example, for the first and second experts with all q values, the best alternative was VR281, followed by VR221. For the third expert with q values of 1, 3 and 5, the best alternative is VR221, followed by VR28. For q values of 7 and 10, the best alternative is VR281, followed by VR221. Moreover, for all q values, the third and fourth ranks are relatively different. However, the effectiveness for q values on the best four alternatives presented in Table 9 did not provide a precise conclusion on the overall 300 alternatives. Therefore, to discuss the real effectiveness of q values on q-ROFDOSM individual ranking results, we calculated the overall variations that occurred in the ranking orders for the individual ranking for each expert.

The results showed that for expert 1, 277 out of 300 alternatives (92.33%) were changed and received different rank orders. A total of 23 alternatives (7.67%) received the same ranking order and did not change when the applied q values were 1, 3, 7 and 10). Moreover, for expert 2, 245 out of 300 alternatives (81.67%) were changed and received different rank orders, and 55 alternatives (18.33%) received the same ranking order and did not change. Finally, for expert 3, 284 out of 300 alternatives (94.67%) were changed and received different rank orders. A total of 16 alternatives (5.33%) received the same ranking order and did not change. Although little variance was observed for the best four ranking orders among alternatives (Table 9), the orders did not reflect the full picture of how q values affected the ranking results. Therefore, we concluded that a large variance occurred on the ranking orders and score values based on q values. This large variance indicated the existence of q values that were effective on vaccine distribution.

The ranking results changed in the three experts. This case showed the significance of variation in experts’ preferences in decision analysis. For instance, as shown in Table 9 and Table A1 (Appendix), for the first and second experts when q = 1, VR281 was the best alternative rank, and scores of 0.54033175 and 0.50524958 were obtained, respectively. For the third expert, VR221 was the first alternative rank, and a score of 0.523566903 was obtained.

After reviewing the scores and ranking orders results for the individual q-ROFDOSM, we found differences among the three experts that were been obtained for the vaccine recipients. Overall, no unique prioritisation result based on the opinions provided by the three experts was observed. Owing to this variance, GDM, is essential to final and unique prioritisation when all the experts’ opinions are considered. Furthermore, GDM is necessary to the resolution of the problem of variations in the final rank. As mentioned in Section 2.1.2, the final results of the three decision-makers were aggregated, and the final GDM raking for COVID-19 vaccine distribution was obtained. In addition, the results of the COVID-19 vaccine distribution based on the GDM-based q-ROFDOSM are presented in Table 10 for q values of 1, 3, 5, 7 and 10 in a sample of 10 vaccine recipients.

Table 10.

Vaccine distribution results based on GDM q-ROFDOSM (first 10 alternatives).

Alternatives	q = 1		q = 3		q = 5		q = 7		q = 10
	Score	Final rank	Score	Final rank	Score	Final rank	Score	Final rank	Score	Final rank
VR1	-0.2879969	234	-0.2298837	234	-0.1262594	228	-0.0662891	226	-0.02466931	217
VR2	0.1861822	53	0.2183817	68	0.1475219	86	0.0894377	101	0.04069889	114
VR3	-0.0807016	166	0.0355225	141	0.0920117	118	0.100076	91	0.0844476	63
VR4	-0.2056802	210	-0.1557731	210	-0.0836673	210	-0.0435386	212	-0.01602858	206
VR5	-0.2013731	209	-0.1306485	198	-0.0583542	198	-0.0217009	196	-0.00273792	194
VR6	0.0247994	116	0.1111214	108	0.0991704	114	0.0723318	116	0.03988728	115
VR7	-0.3478996	258	-0.2922598	258	-0.1726611	249	-0.0995332	245	-0.04463694	243
VR8	-0.2605366	228	-0.214181	228	-0.1267636	230	-0.0739335	231	-0.03397462	232
VR9	0.0669532	95	0.1643745	84	0.1518465	82	0.1170806	80	0.07304372	80
VR10	-0.379279	270	-0.3206686	266	-0.1901438	257	-0.1096338	257	-0.04885261	256

As Tables 10 and A2 (Appendix) illustrate, for q values of 3, 5, 7 and 10, the highest-ranked (rank 1) recipient is VR281, who obtained the highest scores. After the profile data of this alternative were reviewed, the specifications of VR281’s criteria were related to C1, C2, C3, C4 and C5 as he is not a vaccine recipient, has diabetes, is 83 years old, is from a red geographical location and is disabled with epilepsy. Although VR281 did not belong to any recipient memberships (C1), the weight of the age criterion (See Table 7), which indicated that age weight received higher priority for all q values based on the three experts, played a major role in the decision-making process, and the alternative was considered a high priority. Hence, the remaining criteria varied somewhat in terms of importance.

VR170, who was almost located in the middle of the ranking results, ranked 144th when q = 1 (obtained a score of -0.046208476), rank 156th when q = 3 (obtained a score of 0.004883422), rank 157th when q = 5 (obtained a score of 0.031371872), rank 155th when q = 7 (obtained a score of 0.030999934) and rank 150th when q = 10 (obtained a score of 0.019926159). The criterion specifications of VR170 were related to C1, C2, C3, C4 and C5 as he has a recipient membership (fire service employee), is not affected by a chronic disease, 5is 9 years old, is from an orange geographical location and is not affected by disabilities. Clearly, a satisfactory ranking result was assigned to alternative VR170 especially the vaccine distribution criteria specifications are relatively averagely important and earned a middle priority.

The lowest-ranked recipients were the alternatives VR166, VR190, VR205, VR209, VR229 and VR285, and they obtained the same ranking order (rank 293) and same scores for all q values. They received scores (-0.510442612), (-0.468345475), (-0.31952474), (-0.218707219) and (-0.131237497) for q values of 1, 3, 5, 7 and 10, respectively. The closeness of the criterion specifications for these alternatives was the reason for their admission in the same order of priority and their identical scores. For instance, the criterion specifications of VR166 were related to C1, C2, C3, C4 and C5 as he has no vaccine recipient membership, is not affected by a chronic disease, is 43 years old, is from a green geographical location and is not affected by disabilities. The worst ranked had no vaccine recipient membership, were not affected by any chronic condition, were young, were from green or yellow geographic locations and were slightly affected by disabilities.

In line with the results of the analysis on how the q values affected the first four ranking results presented previously for individual q-ROFDOSM (See Table 9), Table 11 presents the best four alternatives based on the GDM q-ROFDOSM.

Table 11.

GDM q-ROFDOSM ranking of the best and worst four alternatives for various values of q.

Experts\q	Best four alternatives
q = 1	VR281>VR221>VR274>VR47
q = 3	VR281>VR221>VR274>VR93
q = 5	VR281>VR221>VR93>VR274
q = 7	VR281>VR221>VR93>VR94
q = 10	VR281>VR221>VR93>VR94

As shown in Table 11, for all q values, the best alternative was VR281, followed by VR221. For q values of 1 and 3, VR274 and VR93 were third in rank, whereas VR93 was third in rank when the q values were 5, 7 and 10. Finally, the fourth in rank was VR47 when q = 1, VR93 when q = 3, VR274 when q = 5 and VR94 when q = 7 and q = 10.

To discuss the effect of q values on GDM q-ROFDOSM, we calculated the variations that occurred in the ranking orders for the GDM ranking results when the q values were 1, 3, 5, 7 and 10). In these contexts, 290 out of 300 alternatives (96.67%) were changed and received different rank orders at these q values, whereas 10 alternatives (3.33%) received the same rank order and did not change. Therefore, with regard to how q values affect GDM q-ROFDOSM ranking orders, the large variance occurred. This conclusion was in line with the individual q-ROFDOSM. Thus, q values play a key role in the overall ranking for the COVID-19 vaccine distribution for individual and GDM q-ROFDOSM and should be considered. Finally, the rank of COVID-19 vaccine distribution is in line when comparing the GDM results with the opinion matrices. Thus, it is considered as the final ranking results for COVID-19 vaccine distribution, which will be evaluated in detail in the next section.

4. Evaluation

In this section, the efficiency of the proposed methods was evaluated and tested through two assessment processes. First, the systematic ranking of the vaccine recipients’ ranking results was evaluated. Second, the impact of changing the criteria weight on the ranking result was examined and analysed under nine scenarios.

4.1. Systematic ranking evaluation

In this section, the systematic ranking assessment was conducted for the assessment of the GDM results of COVID-19 vaccine distribution. In this regard, vaccine recipients were divided into different groups according to their prioritisation order. Such process is known and has been performed in previous MCDM works [85], [86], [87], [88]. Notably, neither group numbers nor the number of vaccine recipients in each group influence validation results [89], [90], [91], [92]. Subsequently, the validation of COVID-19 vaccine distribution results include several procedures as follows:

• •The aggregation of all opinion matrices into one unified matrix
• •The aggregated matrix are sorted according to GDM results of vaccine distribution per each q value
• •The vaccine recipients are divided into 6 equally numbered groups.
• •
  The mean value ($\overline{x}$) for each group is calculated thereafter based on Eq. (13)

  $$\overline{\mathrm{x}}=\frac{1}{\mathrm{n}}{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{x}}_{\mathrm{i}}$$ (13)

Upon the mean calculation for each of the six groups, these results must be compared. This step ensures the validity of the systematic ranking, and certain conditions are required according to the q-ROFDOSM philosophy in the comparison process where the lowest mean value for each group indicates validity as follows:

• •The first group mean is assumed to be the lowest when result validity is checked
• •The first group's mean must be lower than the second group's mean
• •The second group's mean result must be higher than that of the first group
• •The same concept applies to the third, fourth, fifth and sixth groups

Based on the mean results obtained under previous conditions, the evaluation was consistent, and thus its results were considered valid. Table 12 presents the validation results for the group results obtained using the proposed methods.

Table 12.

Validation of group distribution results.

Group #	q1	q3	q5	q7	q10
	Mean value
Group 1	2.705333333	2.716	2.728	2.78	2.854666667
Group 2	3.221333333	3.232	3.265333333	3.284	3.257333333
Group 3	3.554666667	3.578666667	3.554666667	3.505333333	3.474666667
Group 4	3.862666667	3.816	3.796	3.776	3.770666667
Group 5	4.121333333	4.122666667	4.126666667	4.130666667	4.124
Group 6	4.442666667	4.442666667	4.437333333	4.432	4.426666667

Table 12 presents the results of six groups results for each q value (q1, q3, q5, q7 and q10). The ranking results of each group in each q rank was consistent with the q-ROFDOSM philosophy comparison conditions, in which the mean value for the first group in each scenario was smaller than the mean results for group 2. The same concept was applied, and the fact that group mean is smaller than the mean of the next corresponding group in each q rank was considered. After the process was successfully achieved in all the groups, the ranking was considered valid. The mean values based on the statistical validation results indicated that the GDM-based q-ROFDOSM results of COVID-19 vaccine distribution were valid and systematically ranked.

4.2. Sensitivity analysis evaluation

In this second evaluation process, the sensitivity of the proposed methods against the changing criterion weight was analysed. Thus, the sensitivity analysis predicted the impact of changes in criterion weights on the systematic ranking results of the vaccine distribution results. First, the most important criterion was identified for each q value. In this study, out of the five criteria, C3 (age) was the most important criterion for all q values, as presented in Table 7. For the examination of the effect of changes in the weights of the criteria, nine different scenarios for each q value generated from criterion weight relativity were computed using Eq. 13 [93]. The relative change for each criterion over the most important one (age) with respect to each q values were computed using the elasticity coefficient (α_c), as shown in Table 13 .

$$w_c=(1-w_s)\times (w_c^o/W_c^0)=w_c^o-\Delta x{\alpha }_c,$$ (13a)

Table 13.

Elasticity coefficient (α_c) for changing weights.

T value	Criteria	C1	C2	C3	C4	C5
q = 1	αc	0.265029784	0.264919514	0.309581718	0.254094521	0.215956182
q = 3	αc	0.261365974	0.259631919	0.282267619	0.235169164	0.243832944
q = 5	αc	0.272378478	0.260122827	0.318655605	0.211350989	0.256147706
q = 7	αc	0.286538268	0.253515984	0.354018201	0.184625748	0.27532
q = 10	αc	0.311238476	0.237532804	0.403305378	0.145317753	0.305910967

For a q value,

• •w_s is the higher significant contribution.
• •$w_c^o$ represents the original weight values computed using q-ROFWZIC method.
• •$W_c^0$ is the total of original weights for the changing criteria weight values.
• •
  Δx is the range of change applied on the five criteria weight values, which represents the limit values of the most significant criterion in this study (age) as follows:

  • Ø
    For q = 1, − 0.236 ≤ ▵x ≤ 0.763
  • Ø
    For q = 3, − 0.220 ≤ ▵x ≤ 0.779
  • Ø
    For q = 5, − 0.241 ≤ ▵x ≤ 0.758
  • Ø
    For q = 7,  − 0.261 ≤ ▵x ≤ 0.738
  • Ø
    For q = 10, −0.287 ≤ ▵x ≤ 0.712

The q value for each criterion showed changes in their weights according to Eq. 13, as shown in Table 13. For all (α_c) with respect to q values (q = 1, 3, 5,7, 10), age (C3) received the highest weight, whereas geographic location severity (C4) received the lowest weight, except when q = 1, in which Disabilities (C5) had the lowest weight. Then, the interval range of Δx for q values were used in generating nine new weighting values for each criterion. The range was split into nine equal relative values according to the number of scenarios, as shown in Table 14 .

Table 14.

New weights for each criterion for q values under nine scenarios.

q = 1
	C1	C2	C3	C4	C5
q-ROFWZIC	0.202377431	0.202293228	0.236397404	0.194027236	0.164904701
S1	0.202377431	0.202293228	0.236397404	0.194027236	0.164904701
S2	0.265029784	0.264919514	0.00E+00	0.254094521	0.215956182
S3	0.231901061	0.231804574	0.125	0.222332706	0.188961659
S4	0.198772338	0.198689635	0.25	0.190570891	0.161967136
S5	0.165643615	0.165574696	0.375	0.158809075	0.134972613
S6	0.132514892	0.132459757	0.5	0.12704726	0.107978091
S7	0.099386169	0.099344818	0.625	0.095285445	0.080983568
S8	0.066257446	0.066229878	0.75	0.06352363	0.053989045
S9	0.033128723	0.033114939	0.875	0.031761815	0.026994523
q = 3
q-ROFWZIC	0.203831065	0.20247873	0.220131597	0.183401	0.190157608
S1	0.261365974	0.259631919	0.00E+00	0.235169164	0.243832944
S2	0.228695227	0.227177929	0.125	0.205773018	0.213353826
S3	0.19602448	0.194723939	0.25	0.176376873	0.182874708
S4	0.163353734	0.162269949	0.375	0.146980727	0.15239559
S5	0.130682987	0.129815959	0.5	0.117584582	0.121916472
S6	0.09801224	0.09736197	0.625	0.088188436	0.091437354
S7	0.065341493	0.06490798	0.75	0.058792291	0.060958236
S8	0.032670747	0.03245399	0.875	0.029396145	0.030479118
S9	1.00E-05	1.00E-05	0.99996	1.00E-05	1.00E-05
q = 5
q-ROFWZIC	0.206557707	0.197263657	0.241651879	0.160277625	0.194249132
S1	0.272378478	0.260122827	0.00E+00	0.211350989	0.256147706
S2	0.238331168	0.227607473	0.125	0.184932115	0.224129243
S3	0.204283859	0.19509212	0.25	0.158513242	0.19211078
S4	0.170236549	0.162576767	0.375	0.132094368	0.160092317
S5	0.136189239	0.130061413	0.5	0.105675494	0.128073853
S6	0.102141929	0.09754606	0.625	0.079256621	0.09605539
S7	0.06809462	0.065030707	0.75	0.052837747	0.064036927
S8	0.03404731	0.032515353	0.875	0.026418874	0.032018463
S9	1.00E-05	1.00E-05	0.99996	1.00E-05	1.00E-05
q = 7
q-ROFWZIC	0.211620692	0.187232331	0.261457491	0.136353963	0.203335523
S1	0.286538268	0.253515984	2.22E-16	0.184625748	0.27532
S2	0.250720985	0.221826486	0.125	0.16154753	0.240905
S3	0.214903701	0.190136988	0.25	0.138469311	0.20649
S4	0.179086418	0.15844749	0.375	0.115391093	0.172075
S5	0.143269134	0.126757992	0.5	0.092312874	0.13766
S6	0.107451851	0.095068494	0.625	0.069234656	0.103245
S7	0.071634567	0.063378996	0.75	0.046156437	0.06883
S8	0.035817284	0.031689498	0.875	0.023078219	0.034415
S9	1.00E-05	1.00E-05	0.99996	1.00E-05	1.00E-05
q = 10
q-ROFWZIC	0.221789555	0.169266653	0.287396731	0.103553906	0.217993155
S1	0.311238476	0.237532804	1.11E-16	0.145317753	0.305910967
S2	0.272333666	0.207841204	0.125	0.127153034	0.267672096
S3	0.233428857	0.178149603	0.25	0.108988315	0.229433225
S4	0.194524047	0.148458003	0.375	0.090823596	0.191194354
S5	0.155619238	0.118766402	0.5	0.072658876	0.152955484
S6	0.116714428	0.089074802	0.625	0.054494157	0.114716613
S7	0.077809619	0.059383201	0.75	0.036329438	0.076477742
S8	0.038904809	0.029691601	0.875	0.018164719	0.038238871
S9	1.00E-05	1.00E-05	0.99996	1.00E-05	1.00E-05

The ninth new weight value for each q value was used in assessing the sensitivity of the 300 vaccine recipients’ prioritisation at changing criterion weights. The aim was to determine how target q-ROFWZIC weights are affected according to changes under the scenarios for each q value. Fig. 3 illustrates the influences of changes in the criterion weight in the first 10 ranks when q = 1. Figs. A1, A2, A3 and A4 in the Appendix illustrate the influences of changes in criterion weight in the first ten ranks at q values of 3, 5, 7 and 10, respectively. The criterion weights played a vital role in the change in the priority of each vaccine recipient. These scenario results for the nine values supported the research assertion about the significant contribution of the five criteria. Notably, although this change was logical and likely, the unchanged results in most scenarios indicated the efficiency of the proposed integration methods in handling the sensitive cases, which had large datasets, and produced supportive results for the outcomes of systematic ranking.

Fig. 3.

Sensitivity analysis of first 10 vaccine receipts ranks in nine scenarios (q = 1).

Fig. A1.

Sensitivity analysis of first 10 vaccine receipts ranks in 9 scenarios (q = 3).

Fig. A2.

Sensitivity analysis of first 10 vaccine receipts ranks in 9 scenarios (q = 5).

Fig. A3.

Sensitivity analysis of first 10 vaccine receipts ranks in 9 scenarios (q = 7).

Fig. A4.

Sensitivity analysis of first 10 vaccine receipts ranks in 9 scenarios (q = 10).

Based on sensitively analyses results visualised in Figs. 3, A1, A2, A3 and A4, the new ranking results obtained based on the ninth scenario weights for all q values needed to be compared with previous ranking results obtained based on q-ROFWZIC weights (the weights presented in Table 7). The sensitively analysis comparisons can be discussed from two points of view as follows:

First three ranks effectiveness: the comparison with respect to the first three ranking alternatives needed to be discussed because of the vaccine recipients received important orders. When q = 1, the scenarios S3, S4, S5, S6, S7, S8 and S9 had the same ranking results as q-ROFWZIC. The results were obtained by the first three alternatives (V48, V98 and V155), and other scenarios (S1 and S2) were relatively different.

When q = 3, scenarios S3, S4, S5, S6, S7, S8 and S9 had the same ranking results as q-ROFWZIC, which were obtained by the first three alternatives (V271, V289 and V115). THe other scenarios (S1 and S2) were relatively different. When q = 5, 3 and 10, scenarios S3, S4, S5, S6, S7 and S8 had the same ranking results as q-ROFWZIC, which were obtained by the first three alternatives (V271, V289 and V77). The other scenarios (S1, S2 and S9) were relatively different. When the above new results were compared with the first three ranks obtained from q-ROFWZIC weights, no large differences among the first three ranking results for the sensitively of q values were observed. However, the first three ranks cannot provide the full sensitive analyses for the overall changing occurred in the ranking results. Therefore, the overall effect should be discussed.

Overall rank effectiveness: after the overall ranking results were obtained, we found the changing behaviour of the nine scenarios with respect to each q value. How exactly the overall new ranking results affected the previous ranking results obtained from q-ROFWZIC weights must be determined. We measured the effectiveness by calculating the changes that occurred in the orders among the ranks, then we calculated the changes in percentages in the ranking orders. In other words, for q = 1, the number of changes that occurred in the ranking orders obtained from q-ROFWZIC weights after S1 weights were applied was 295 (98.33%), and only five orders did not change and had the same order. Table 15 explains the overall effectiveness on the ranking results among the ninth scenario's weights and q-ROFWZIC weights.

Table 15.

Overall effectiveness (percentages %) between ranks of ninth scenarios weights and q-ROFWZIC weights.

	Scenarios	q = 1	q = 3	q = 5	q = 7	q = 10
Changing percentage (%) in rank towards q-ROFWZIC	S1	98.33	98.33	99.33	98.67	98.67
	S2	95.67	92.67	92.67	89.00	85.33
	S3	45.00	62.67	52.67	51.67	68.33
	S4	88.33	90.67	92.00	87.67	91.33
	S5	89.67	92.33	92.00	92.33	92.00
	S6	89.67	92.33	92.00	92.00	92.67
	S7	90.00	91.67	91.33	91.67	92.67
	S8	89.67	91.67	91.33	91.67	93.33
	S9	95.00	91.67	92.00	90.00	93.33
	mean	86.81	89.33	88.37	87.19	89.74

Table 15 presents the final sensitive analyses for all scenarios with respect to all q values. The highest mean value was obtained when q = 10 (89.74%). The lowest mean value was obtained when q = 1 (86.81%). These interesting results indicated that the rank stability was almost highly sensitive and similar to each other with respect to all q values, and then ranking obtained by q-ROFWZIC weight was affected by the nine scenarios. Surely, these widely changing results in the weights’ numbers changed the overall ranking results. This concept was already reported and considered one of the other MCDM issues and an ‘important criteria’. If we review these issues concepts, we can realise that the ‘important criteria’ have been sensitively recognised and proven here and is a vaccine distribution. At this step, sensitivity analysis was perform for the investigation of the priority ranking stability. However, the sensitivity of the priority ranks of the q values for the nine scenarios were influenced by changes in the criterion weights, and the overall ranks for all vaccine recipients also changed, except some priority ranks (the first three ranks). This fact was probably because of some important issues of criterion importance and has been demonstrated for q-ROFWZIC weights. Finally, the Spearman correlation coefficient (SCC) was used in statistically evaluating the relationships among the results of the 15 scenarios [93]. Fig. 4 shows the high-level correlation among the nine scenarios for all 300 vaccine recipients when q = 1. The remaining correlations for other q values are shown in Figs. A5 , A6 , Fig. A7, Fig. A8 .

Fig. 4.

Correlation of ranks among nine scenarios for all 300 vaccine recipients for q of 1.

Fig. A5.

Correlation of ranks among 9 scenarios for all 300 vaccine recipients for q = 3.

Fig. A6.

Correlation of ranks among 9 scenarios for all 300 vaccine recipients for q = 5.

Fig. A7.

Correlation of ranks among 9 scenarios for all 300 vaccine recipients for q = 7.

Fig. A8.

Correlation of ranks among 9 scenarios for all 300 vaccine recipients for q = 10.

Fig. 4 illustrates the correlation analysis results for the vaccine recipients’ ranking under nine scenarios according to the obtained correlation values for a q value of 1. A high correlation of ranks was observed in all scenarios. For the scenarios S2, S3 and S4, the high SCC values were 0.9872, 0.9998 and 0.9866, respectively, whereas the S9 had the lowest SCC value (0.8658). In the same context, the other correlation results were summarised as follows. For q = 3, the scenarios (S2, S3 and S4) obtained height correlation, where the SCC values were 0.991068166, 0.999110381 and 0.983735559, respectively. S9 had the lowest SCC value of 0.843518692. When q = 5, the scenarios (S2, S3 and S4) obtained height correlation, where the SCC values were 0.987873209, 0.99981133 and 0.988569992, respectively, whereas S9 had the lowest SCC value (0.842974338). When q = 7, scenarios S2, S3 and S4 had height correlation, where the SCC values were 0.983886001, 0.999838187 and 0.992322563, respectively, whereas S9 had the lowest SCC value (0.835992688). When q = 10, scenarios S1, S2, S3, S4, S5 and S6 had the highest correlation results. The SCC values were 0.93096899, 0.981698586, 0.999229063, 0.995156505, 0.976486891 and 0.936642031, respectively. S9 had the lowest SCC value (0.820391763).

In conclusion, for all q values, the highest correlation SCC value corresponded to a q value of 10, in which all the scenarios obtained high correlation analysis results. Accordingly, these high correlation values indicated a significant correlation of the rank outcomes, which in turn supported the systematic ranking results for the q values.

5. Conclusion

The main contribution of this study is a novel extension of FWZIC and FDOSM under the fuzzy environment of q-ROFS. The study methodology was presented on the basis of two phases (Fig. 2), which formulated the steps of the q-ROFWZIC method for criterion weighting and its integration with q-ROFDOSM for alternative ranking. The proposed extension of the methods was applied to the interesting case study of COVID-19 vaccine dose distribution. The robustness of the proposed methods was tested and evaluated with two systematic ranking assessment methods and sensitivity analysis. However, the proposed methods had three main limitations that might be solved in the future works. First, q-ROFWZIC and q-ROFDOSM methods were formulated with one aggregation operator. Second, both methods utilised only one defuzzification technique to produce the final weighting and ranking results. Third, the importance measurement reflected on each decision maker preferences involved in both methods was not considered. Several future directions are recommended: (1) presenting and processing a huge dataset of COVID-19 vaccine recipients by considering all probabilities for each alternative and distribution criteria; (2), performing the proposed MCDM method should be based on two levels: firstly, each vaccine recipient membership (i.e. frontline health workers, key workers and frontline staff employees and none or both children and homemakers will be prioritised, and secondly each alternative within each membership will be prioritised, followed by accumulating them effectively. This direction might investigate other distribution criteria and their effectiveness including the family income and nutritional habits.

CRediT authorship contribution statement

A.S. Albahri: Data curation, Writing – original draft, Visualization. O.S. Albahri: Software, Supervision. A.A. Zaidan: Software, Supervision. Alhamzah Alnoor: Data curation, Writing – original draft, Visualization. H.A. Alsattar: Conceptualization, Methodology. Rawia Mohammed: Data curation, Writing – original draft, Visualization. A.H. Alamoodi: Investigation, Software, Validation, Writing – review & editing. B.B. Zaidan: Investigation, Software, Validation, Writing – review & editing. Uwe Aickelin: Software, Supervision. Mamoun Alazab: Software, Supervision. Salem Garfan: Conceptualization, Methodology. Ibraheem Y.Y. Ahmaro: Conceptualization, Methodology. M.A. Ahmed: Conceptualization, Methodology.

Declaration of competing interest

The authors declares no conflict of interest

Appendix

Tables A1 and A2

Table A1.

Results of individual q-ROFDOSM.

q = 1
Alternatives	Expert 1		Expert 2		Expert 3
	Score	Final rank	Score	Final rank	Score	Final rank
VR1	-0.190854	218	-0.378625	248	-0.294512	241
VR2	0.241797	54	0.133978	60	0.182772	56
VR3	-0.021543	144	-0.110281	145	-0.110281	171
VR4	-0.115005	190	-0.289401	209	-0.212635	209
VR5	-0.13084	204	-0.31839	244	-0.15489	196
VR6	0.078329	114	-0.001965	106	-0.001965	135
VR7	-0.269037	235	-0.48015	269	-0.294512	241
VR8	-0.186338	208	-0.382637	250	-0.212635	209
VR9	0.035383	128	0.012109	96	0.153367	61
VR10	-0.363175	263	-0.48015	269	-0.294512	241
VR11	0.330179	21	0.27567	22	0.322667	16
VR12	0.209614	74	0.080889	70	0.18726	51
VR13	0.020571	136	-0.065652	129	0.002195	132
VR14	-0.037938	169	-0.128636	167	0.00455	130
VR15	0.109813	99	0.17791	39	0.095576	83
VR16	-0.190854	218	-0.378625	248	-0.294512	241
VR17	-0.115005	190	-0.289401	209	-0.212635	209
VR18	0.284053	41	0.164875	40	0.09146	86
VR19	0.097806	102	-0.14555	176	0.018381	118
VR20	0.253721	52	0.139748	55	0.18726	51
VR21	-0.052779	174	-0.065652	129	-0.065652	170
VR22	-0.4627	291	-0.48015	269	-0.588478	293
VR23	-0.363175	263	-0.48015	269	-0.294512	241
VR24	0.427625	6	0.331839	10	0.373441	11
VR25	-0.251335	231	-0.48015	269	-0.254023	230
VR26	0.125322	93	0.048068	80	0.108069	79
VR27	-0.108997	179	-0.205331	186	-0.125477	180
VR28	0.230994	57	-0.128636	167	0.085559	90
VR29	-0.272756	243	-0.212635	194	-0.289401	233
VR30	-0.169193	205	-0.190854	181	-0.021543	138
VR31	0.083372	111	-0.065652	129	0.056836	102
VR32	0.139302	90	-0.001965	106	0.117522	78
VR33	0.216527	65	-0.212635	194	0.147256	66
VR34	-0.040551	171	-0.131448	173	-0.057712	166
VR35	0.319497	29	0.274031	23	0.274031	25
VR36	-0.099267	176	-0.035011	117	-0.190854	199
VR37	0.150309	86	0.020571	88	0.134092	75
VR38	-0.197354	220	-0.301518	216	-0.21566	219
VR39	-0.186338	208	-0.212635	194	-0.039635	150
VR40	0.143588	89	0.073855	77	0.133978	76
VR41	0.083372	111	-0.065652	129	0.056836	102
VR42	-0.117815	195	-0.301518	216	-0.14555	186
VR43	-0.021543	144	-0.110281	145	-0.110281	171
VR44	0.254314	51	0.052912	79	0.188546	50
VR45	0.307268	37	0.139748	55	0.253721	30
VR46	0.164875	81	0.09146	67	0.09146	86
VR47	0.412919	7	0.454382	3	0.454382	4
VR48	-0.197354	220	-0.301518	216	-0.21566	219
VR49	-0.117815	195	-0.301518	216	-0.14555	186
VR50	-0.024535	149	-0.033676	114	-0.033676	146
VR51	0.03865	126	-0.040551	123	0.083372	93
VR52	-0.197354	220	-0.301518	216	-0.21566	219
VR53	-0.366242	280	-0.272756	205	-0.289401	233
VR54	-0.285972	250	-0.301518	216	-0.21566	219
VR55	-0.099359	177	-0.205331	186	-0.035011	148
VR56	-0.186338	208	-0.382637	250	-0.212635	209
VR57	-0.213866	229	-0.15489	178	-0.228829	229
VR58	-0.115005	190	-0.289401	209	-0.212635	209
VR59	-0.030723	151	-0.186338	180	-0.115005	175
VR60	0.05749	117	-0.294512	212	-0.021543	138
VR61	-0.366242	280	-0.382637	250	-0.382637	271
VR62	0.02854	135	-0.117594	148	0.018762	117
VR63	-0.110029	183	-0.123423	149	-0.206604	204
VR64	-0.117815	195	-0.301518	216	-0.14555	186
VR65	0.331839	20	0.331839	10	0.373441	11
VR66	-0.285972	250	-0.301518	216	-0.398073	275
VR67	0.097806	102	0.018381	93	0.018381	118
VR68	0.043912	120	-0.212635	194	-0.039635	150
VR69	-0.272756	243	-0.212635	194	-0.289401	233
VR70	0.122533	94	-0.108997	143	0.164822	58
VR71	0.213142	70	0.330179	13	0.267667	26
VR72	-0.285972	250	-0.301518	216	-0.398073	275
VR73	-0.030815	153	-0.105112	139	-0.033241	143
VR74	-0.251335	231	-0.254023	203	-0.254023	230
VR75	0.134092	91	0.002195	105	0.056836	102
VR76	0.04377	122	-0.128636	167	-0.128636	184
VR77	0.097806	102	0.018381	93	0.018381	118
VR78	0.27986	44	0.155125	43	0.091972	85
VR79	0.271902	47	0.15359	47	0.250681	31
VR80	0.116614	96	0.043912	84	0.043912	106
VR81	0.22175	61	0.012109	96	0.153367	61
VR82	-0.023197	148	-0.108997	143	-0.035011	148
VR83	-0.272756	243	-0.382637	250	-0.289401	233
VR84	-0.363175	263	-0.48015	269	-0.294512	241
VR85	0.248774	53	0.143588	54	0.241797	33
VR86	0.223245	59	0.134092	59	0.083372	93
VR87	0.209633	73	0.087637	68	0.139768	73
VR88	0.097806	102	0.018381	93	0.018381	118
VR89	0.035383	128	-0.123423	149	0.012109	122
VR90	-0.197354	220	-0.301518	216	-0.21566	219
VR91	-0.363175	263	-0.48015	269	-0.378625	258
VR92	-0.285972	250	-0.301518	216	-0.398073	275
VR93	0.394863	12	0.43757	5	0.43757	6
VR94	0.359892	16	0.316397	14	0.394912	10
VR95	-0.033676	159	-0.123423	149	-0.048888	154
VR96	0.213142	70	0.218326	29	0.267667	26
VR97	0.04099	123	-0.037938	118	0.030116	111
VR98	-0.18749	215	-0.197354	182	-0.197354	201
VR99	0.116614	96	0.043912	84	0.043912	106
VR100	0.279965	43	0.22175	28	0.22175	39
VR101	-0.052692	173	-0.21566	201	-0.14555	186
VR102	-0.4627	291	-0.48015	269	-0.48015	285
VR103	-0.363175	263	-0.48015	269	-0.378625	258
VR104	-0.030815	153	-0.105112	139	-0.033241	143
VR105	0.147786	87	-0.091187	137	0.036678	109
VR106	-0.110029	183	-0.123423	149	-0.123423	178
VR107	0.010019	142	-0.001965	106	-0.001965	135
VR108	-0.197354	220	-0.301518	216	-0.21566	219
VR109	0.092047	108	-0.048888	125	0.012109	122
VR110	0.216527	65	0.147256	51	0.147256	66
VR111	-0.108997	179	-0.205331	186	-0.125477	180
VR112	-0.110029	183	-0.123423	149	-0.206604	204
VR113	-0.033676	159	0.080889	70	-0.048888	154
VR114	-0.18749	215	0.020571	88	-0.197354	201
VR115	-0.4627	291	-0.205331	186	-0.48015	285
VR116	-0.033676	159	0.080889	70	0.012109	122
VR117	0.216527	65	0.00455	101	0.147256	66
VR118	0.018681	140	0.011114	100	-0.062214	169
VR119	-0.033241	156	-0.197354	182	-0.052692	162
VR120	0.213142	70	0.218326	29	0.218326	40
VR121	0.160425	82	-0.065652	129	0.192395	49
VR122	-0.033301	158	-0.040551	123	0.083372	93
VR123	-0.269037	235	-0.48015	269	-0.294512	241
VR124	0.121118	95	-0.023197	111	0.05735	101
VR125	0.463481	3	0.331839	10	0.406643	9
VR126	0.317158	33	0.04602	82	0.106656	80
VR127	0.27567	46	0.17915	38	0.139748	74
VR128	0.011114	141	-0.205331	186	-0.004554	137
VR129	-0.363175	263	-0.205331	186	-0.378625	258
VR130	0.284053	41	-0.060162	128	0.09146	86
VR131	-0.169193	205	-0.363175	245	-0.190854	199
VR132	0.020571	136	-0.065652	129	0.002195	132
VR133	-0.117815	195	-0.301518	216	-0.14555	186
VR134	-0.117815	195	-0.301518	216	-0.14555	186
VR135	0.305207	38	0.225928	26	0.167589	57
VR136	-0.366242	280	-0.382637	250	-0.382637	271
VR137	-0.172547	207	-0.272756	205	-0.186338	198
VR138	-0.366242	280	-0.382637	250	-0.484438	287
VR139	-0.366242	280	-0.382637	250	-0.382637	271
VR140	-0.18749	215	-0.197354	182	-0.197354	201
VR141	0.317871	32	0.264468	25	0.310503	19
VR142	-0.11788	203	-0.131448	173	-0.131448	185
VR143	0.364872	13	0.056836	78	0.192447	47
VR144	0.164904	79	0.097806	63	0.097806	81
VR145	0.152271	84	0.030116	87	0.085559	90
VR146	-0.269037	235	-0.48015	269	-0.294512	241
VR147	-0.363175	263	-0.294512	212	-0.378625	258
VR148	-0.186338	208	-0.382637	250	-0.212635	209
VR149	-0.117815	195	-0.301518	216	-0.14555	186
VR150	-0.366242	280	-0.382637	250	-0.484438	287
VR151	-0.254023	233	-0.363175	245	-0.269037	232
VR152	0.231564	56	0.158964	41	0.226656	36
VR153	0.318581	30	0.366786	8	0.366786	14
VR154	0.230994	57	-0.037938	118	0.085559	90
VR155	0.108786	100	-0.033676	114	0.092047	84
VR156	-0.021543	144	-0.110281	145	-0.110281	171
VR157	-0.021543	144	-0.294512	212	-0.110281	171
VR158	0.360842	14	0.304029	16	0.304029	22
VR159	-0.108997	179	-0.205331	186	-0.125477	180
VR160	-0.040551	171	-0.131448	173	-0.057712	166
VR161	-0.108997	179	-0.205331	186	-0.125477	180
VR162	0.10372	101	0.138703	58	0.087904	89
VR163	-0.366242	280	-0.382637	250	-0.484438	287
VR164	-0.363175	263	-0.48015	269	-0.378625	258
VR165	0.04099	123	-0.037938	118	0.030116	111
VR166	-0.4627	291	-0.48015	269	-0.588478	293
VR167	-0.117815	195	-0.301518	216	-0.14555	186
VR168	0.049247	119	-0.033512	113	0.034551	110
VR169	-0.037938	169	0.00455	101	-0.055153	165
VR170	-0.033241	156	-0.052692	126	-0.052692	162
VR171	0.349987	17	0.280207	20	0.240068	34
VR172	0.05749	117	-0.021543	110	-0.021543	138
VR173	0.203123	76	0.093415	64	0.195862	46
VR174	-0.110029	183	-0.123423	149	-0.206604	204
VR175	0.360842	14	0.18726	37	0.304029	22
VR176	0.322667	27	0.080889	70	0.18726	51
VR177	0.209614	74	0.080889	70	0.18726	51
VR178	0.043912	120	-0.039635	122	-0.039635	150
VR179	0.216527	65	0.147256	51	0.147256	66
VR180	-0.033676	159	-0.123423	149	0.012109	122
VR181	0.073855	116	-0.007345	109	0.057589	100
VR182	0.330179	21	0.155125	43	0.209614	42
VR183	0.159489	83	0.155125	43	0.209614	42
VR184	-0.024535	149	-0.033676	114	-0.033676	146
VR185	0.035383	128	-0.123423	149	0.012109	122
VR186	-0.033676	159	-0.123423	149	-0.048888	154
VR187	-0.366242	280	-0.382637	250	-0.484438	287
VR188	-0.285972	250	-0.301518	216	-0.398073	275
VR189	0.412158	9	0.365848	9	0.437775	5
VR190	-0.4627	291	-0.48015	269	-0.588478	293
VR191	-0.197354	220	-0.301518	216	-0.21566	219
VR192	-0.363175	263	-0.48015	269	-0.378625	258
VR193	-0.366242	280	-0.382637	250	-0.382637	271
VR194	-0.030808	152	-0.037938	118	-0.115098	177
VR195	-0.269037	235	-0.48015	269	-0.294512	241
VR196	0.255951	50	0.149041	50	0.248837	32
VR197	0.328602	23	0.00455	101	0.147256	66
VR198	-0.363175	263	-0.48015	269	-0.378625	258
VR199	-0.197354	220	-0.301518	216	-0.21566	219
VR200	0.151307	85	0.093415	64	0.150309	65
VR201	-0.016633	143	-0.104598	138	-0.030584	142
VR202	0.322667	27	0.080889	70	0.18726	51
VR203	-0.186338	208	-0.212635	194	-0.039635	150
VR204	-0.110029	183	-0.123423	149	-0.123423	178
VR205	-0.4627	291	-0.48015	269	-0.588478	293
VR206	0.406533	10	0.412158	6	0.367572	13
VR207	-0.197354	220	-0.301518	216	-0.21566	219
VR208	-0.272756	243	-0.382637	250	-0.289401	233
VR209	-0.4627	291	-0.48015	269	-0.588478	293
VR210	-0.363175	263	-0.48015	269	-0.378625	258
VR211	-0.272756	243	-0.212635	194	-0.289401	233
VR212	-0.033676	159	-0.123423	149	-0.048888	154
VR213	-0.285972	250	-0.301518	216	-0.398073	275
VR214	0.03442	133	-0.105112	139	0.025128	115
VR215	0.326335	25	0.279965	21	0.279965	24
VR216	0.116614	96	0.043912	84	-0.115005	175
VR217	0.238582	55	0.117164	62	0.224268	38
VR218	0.091972	109	0.080889	70	0.012028	129
VR219	0.344544	18	0.288536	19	0.235052	35
VR220	-0.285972	250	-0.301518	216	-0.398073	275
VR221	0.498403	2	0.466378	2	0.523567	1
VR222	-0.272756	243	-0.382637	250	-0.289401	233
VR223	0.277107	45	0.158964	41	0.257625	29
VR224	0.182402	77	-0.023197	111	0.043635	108
VR225	-0.285972	250	-0.301518	216	-0.398073	275
VR226	0.03865	126	-0.182419	179	0.027739	114
VR227	-0.363175	263	-0.48015	269	-0.378625	258
VR228	0.318581	30	0.292041	18	0.318581	17
VR229	-0.4627	291	-0.48015	269	-0.588478	293
VR230	0.216527	65	0.147256	51	0.147256	66
VR231	0.167637	78	0.04641	81	0.159557	59
VR232	0.446754	5	0.195862	35	0.311698	18
VR233	-0.269037	235	-0.48015	269	-0.294512	241
VR234	-0.030815	153	-0.105112	139	-0.033241	143
VR235	0.412919	7	0.389848	7	0.412919	7
VR236	-0.285972	250	-0.301518	216	-0.301518	255
VR237	0.14369	88	0.04602	82	-0.025628	141
VR238	-0.272756	243	-0.382637	250	-0.289401	233
VR239	0.093415	106	0.020571	88	0.083372	93
VR240	-0.285972	250	-0.301518	216	-0.301518	255
VR241	0.218326	64	0.155125	43	0.209614	42
VR242	0.343626	19	0.268667	24	0.213142	41
VR243	-0.366242	280	-0.382637	250	-0.484438	287
VR244	0.020571	136	-0.065652	129	0.002195	132
VR245	0.22175	61	0.153367	48	0.153367	61
VR246	0.326238	26	0.218326	29	0.159489	60
VR247	0.018762	139	-0.269037	204	-0.062125	168
VR248	-0.115098	193	-0.128636	167	-0.212736	217
VR249	-0.2593	234	-0.272756	205	-0.366242	257
VR250	-0.285972	250	-0.301518	216	-0.398073	275
VR251	0.268667	48	0.218326	29	0.267667	26
VR252	-0.363175	263	-0.48015	269	-0.294512	241
VR253	-0.269037	235	-0.48015	269	-0.294512	241
VR254	0.093415	106	0.020571	88	0.083372	93
VR255	0.397344	11	0.301519	17	0.345168	15
VR256	-0.110029	183	-0.123423	149	-0.206604	204
VR257	0.035383	128	-0.123423	149	0.012109	122
VR258	-0.104911	178	-0.200702	185	-0.055127	164
VR259	-0.363175	263	-0.48015	269	-0.378625	258
VR260	0.22175	61	0.012109	96	0.153367	61
VR261	-0.285972	250	-0.301518	216	-0.398073	275
VR262	0.04099	123	0.085559	69	0.030116	111
VR263	-0.363175	263	-0.294512	212	-0.378625	258
VR264	-0.033676	159	-0.123423	149	-0.048888	154
VR265	0.128432	92	0.125322	61	0.125322	77
VR266	0.223245	59	0.020571	88	0.083372	93
VR267	-0.186338	208	-0.382637	250	-0.212635	209
VR268	0.030116	134	-0.128636	167	0.00455	130
VR269	-0.4627	291	-0.48015	269	-0.588478	293
VR270	-0.110029	183	-0.123423	149	-0.206604	204
VR271	-0.346253	262	-0.363175	245	-0.4627	284
VR272	0.035383	128	0.012109	96	0.012109	122
VR273	-0.088215	175	-0.284314	208	-0.169261	197
VR274	0.454382	4	0.454382	3	0.48779	3
VR275	0.083372	111	-0.065652	129	0.056836	102
VR276	0.328602	23	0.00455	101	0.147256	66
VR277	0.164904	79	-0.052692	126	0.097806	81
VR278	-0.115098	193	-0.128636	167	-0.212736	217
VR279	-0.363175	263	-0.48015	269	-0.378625	258
VR280	0.086757	110	0.093415	64	0.025049	116
VR281	0.50525	1	0.540332	1	0.50525	2
VR282	0.305207	38	0.225928	26	0.225928	37
VR283	0.313579	34	0.218326	29	0.307268	20
VR284	0.313579	34	0.218326	29	0.307268	20
VR285	-0.4627	291	-0.48015	269	-0.588478	293
VR286	0.074737	115	0.13932	57	0.074737	99
VR287	-0.033676	159	-0.123423	149	-0.048888	154
VR288	0.313579	34	0.307268	15	0.406982	8
VR289	-0.217709	230	-0.23237	202	-0.150076	195
VR290	-0.363175	263	-0.48015	269	-0.378625	258
VR291	-0.366242	280	-0.382637	250	-0.484438	287
VR292	0.258479	49	0.192447	36	0.192447	47
VR293	-0.269037	235	-0.48015	269	-0.294512	241
VR294	-0.186338	208	-0.382637	250	-0.212635	209
VR295	-0.269037	235	-0.48015	269	-0.294512	241
VR296	-0.197354	220	-0.301518	216	-0.21566	219
VR297	0.292041	40	0.151307	49	0.203123	45
VR298	-0.117815	195	-0.14555	176	-0.14555	186
VR299	-0.033676	159	-0.123423	149	-0.048888	154
VR300	-0.033676	159	-0.123423	149	-0.048888	154
q = 3
Alternatives	Expert 1		Expert 2		Expert 3
	Score	final rank	Score	final rank	Score	final rank
VR1	-0.130612	205	-0.327956	248	-0.231083	233
VR2	0.27259	69	0.159673	71	0.222882	71
VR3	0.078316	131	0.014126	118	0.014126	157
VR4	-0.064433	189	-0.247035	214	-0.155851	209
VR5	-0.079331	204	-0.239367	213	-0.073248	185
VR6	0.145141	111	0.094111	93	0.094111	122
VR7	-0.22061	234	-0.425087	269	-0.231083	233
VR8	-0.149352	219	-0.33734	250	-0.155851	209
VR9	0.105552	123	0.114789	86	0.272782	47
VR10	-0.305836	262	-0.425087	269	-0.231083	233
VR11	0.377745	28	0.337076	20	0.37483	20
VR12	0.260942	74	0.167456	62	0.276996	41
VR13	0.06881	136	-0.000572	131	0.064082	138
VR14	0.001663	168	-0.07201	166	0.071259	131
VR15	0.170959	104	0.223638	48	0.176582	83
VR16	-0.130612	205	-0.327956	248	-0.231083	233
VR17	-0.064433	189	-0.247035	214	-0.155851	209
VR18	0.356714	41	0.238963	47	0.194821	76
VR19	0.188102	92	-0.079571	174	0.132984	100
VR20	0.316605	51	0.218567	49	0.276996	41
VR21	0.00514	167	-0.000572	131	-0.000572	170
VR22	-0.415233	291	-0.425087	269	-0.564717	293
VR23	-0.305836	262	-0.425087	269	-0.231083	233
VR24	0.452275	12	0.360692	13	0.39699	13
VR25	-0.208595	231	-0.425087	269	-0.214075	230
VR26	0.166931	105	0.115163	85	0.169972	86
VR27	-0.058042	185	-0.1389	180	-0.064842	179
VR28	0.269094	70	-0.07201	166	0.133424	93
VR29	-0.228857	242	-0.155851	193	-0.247035	247
VR30	-0.135662	207	-0.130612	179	0.078316	125
VR31	0.126665	119	-0.000572	131	0.133252	96
VR32	0.195892	89	0.094111	93	0.21331	75
VR33	0.279536	61	-0.155851	193	0.239195	60
VR34	-0.005596	173	-0.07973	176	-0.010142	173
VR35	0.379934	25	0.32507	23	0.32507	27
VR36	-0.05172	183	0.008072	124	-0.130612	202
VR37	0.184598	99	0.06881	104	0.191793	79
VR38	-0.14704	210	-0.24925	217	-0.164679	220
VR39	-0.149352	219	-0.155851	193	0.070729	133
VR40	0.163783	107	0.106309	91	0.159673	89
VR41	0.126665	119	-0.000572	131	0.133252	96
VR42	-0.072651	194	-0.24925	217	-0.079571	186
VR43	0.078316	131	0.014126	118	0.014126	157
VR44	0.309457	55	0.127636	84	0.276007	46
VR45	0.360064	40	0.218567	49	0.316605	29
VR46	0.238963	80	0.194821	58	0.194821	76
VR47	0.465015	8	0.482826	4	0.482826	6
VR48	-0.14704	210	-0.24925	217	-0.164679	220
VR49	-0.072651	194	-0.24925	217	-0.079571	186
VR50	0.054009	148	0.046851	114	0.046851	146
VR51	0.061525	145	-0.005596	139	0.126665	106
VR52	-0.14704	210	-0.24925	217	-0.164679	220
VR53	-0.32838	280	-0.228857	206	-0.247035	247
VR54	-0.240808	250	-0.24925	217	-0.164679	220
VR55	-0.05321	184	-0.1389	180	0.008072	161
VR56	-0.149352	219	-0.33734	250	-0.155851	209
VR57	-0.151289	229	-0.073248	172	-0.158754	219
VR58	-0.064433	189	-0.247035	214	-0.155851	209
VR59	0.009207	164	-0.149352	192	-0.064433	177
VR60	0.139085	112	-0.231083	209	0.078316	125
VR61	-0.32838	280	-0.33734	250	-0.33734	271
VR62	0.073623	135	-0.073802	173	0.06786	137
VR63	-0.015776	175	-0.02139	141	-0.100572	197
VR64	-0.072651	194	-0.24925	217	-0.079571	186
VR65	0.360692	39	0.360692	13	0.39699	13
VR66	-0.240808	250	-0.24925	217	-0.36883	275
VR67	0.188102	92	0.132984	75	0.132984	100
VR68	0.129269	116	-0.155851	193	0.070729	133
VR69	-0.228857	242	-0.155851	193	-0.247035	247
VR70	0.180021	100	-0.058042	160	0.238066	67
VR71	0.288297	57	0.377745	12	0.30785	31
VR72	-0.240808	250	-0.24925	217	-0.36883	275
VR73	0.017897	160	-0.066946	162	0.001538	165
VR74	-0.208595	231	-0.214075	203	-0.214075	230
VR75	0.191793	90	0.064082	109	0.133252	96
VR76	0.127038	118	-0.07201	166	-0.07201	184
VR77	0.188102	92	0.132984	75	0.132984	100
VR78	0.352101	44	0.214307	51	0.171294	85
VR79	0.33441	48	0.258966	41	0.35533	25
VR80	0.186258	96	0.129269	81	0.129269	104
VR81	0.310251	52	0.114789	86	0.272782	47
VR82	0.013153	163	-0.058042	160	0.008072	161
VR83	-0.228857	242	-0.33734	250	-0.247035	247
VR84	-0.305836	262	-0.425087	269	-0.231083	233
VR85	0.277132	66	0.163783	70	0.27259	51
VR86	0.276528	67	0.191793	60	0.126665	106
VR87	0.261326	73	0.155817	72	0.21897	72
VR88	0.188102	92	0.132984	75	0.132984	100
VR89	0.105552	123	-0.02139	141	0.114789	112
VR90	-0.14704	210	-0.24925	217	-0.164679	220
VR91	-0.305836	262	-0.425087	269	-0.327956	257
VR92	-0.240808	250	-0.24925	217	-0.36883	275
VR93	0.469215	7	0.486764	3	0.486764	5
VR94	0.426166	14	0.391824	11	0.469824	7
VR95	0.046851	150	-0.02139	141	0.043972	148
VR96	0.288297	57	0.264536	35	0.30785	31
VR97	0.068315	139	0.001663	127	0.063557	141
VR98	-0.150672	226	-0.14704	189	-0.14704	205
VR99	0.186258	96	0.129269	81	0.129269	104
VR100	0.353613	43	0.310251	26	0.310251	30
VR101	0.006556	166	-0.164679	201	-0.079571	186
VR102	-0.415233	291	-0.425087	269	-0.425087	285
VR103	-0.305836	262	-0.425087	269	-0.327956	257
VR104	0.017897	160	-0.066946	162	0.001538	165
VR105	0.203193	87	-0.052292	159	0.088166	124
VR106	-0.015776	175	-0.02139	141	-0.02139	175
VR107	0.098292	129	0.094111	93	0.094111	122
VR108	-0.14704	210	-0.24925	217	-0.164679	220
VR109	0.172385	102	0.043972	117	0.114789	112
VR110	0.279536	61	0.239195	44	0.239195	60
VR111	-0.058042	185	-0.1389	180	-0.064842	179
VR112	-0.015776	175	-0.02139	141	-0.100572	197
VR113	0.046851	150	0.167456	62	0.043972	148
VR114	-0.150672	226	0.06881	104	-0.14704	205
VR115	-0.415233	291	-0.1389	180	-0.425087	285
VR116	0.046851	150	0.167456	62	0.114789	112
VR117	0.279536	61	0.071259	99	0.239195	60
VR118	0.066622	143	0.055009	111	-0.000295	169
VR119	0.001538	170	-0.14704	189	0.006556	163
VR120	0.288297	57	0.264536	35	0.264536	54
VR121	0.227345	82	-0.000572	131	0.289745	39
VR122	0.000652	172	-0.005596	139	0.126665	106
VR123	-0.22061	234	-0.425087	269	-0.231083	233
VR124	0.206411	86	0.013153	122	0.136885	92
VR125	0.482408	6	0.360692	13	0.442818	11
VR126	0.371885	32	0.092298	96	0.14863	91
VR127	0.337076	47	0.252637	42	0.218567	73
VR128	0.055009	147	-0.1389	180	0.057382	144
VR129	-0.305836	262	-0.1389	180	-0.327956	257
VR130	0.356714	41	0.013739	121	0.194821	76
VR131	-0.135662	207	-0.305836	245	-0.130612	202
VR132	0.06881	136	-0.000572	131	0.064082	138
VR133	-0.072651	194	-0.24925	217	-0.079571	186
VR134	-0.072651	194	-0.24925	217	-0.079571	186
VR135	0.365877	33	0.269508	33	0.231136	68
VR136	-0.32838	280	-0.33734	250	-0.33734	271
VR137	-0.143254	209	-0.228857	206	-0.149352	208
VR138	-0.32838	280	-0.33734	250	-0.464217	287
VR139	-0.32838	280	-0.33734	250	-0.33734	271
VR140	-0.150672	226	-0.14704	189	-0.14704	205
VR141	0.382917	24	0.342148	19	0.379996	18
VR142	-0.073628	202	-0.07973	176	-0.07973	195
VR143	0.431553	13	0.133252	74	0.290635	37
VR144	0.241347	78	0.188102	61	0.188102	80
VR145	0.190923	91	0.063557	110	0.133424	93
VR146	-0.22061	234	-0.425087	269	-0.231083	233
VR147	-0.305836	262	-0.231083	209	-0.327956	257
VR148	-0.149352	219	-0.33734	250	-0.155851	209
VR149	-0.072651	194	-0.24925	217	-0.079571	186
VR150	-0.32838	280	-0.33734	250	-0.464217	287
VR151	-0.214075	233	-0.305836	245	-0.22061	232
VR152	0.338101	46	0.290817	27	0.32326	28
VR153	0.379236	26	0.40453	9	0.40453	12
VR154	0.269094	70	0.001663	127	0.133424	93
VR155	0.164382	106	0.046851	114	0.172385	84
VR156	0.078316	131	0.014126	118	0.014126	157
VR157	0.078316	131	-0.231083	209	0.014126	157
VR158	0.422933	15	0.396739	10	0.396739	15
VR159	-0.058042	185	-0.1389	180	-0.064842	179
VR160	-0.005596	173	-0.07973	176	-0.010142	173
VR161	-0.058042	185	-0.1389	180	-0.064842	179
VR162	0.209998	85	0.272933	31	0.214184	74
VR163	-0.32838	280	-0.33734	250	-0.464217	287
VR164	-0.305836	262	-0.425087	269	-0.327956	257
VR165	0.068315	139	0.001663	127	0.063557	141
VR166	-0.415233	291	-0.425087	269	-0.564717	293
VR167	-0.072651	194	-0.24925	217	-0.079571	186
VR168	0.152411	109	0.102211	92	0.157248	90
VR169	0.001663	168	0.071259	99	-0.002902	172
VR170	0.001538	170	0.006556	125	0.006556	163
VR171	0.396056	21	0.322077	25	0.266858	53
VR172	0.139085	112	0.078316	98	0.078316	125
VR173	0.250201	76	0.131112	78	0.245531	59
VR174	-0.015776	175	-0.02139	141	-0.100572	197
VR175	0.422933	15	0.276996	30	0.396739	15
VR176	0.37483	30	0.167456	62	0.276996	41
VR177	0.260942	74	0.167456	62	0.276996	41
VR178	0.129269	116	0.070729	103	0.070729	133
VR179	0.279536	61	0.239195	44	0.239195	60
VR180	0.046851	150	-0.02139	141	0.114789	112
VR181	0.106309	122	0.051311	112	0.10995	120
VR182	0.377745	28	0.214307	51	0.260942	55
VR183	0.225938	83	0.214307	51	0.260942	55
VR184	0.054009	148	0.046851	114	0.046851	146
VR185	0.105552	123	-0.02139	141	0.114789	112
VR186	0.046851	150	-0.02139	141	0.043972	148
VR187	-0.32838	280	-0.33734	250	-0.464217	287
VR188	-0.240808	250	-0.24925	217	-0.36883	275
VR189	0.464918	10	0.430736	8	0.503466	4
VR190	-0.415233	291	-0.425087	269	-0.564717	293
VR191	-0.14704	210	-0.24925	217	-0.164679	220
VR192	-0.305836	262	-0.425087	269	-0.327956	257
VR193	-0.32838	280	-0.33734	250	-0.33734	271
VR194	0.007821	165	0.001663	127	-0.065945	183
VR195	-0.22061	234	-0.425087	269	-0.231083	233
VR196	0.308098	56	0.199802	57	0.303745	34
VR197	0.389648	22	0.071259	99	0.239195	60
VR198	-0.305836	262	-0.425087	269	-0.327956	257
VR199	-0.14704	210	-0.24925	217	-0.164679	220
VR200	0.200886	88	0.131112	78	0.184598	82
VR201	0.104142	128	0.049175	113	0.107908	121
VR202	0.37483	30	0.167456	62	0.276996	41
VR203	-0.149352	219	-0.155851	193	0.070729	133
VR204	-0.015776	175	-0.02139	141	-0.02139	175
VR205	-0.415233	291	-0.425087	269	-0.564717	293
VR206	0.491209	4	0.464918	6	0.445894	10
VR207	-0.14704	210	-0.24925	217	-0.164679	220
VR208	-0.228857	242	-0.33734	250	-0.247035	247
VR209	-0.415233	291	-0.425087	269	-0.564717	293
VR210	-0.305836	262	-0.425087	269	-0.327956	257
VR211	-0.228857	242	-0.155851	193	-0.247035	247
VR212	0.046851	150	-0.02139	141	0.043972	148
VR213	-0.240808	250	-0.24925	217	-0.36883	275
VR214	0.081113	130	-0.066946	162	0.075446	128
VR215	0.406214	18	0.353613	17	0.353613	26
VR216	0.186258	96	0.129269	81	-0.064433	177
VR217	0.287752	60	0.194427	59	0.298398	35
VR218	0.171294	103	0.167456	62	0.113552	119
VR219	0.403641	20	0.325966	22	0.296614	36
VR220	-0.240808	250	-0.24925	217	-0.36883	275
VR221	0.548557	2	0.522165	2	0.583051	1
VR222	-0.228857	242	-0.33734	250	-0.247035	247
VR223	0.361952	38	0.290817	27	0.382883	17
VR224	0.246511	77	0.013153	122	0.074239	129
VR225	-0.240808	250	-0.24925	217	-0.36883	275
VR226	0.061525	145	-0.142464	188	0.056734	145
VR227	-0.305836	262	-0.425087	269	-0.327956	257
VR228	0.379236	26	0.345244	18	0.379236	19
VR229	-0.415233	291	-0.425087	269	-0.564717	293
VR230	0.279536	61	0.239195	44	0.239195	60
VR231	0.231738	81	0.110066	90	0.226943	69
VR232	0.509882	3	0.245531	43	0.371102	21
VR233	-0.22061	234	-0.425087	269	-0.231083	233
VR234	0.017897	160	-0.066946	162	0.001538	165
VR235	0.465015	8	0.436536	7	0.465015	8
VR236	-0.240808	250	-0.24925	217	-0.24925	255
VR237	0.219301	84	0.092298	96	0.030548	156
VR238	-0.228857	242	-0.33734	250	-0.247035	247
VR239	0.131112	114	0.06881	104	0.126665	106
VR240	-0.240808	250	-0.24925	217	-0.24925	255
VR241	0.264536	72	0.214307	51	0.260942	55
VR242	0.413532	17	0.324179	24	0.288297	40
VR243	-0.32838	280	-0.33734	250	-0.464217	287
VR244	0.06881	136	-0.000572	131	0.064082	138
VR245	0.310251	52	0.272782	32	0.272782	47
VR246	0.40482	19	0.264536	35	0.225938	70
VR247	0.06786	142	-0.22061	204	0.001051	168
VR248	-0.065945	192	-0.07201	166	-0.157601	217
VR249	-0.232128	249	-0.228857	206	-0.32838	270
VR250	-0.240808	250	-0.24925	217	-0.36883	275
VR251	0.324179	50	0.264536	35	0.30785	31
VR252	-0.305836	262	-0.425087	269	-0.231083	233
VR253	-0.22061	234	-0.425087	269	-0.231083	233
VR254	0.131112	114	0.06881	104	0.126665	106
VR255	0.457579	11	0.332181	21	0.37034	22
VR256	-0.015776	175	-0.02139	141	-0.100572	197
VR257	0.105552	123	-0.02139	141	0.114789	112
VR258	-0.078151	203	-0.156871	200	-0.002391	171
VR259	-0.305836	262	-0.425087	269	-0.327956	257
VR260	0.310251	52	0.114789	86	0.272782	47
VR261	-0.240808	250	-0.24925	217	-0.36883	275
VR262	0.068315	139	0.133424	73	0.063557	141
VR263	-0.305836	262	-0.231083	209	-0.327956	257
VR264	0.046851	150	-0.02139	141	0.043972	148
VR265	0.177988	101	0.166931	69	0.166931	87
VR266	0.276528	67	0.06881	104	0.126665	106
VR267	-0.149352	219	-0.33734	250	-0.155851	209
VR268	0.063557	144	-0.07201	166	0.071259	131
VR269	-0.415233	291	-0.425087	269	-0.564717	293
VR270	-0.015776	175	-0.02139	141	-0.100572	197
VR271	-0.311733	279	-0.305836	245	-0.415233	284
VR272	0.105552	123	0.114789	86	0.114789	112
VR273	-0.046232	182	-0.228853	205	-0.136685	204
VR274	0.482826	5	0.482826	4	0.511385	3
VR275	0.126665	119	-0.000572	131	0.133252	96
VR276	0.389648	22	0.071259	99	0.239195	60
VR277	0.241347	78	0.006556	125	0.188102	80
VR278	-0.065945	192	-0.07201	166	-0.157601	217
VR279	-0.305836	262	-0.425087	269	-0.327956	257
VR280	0.147887	110	0.131112	78	0.074148	130
VR281	0.569452	1	0.581347	1	0.569452	2
VR282	0.365877	33	0.269508	33	0.269508	52
VR283	0.364065	35	0.264536	35	0.360064	23
VR284	0.364065	35	0.264536	35	0.360064	23
VR285	-0.415233	291	-0.425087	269	-0.564717	293
VR286	0.16105	108	0.209246	55	0.16105	88
VR287	0.046851	150	-0.02139	141	0.043972	148
VR288	0.364065	35	0.360064	16	0.458179	9
VR289	-0.15995	230	-0.166556	202	-0.091334	196
VR290	-0.305836	262	-0.425087	269	-0.327956	257
VR291	-0.32838	280	-0.33734	250	-0.464217	287
VR292	0.328595	49	0.290635	29	0.290635	37
VR293	-0.22061	234	-0.425087	269	-0.231083	233
VR294	-0.149352	219	-0.33734	250	-0.155851	209
VR295	-0.22061	234	-0.425087	269	-0.231083	233
VR296	-0.14704	210	-0.24925	217	-0.164679	220
VR297	0.345244	45	0.200886	56	0.250201	58
VR298	-0.072651	194	-0.079571	174	-0.079571	186
VR299	0.046851	150	-0.02139	141	0.043972	148
VR300	0.046851	150	-0.02139	141	0.043972	148
q = 5
Alternatives	Expert 1		Expert 2		Expert 3
	Score	final rank	Score	final rank	Score	final rank
VR1	-0.045117	205	-0.205559	248	-0.128103	233
VR2	0.18326	86	0.104189	91	0.155117	81
VR3	0.116648	117	0.079693	100	0.079693	132
VR4	-0.011278	189	-0.156481	214	-0.083244	210
VR5	-0.028273	202	-0.13111	213	-0.015679	179
VR6	0.117504	116	0.090003	97	0.090003	129
VR7	-0.113159	234	-0.276722	269	-0.128103	233
VR8	-0.076365	220	-0.220682	250	-0.083244	210
VR9	0.098267	127	0.115263	80	0.242009	33
VR10	-0.165607	262	-0.276722	269	-0.128103	233
VR11	0.283182	33	0.260493	20	0.279962	21
VR12	0.190947	81	0.141684	65	0.21817	43
VR13	0.06745	139	0.021789	131	0.061079	145
VR14	0.02265	175	-0.026943	168	0.073968	137
VR15	0.148018	102	0.176732	51	0.153108	82
VR16	-0.045117	205	-0.205559	248	-0.128103	233
VR17	-0.011278	189	-0.156481	214	-0.083244	210
VR18	0.293071	29	0.206362	38	0.186869	68
VR19	0.177801	89	-0.029896	174	0.148164	86
VR20	0.236851	54	0.170219	52	0.21817	43
VR21	0.029819	166	0.021789	131	0.021789	167
VR22	-0.257096	291	-0.276722	269	-0.424756	293
VR23	-0.165607	262	-0.276722	269	-0.128103	233
VR24	0.349438	10	0.27693	15	0.295287	17
VR25	-0.091507	231	-0.276722	269	-0.104831	230
VR26	0.117826	115	0.091169	96	0.121587	97
VR27	-0.005647	185	-0.062741	180	-0.017166	180
VR28	0.199749	73	-0.026943	168	0.111207	113
VR29	-0.124389	242	-0.083244	193	-0.156481	247
VR30	-0.058836	207	-0.045117	179	0.116648	103
VR31	0.099213	124	0.021789	131	0.117173	99
VR32	0.143856	106	0.090003	97	0.171722	79
VR33	0.223904	60	-0.083244	193	0.206843	51
VR34	0.011994	180	-0.038555	176	0.003958	175
VR35	0.298077	28	0.248936	23	0.248936	29
VR36	0.004864	183	0.030457	126	-0.045117	201
VR37	0.133237	110	0.06745	108	0.151473	83
VR38	-0.070479	211	-0.159064	217	-0.099202	220
VR39	-0.076365	220	-0.083244	193	0.106865	117
VR40	0.108702	121	0.076582	103	0.104189	121
VR41	0.099213	124	0.021789	131	0.117173	99
VR42	-0.025486	194	-0.159064	217	-0.029896	186
VR43	0.116648	117	0.079693	100	0.079693	132
VR44	0.236583	55	0.110257	85	0.224809	41
VR45	0.261982	46	0.170219	52	0.236851	38
VR46	0.206362	72	0.186869	47	0.186869	68
VR47	0.361265	8	0.365367	4	0.365367	7
VR48	-0.070479	211	-0.159064	217	-0.099202	220
VR49	-0.025486	194	-0.159064	217	-0.029896	186
VR50	0.071981	136	0.066122	113	0.066122	143
VR51	0.051678	161	0.011994	157	0.099213	123
VR52	-0.070479	211	-0.159064	217	-0.099202	220
VR53	-0.203683	280	-0.124389	205	-0.156481	247
VR54	-0.143429	250	-0.159064	217	-0.099202	220
VR55	-0.001789	184	-0.062741	180	0.030457	164
VR56	-0.076365	220	-0.220682	250	-0.083244	210
VR57	-0.067341	209	-0.015679	162	-0.081445	209
VR58	-0.011278	189	-0.156481	214	-0.083244	210
VR59	0.034825	165	-0.076365	192	-0.011278	177
VR60	0.149894	100	-0.128103	208	0.116648	103
VR61	-0.203683	280	-0.220682	250	-0.220682	271
VR62	0.079921	134	-0.021987	167	0.070529	140
VR63	0.027261	168	0.018966	139	-0.043342	196
VR64	-0.025486	194	-0.159064	217	-0.029896	186
VR65	0.27693	40	0.27693	15	0.295287	17
VR66	-0.143429	250	-0.159064	217	-0.276918	278
VR67	0.177801	89	0.148164	61	0.148164	86
VR68	0.139032	107	-0.083244	193	0.106865	117
VR69	-0.124389	242	-0.083244	193	-0.156481	247
VR70	0.157921	97	-0.005647	160	0.201753	59
VR71	0.233374	56	0.283182	13	0.217839	48
VR72	-0.143429	250	-0.159064	217	-0.276918	278
VR73	0.052943	158	-0.018312	163	0.021465	168
VR74	-0.091507	231	-0.104831	203	-0.104831	230
VR75	0.151473	98	0.061079	116	0.117173	99
VR76	0.1288	113	-0.026943	168	-0.026943	185
VR77	0.177801	89	0.148164	61	0.148164	86
VR78	0.274982	41	0.166361	54	0.145998	90
VR79	0.244373	53	0.211042	33	0.276735	23
VR80	0.170391	93	0.139032	72	0.139032	92
VR81	0.258237	48	0.115263	80	0.242009	33
VR82	0.036275	164	-0.005647	160	0.030457	164
VR83	-0.124389	242	-0.220682	250	-0.156481	247
VR84	-0.165607	262	-0.276722	269	-0.128103	233
VR85	0.191289	79	0.108702	86	0.18326	71
VR86	0.213094	67	0.151473	60	0.099213	123
VR87	0.193072	78	0.121559	75	0.172442	78
VR88	0.177801	89	0.148164	61	0.148164	86
VR89	0.098267	127	0.018966	139	0.115263	106
VR90	-0.070479	211	-0.159064	217	-0.099202	220
VR91	-0.165607	262	-0.276722	269	-0.205559	258
VR92	-0.143429	250	-0.159064	217	-0.276918	278
VR93	0.378715	5	0.382379	3	0.382379	3
VR94	0.344822	12	0.327954	8	0.381198	4
VR95	0.066122	142	0.018966	139	0.058895	148
VR96	0.233374	56	0.194971	41	0.217839	48
VR97	0.061795	153	0.02265	127	0.056349	156
VR98	-0.077168	227	-0.070479	189	-0.070479	205
VR99	0.170391	93	0.139032	72	0.139032	92
VR100	0.282139	35	0.258237	21	0.258237	26
VR101	0.036325	163	-0.099202	202	-0.029896	186
VR102	-0.257096	291	-0.276722	269	-0.276722	276
VR103	-0.165607	262	-0.276722	269	-0.205559	258
VR104	0.052943	158	-0.018312	163	0.021465	168
VR105	0.197166	76	0.006301	159	0.101514	122
VR106	0.027261	168	0.018966	139	0.018966	171
VR107	0.094815	132	0.090003	97	0.090003	129
VR108	-0.070479	211	-0.159064	217	-0.099202	220
VR109	0.150674	99	0.058895	117	0.115263	106
VR110	0.223904	60	0.206843	35	0.206843	51
VR111	-0.005647	185	-0.062741	180	-0.017166	180
VR112	0.027261	168	0.018966	139	-0.043342	196
VR113	0.066122	142	0.141684	65	0.058895	148
VR114	-0.077168	227	0.06745	108	-0.070479	205
VR115	-0.257096	291	-0.062741	180	-0.276722	276
VR116	0.066122	142	0.141684	65	0.115263	106
VR117	0.223904	60	0.073968	104	0.206843	51
VR118	0.065414	152	0.053807	119	0.026448	166
VR119	0.021465	177	-0.070479	189	0.036325	161
VR120	0.233374	56	0.194971	41	0.194971	60
VR121	0.185866	85	0.021789	131	0.237661	37
VR122	0.017937	179	0.011994	157	0.099213	123
VR123	-0.113159	234	-0.276722	269	-0.128103	233
VR124	0.197653	75	0.036275	124	0.139971	91
VR125	0.365202	7	0.27693	15	0.334469	11
VR126	0.316446	21	0.101819	93	0.131657	95
VR127	0.260493	47	0.186115	48	0.170219	80
VR128	0.053807	157	-0.062741	180	0.05513	159
VR129	-0.165607	262	-0.062741	180	-0.205559	258
VR130	0.293071	29	0.044392	121	0.186869	68
VR131	-0.058836	207	-0.165607	245	-0.045117	201
VR132	0.06745	139	0.021789	131	0.061079	145
VR133	-0.025486	194	-0.159064	217	-0.029896	186
VR134	-0.025486	194	-0.159064	217	-0.029896	186
VR135	0.302294	24	0.20501	39	0.188759	66
VR136	-0.203683	280	-0.220682	250	-0.220682	271
VR137	-0.068716	210	-0.124389	205	-0.076365	208
VR138	-0.203683	280	-0.220682	250	-0.348835	287
VR139	-0.203683	280	-0.220682	250	-0.220682	271
VR140	-0.077168	227	-0.070479	189	-0.070479	205
VR141	0.280577	36	0.257847	22	0.277351	22
VR142	-0.029662	203	-0.038555	176	-0.038555	195
VR143	0.337388	15	0.117173	78	0.242382	31
VR144	0.207455	70	0.177801	50	0.177801	75
VR145	0.144673	105	0.056349	118	0.111207	113
VR146	-0.113159	234	-0.276722	269	-0.128103	233
VR147	-0.165607	262	-0.128103	208	-0.205559	258
VR148	-0.076365	220	-0.220682	250	-0.083244	210
VR149	-0.025486	194	-0.159064	217	-0.029896	186
VR150	-0.203683	280	-0.220682	250	-0.348835	287
VR151	-0.104831	233	-0.165607	245	-0.113159	232
VR152	0.272629	42	0.245964	25	0.258173	27
VR153	0.301614	26	0.308391	11	0.308391	15
VR154	0.199749	73	0.02265	127	0.111207	113
VR155	0.132652	111	0.066122	113	0.150674	84
VR156	0.116648	117	0.079693	100	0.079693	132
VR157	0.116648	117	-0.128103	208	0.079693	132
VR158	0.323698	18	0.314779	10	0.314779	12
VR159	-0.005647	185	-0.062741	180	-0.017166	180
VR160	0.011994	180	-0.038555	176	0.003958	175
VR161	-0.005647	185	-0.062741	180	-0.017166	180
VR162	0.183046	87	0.234847	29	0.188162	67
VR163	-0.203683	280	-0.220682	250	-0.348835	287
VR164	-0.165607	262	-0.276722	269	-0.205559	258
VR165	0.061795	153	0.02265	127	0.056349	156
VR166	-0.257096	291	-0.276722	269	-0.424756	293
VR167	-0.025486	194	-0.159064	217	-0.029896	186
VR168	0.145041	104	0.121263	76	0.149904	85
VR169	0.02265	175	0.073968	104	0.014943	174
VR170	0.021465	177	0.036325	122	0.036325	161
VR171	0.291195	31	0.219274	31	0.172548	77
VR172	0.149894	100	0.116648	79	0.116648	103
VR173	0.191252	80	0.104351	88	0.183083	72
VR174	0.027261	168	0.018966	139	-0.043342	196
VR175	0.323698	18	0.21817	32	0.314779	12
VR176	0.279962	37	0.141684	65	0.21817	43
VR177	0.190947	81	0.141684	65	0.21817	43
VR178	0.139032	107	0.106865	87	0.106865	117
VR179	0.223904	60	0.206843	35	0.206843	51
VR180	0.066122	142	0.018966	139	0.115263	106
VR181	0.076582	135	0.047665	120	0.079919	131
VR182	0.283182	33	0.166361	54	0.190947	62
VR183	0.178353	88	0.166361	54	0.190947	62
VR184	0.071981	136	0.066122	113	0.066122	143
VR185	0.098267	127	0.018966	139	0.115263	106
VR186	0.066122	142	0.018966	139	0.058895	148
VR187	-0.203683	280	-0.220682	250	-0.348835	287
VR188	-0.143429	250	-0.159064	217	-0.276918	278
VR189	0.340684	13	0.32096	9	0.374598	6
VR190	-0.257096	291	-0.276722	269	-0.424756	293
VR191	-0.070479	211	-0.159064	217	-0.099202	220
VR192	-0.165607	262	-0.276722	269	-0.205559	258
VR193	-0.203683	280	-0.220682	250	-0.220682	271
VR194	0.028688	167	0.02265	127	-0.01822	184
VR195	-0.113159	234	-0.276722	269	-0.128103	233
VR196	0.227062	59	0.148164	64	0.21939	42
VR197	0.307244	22	0.073968	104	0.206843	51
VR198	-0.165607	262	-0.276722	269	-0.205559	258
VR199	-0.070479	211	-0.159064	217	-0.099202	220
VR200	0.164742	96	0.104351	88	0.133237	94
VR201	0.124616	114	0.097373	95	0.12788	96
VR202	0.279962	37	0.141684	65	0.21817	43
VR203	-0.076365	220	-0.083244	193	0.106865	117
VR204	0.027261	168	0.018966	139	0.018966	171
VR205	-0.257096	291	-0.276722	269	-0.424756	293
VR206	0.378923	4	0.340684	7	0.335853	10
VR207	-0.070479	211	-0.159064	217	-0.099202	220
VR208	-0.124389	242	-0.220682	250	-0.156481	247
VR209	-0.257096	291	-0.276722	269	-0.424756	293
VR210	-0.165607	262	-0.276722	269	-0.205559	258
VR211	-0.124389	242	-0.083244	193	-0.156481	247
VR212	0.066122	142	0.018966	139	0.058895	148
VR213	-0.143429	250	-0.159064	217	-0.276918	278
VR214	0.08913	133	-0.018312	163	0.079619	136
VR215	0.329103	17	0.282139	14	0.282139	19
VR216	0.170391	93	0.139032	72	-0.011278	177
VR217	0.209984	69	0.162202	59	0.230552	40
VR218	0.145998	103	0.141684	65	0.109484	116
VR219	0.332446	16	0.262148	18	0.253889	28
VR220	-0.143429	250	-0.159064	217	-0.276918	278
VR221	0.42333	2	0.409062	2	0.455195	1
VR222	-0.124389	242	-0.220682	250	-0.156481	247
VR223	0.277752	39	0.245964	25	0.308723	14
VR224	0.21355	66	0.036275	124	0.068862	141
VR225	-0.143429	250	-0.159064	217	-0.276918	278
VR226	0.051678	161	-0.066124	188	0.046157	160
VR227	-0.165607	262	-0.276722	269	-0.205559	258
VR228	0.301614	26	0.283965	12	0.301614	16
VR229	-0.257096	291	-0.276722	269	-0.424756	293
VR230	0.223904	60	0.206843	35	0.206843	51
VR231	0.190792	83	0.103463	92	0.182607	73
VR232	0.398542	3	0.183083	49	0.281906	20
VR233	-0.113159	234	-0.276722	269	-0.128103	233
VR234	0.052943	158	-0.018312	163	0.021465	168
VR235	0.361265	8	0.345999	6	0.361265	8
VR236	-0.143429	250	-0.159064	217	-0.159064	255
VR237	0.221105	65	0.101819	93	0.068203	142
VR238	-0.124389	242	-0.220682	250	-0.156481	247
VR239	0.104351	122	0.06745	108	0.099213	123
VR240	-0.143429	250	-0.159064	217	-0.159064	255
VR241	0.194971	77	0.166361	54	0.190947	62
VR242	0.339707	14	0.248095	24	0.233374	39
VR243	-0.203683	280	-0.220682	250	-0.348835	287
VR244	0.06745	139	0.021789	131	0.061079	145
VR245	0.258237	48	0.242009	28	0.242009	33
VR246	0.322477	20	0.194971	41	0.178353	74
VR247	0.070529	138	-0.113159	204	0.03212	163
VR248	-0.01822	192	-0.026943	168	-0.092478	218
VR249	-0.132675	249	-0.124389	205	-0.203683	257
VR250	-0.143429	250	-0.159064	217	-0.276918	278
VR251	0.248095	52	0.194971	41	0.217839	48
VR252	-0.165607	262	-0.276722	269	-0.128103	233
VR253	-0.113159	234	-0.276722	269	-0.128103	233
VR254	0.104351	122	0.06745	108	0.099213	123
VR255	0.345619	11	0.225857	30	0.246147	30
VR256	0.027261	168	0.018966	139	-0.043342	196
VR257	0.098267	127	0.018966	139	0.115263	106
VR258	-0.035619	204	-0.090527	200	0.017684	173
VR259	-0.165607	262	-0.276722	269	-0.205559	258
VR260	0.258237	48	0.115263	80	0.242009	33
VR261	-0.143429	250	-0.159064	217	-0.276918	278
VR262	0.061795	153	0.111207	84	0.056349	156
VR263	-0.165607	262	-0.128103	208	-0.205559	258
VR264	0.066122	142	0.018966	139	0.058895	148
VR265	0.130305	112	0.117826	77	0.117826	98
VR266	0.213094	67	0.06745	108	0.099213	123
VR267	-0.076365	220	-0.220682	250	-0.083244	210
VR268	0.056349	156	-0.026943	168	0.073968	137
VR269	-0.257096	291	-0.276722	269	-0.424756	293
VR270	0.027261	168	0.018966	139	-0.043342	196
VR271	-0.178581	279	-0.165607	245	-0.257096	275
VR272	0.098267	127	0.115263	80	0.115263	106
VR273	0.011477	182	-0.12935	212	-0.063082	204
VR274	0.365367	6	0.365367	4	0.380814	5
VR275	0.099213	124	0.021789	131	0.117173	99
VR276	0.307244	22	0.073968	104	0.206843	51
VR277	0.207455	70	0.036325	122	0.177801	75
VR278	-0.01822	192	-0.026943	168	-0.092478	218
VR279	-0.165607	262	-0.276722	269	-0.205559	258
VR280	0.137796	109	0.104351	88	0.073855	139
VR281	0.453635	1	0.455904	1	0.453635	2
VR282	0.302294	24	0.20501	39	0.20501	58
VR283	0.269224	43	0.194971	41	0.261982	24
VR284	0.269224	43	0.194971	41	0.261982	24
VR285	-0.257096	291	-0.276722	269	-0.424756	293
VR286	0.188846	84	0.209235	34	0.188846	65
VR287	0.066122	142	0.018966	139	0.058895	148
VR288	0.269224	43	0.261982	19	0.343898	9
VR289	-0.082344	230	-0.092089	201	-0.046528	203
VR290	-0.165607	262	-0.276722	269	-0.205559	258
VR291	-0.203683	280	-0.220682	250	-0.348835	287
VR292	0.25813	51	0.242382	27	0.242382	31
VR293	-0.113159	234	-0.276722	269	-0.128103	233
VR294	-0.076365	220	-0.220682	250	-0.083244	210
VR295	-0.113159	234	-0.276722	269	-0.128103	233
VR296	-0.070479	211	-0.159064	217	-0.099202	220
VR297	0.283965	32	0.164742	58	0.191252	61
VR298	-0.025486	194	-0.029896	174	-0.029896	186
VR299	0.066122	142	0.018966	139	0.058895	148
VR300	0.066122	142	0.018966	139	0.058895	148
q = 7
Alternatives	Expert 1		Expert 2		Expert 3
	Score	final rank	Score	final rank	Score	final rank
VR1	-0.006175	194	-0.12517	248	-0.067522	233
VR2	0.110879	108	0.060162	101	0.097272	101
VR3	0.112545	103	0.093842	79	0.093842	103
VR4	0.008955	189	-0.096914	217	-0.042656	210
VR5	-0.006762	196	-0.066428	208	0.008087	177
VR6	0.082033	117	0.067481	94	0.067481	126
VR7	-0.053512	234	-0.177565	269	-0.067522	233
VR8	-0.036637	222	-0.142507	250	-0.042656	210
VR9	0.072285	120	0.088602	82	0.190354	27
VR10	-0.083814	250	-0.177565	269	-0.067522	233
VR11	0.197748	37	0.186347	23	0.195614	24
VR12	0.124841	93	0.09949	71	0.150465	54
VR13	0.048069	151	0.019086	150	0.041485	153
VR14	0.021653	176	-0.010365	171	0.05642	137
VR15	0.1115	107	0.125416	53	0.114137	87
VR16	-0.006175	194	-0.12517	248	-0.067522	233
VR17	0.008955	189	-0.096914	217	-0.042656	210
VR18	0.22676	26	0.160027	35	0.152282	49
VR19	0.143859	77	-0.009754	169	0.12957	68
VR20	0.159429	68	0.114408	59	0.150465	54
VR21	0.026359	174	0.019086	150	0.019086	172
VR22	-0.153987	291	-0.177565	269	-0.32457	293
VR23	-0.083814	250	-0.177565	269	-0.067522	233
VR24	0.265511	11	0.205076	14	0.213592	17
VR25	-0.031444	211	-0.177565	269	-0.047129	218
VR26	0.072211	125	0.059437	102	0.074418	124
VR27	0.009875	185	-0.028156	180	-0.001368	180
VR28	0.135979	81	-0.010365	171	0.077449	121
VR29	-0.063665	242	-0.042656	193	-0.096914	247
VR30	-0.022652	207	-0.006175	168	0.112545	88
VR31	0.063698	130	0.019086	150	0.082724	115
VR32	0.094346	114	0.067481	94	0.12056	81
VR33	0.166607	57	-0.042656	193	0.160044	41
VR34	0.011569	182	-0.021662	177	0.002985	178
VR35	0.217985	30	0.178665	27	0.178665	33
VR36	0.021551	178	0.027754	126	-0.006175	185
VR37	0.080903	118	0.048069	110	0.101769	99
VR38	-0.032113	213	-0.103442	220	-0.061492	223
VR39	-0.036637	222	-0.042656	193	0.105188	94
VR40	0.062999	133	0.047593	115	0.060162	136
VR41	0.063698	130	0.019086	150	0.082724	115
VR42	-0.006952	197	-0.103442	220	-0.009754	187
VR43	0.112545	103	0.093842	79	0.093842	103
VR44	0.172306	53	0.07875	90	0.168753	38
VR45	0.172169	54	0.114408	59	0.159429	48
VR46	0.160027	67	0.152282	36	0.152282	49
VR47	0.267577	9	0.268401	4	0.268401	7
VR48	-0.032113	213	-0.103442	220	-0.061492	223
VR49	-0.006952	197	-0.103442	220	-0.009754	187
VR50	0.058036	135	0.055889	107	0.055889	139
VR51	0.032143	163	0.011569	158	0.063698	128
VR52	-0.032113	213	-0.103442	220	-0.061492	223
VR53	-0.122682	280	-0.063665	205	-0.096914	247
VR54	-0.085508	267	-0.103442	220	-0.061492	223
VR55	0.011163	184	-0.028156	180	0.027754	164
VR56	-0.036637	222	-0.142507	250	-0.042656	210
VR57	-0.025581	209	0.008087	162	-0.038036	209
VR58	0.008955	189	-0.096914	217	-0.042656	210
VR59	0.034091	162	-0.036637	192	0.008955	175
VR60	0.128272	89	-0.067522	209	0.112545	88
VR61	-0.122682	280	-0.142507	250	-0.142507	271
VR62	0.062735	134	-0.002665	167	0.053582	141
VR63	0.031105	166	0.022797	128	-0.028913	200
VR64	-0.006952	197	-0.103442	220	-0.009754	187
VR65	0.205076	33	0.205076	14	0.213592	17
VR66	-0.085508	267	-0.103442	220	-0.215221	278
VR67	0.143859	77	0.12957	43	0.12957	68
VR68	0.12096	96	-0.042656	193	0.105188	94
VR69	-0.063665	242	-0.042656	193	-0.096914	247
VR70	0.118293	100	0.009875	160	0.150548	53
VR71	0.163709	63	0.197748	18	0.138376	64
VR72	-0.085508	267	-0.103442	220	-0.215221	278
VR73	0.051631	148	-0.001603	163	0.019105	169
VR74	-0.031444	211	-0.047129	200	-0.047129	218
VR75	0.101769	112	0.041485	118	0.082724	115
VR76	0.103026	110	-0.010365	171	-0.010365	196
VR77	0.143859	77	0.12957	43	0.12957	68
VR78	0.195031	45	0.113047	62	0.102881	98
VR79	0.174001	52	0.160615	31	0.20324	20
VR80	0.13586	83	0.12096	55	0.12096	79
VR81	0.197118	39	0.088602	82	0.190354	27
VR82	0.031652	165	0.009875	160	0.027754	164
VR83	-0.063665	242	-0.142507	250	-0.096914	247
VR84	-0.083814	250	-0.177565	269	-0.067522	233
VR85	0.1192	99	0.062999	100	0.110879	92
VR86	0.147716	74	0.101769	70	0.063698	128
VR87	0.128904	88	0.081012	87	0.118653	83
VR88	0.143859	77	0.12957	43	0.12957	68
VR89	0.072285	120	0.022797	128	0.088602	107
VR90	-0.032113	213	-0.103442	220	-0.061492	223
VR91	-0.083814	250	-0.177565	269	-0.12517	258
VR92	-0.085508	267	-0.103442	220	-0.215221	278
VR93	0.29684	3	0.297454	3	0.297454	4
VR94	0.272932	7	0.265155	6	0.300952	3
VR95	0.055889	137	0.022797	128	0.046937	145
VR96	0.163709	63	0.1275	47	0.138376	64
VR97	0.041802	156	0.021653	146	0.038175	157
VR98	-0.039938	230	-0.032113	189	-0.032113	205
VR99	0.13586	83	0.12096	55	0.12096	79
VR100	0.208843	32	0.197118	19	0.197118	23
VR101	0.036947	161	-0.061492	204	-0.009754	187
VR102	-0.153987	291	-0.177565	269	-0.177565	276
VR103	-0.083814	250	-0.177565	269	-0.12517	258
VR104	0.051631	148	-0.001603	163	0.019105	169
VR105	0.163782	62	0.024337	127	0.083995	114
VR106	0.031105	166	0.022797	128	0.022797	167
VR107	0.071122	126	0.067481	94	0.067481	126
VR108	-0.032113	213	-0.103442	220	-0.061492	223
VR109	0.110329	109	0.046937	116	0.088602	107
VR110	0.166607	57	0.160044	32	0.160044	41
VR111	0.009875	185	-0.028156	180	-0.001368	180
VR112	0.031105	166	0.022797	128	-0.028913	200
VR113	0.055889	137	0.09949	71	0.046937	145
VR114	-0.039938	230	0.048069	110	-0.032113	205
VR115	-0.153987	291	-0.028156	180	-0.177565	276
VR116	0.055889	137	0.09949	71	0.088602	107
VR117	0.166607	57	0.05642	103	0.160044	41
VR118	0.046075	155	0.038975	119	0.026455	166
VR119	0.019105	179	-0.032113	189	0.036947	160
VR120	0.163709	63	0.1275	47	0.1275	72
VR121	0.134347	87	0.019086	150	0.172005	36
VR122	0.014226	181	0.011569	158	0.063698	128
VR123	-0.053512	234	-0.177565	269	-0.067522	233
VR124	0.155001	71	0.031652	124	0.111027	91
VR125	0.273161	6	0.205076	14	0.243935	10
VR126	0.252035	14	0.080538	88	0.094524	102
VR127	0.186347	47	0.122655	54	0.114408	86
VR128	0.038975	159	-0.028156	180	0.039329	156
VR129	-0.083814	250	-0.028156	180	-0.12517	258
VR130	0.22676	26	0.042914	117	0.152282	49
VR131	-0.022652	207	-0.083814	214	-0.006175	185
VR132	0.048069	151	0.019086	150	0.041485	153
VR133	-0.006952	197	-0.103442	220	-0.009754	187
VR134	-0.006952	197	-0.103442	220	-0.009754	187
VR135	0.231929	24	0.139746	40	0.132762	67
VR136	-0.122682	280	-0.142507	250	-0.142507	271
VR137	-0.030907	210	-0.063665	205	-0.036637	208
VR138	-0.122682	280	-0.142507	250	-0.266085	287
VR139	-0.122682	280	-0.142507	250	-0.142507	271
VR140	-0.039938	230	-0.032113	189	-0.032113	205
VR141	0.196857	42	0.185743	24	0.19477	26
VR142	-0.01332	205	-0.021662	177	-0.021662	197
VR143	0.251498	15	0.082724	86	0.181817	31
VR144	0.158107	69	0.143859	38	0.143859	60
VR145	0.09419	115	0.038175	120	0.077449	121
VR146	-0.053512	234	-0.177565	269	-0.067522	233
VR147	-0.083814	250	-0.067522	209	-0.12517	258
VR148	-0.036637	222	-0.142507	250	-0.042656	210
VR149	-0.006952	197	-0.103442	220	-0.009754	187
VR150	-0.122682	280	-0.142507	250	-0.266085	287
VR151	-0.047129	233	-0.083814	214	-0.053512	220
VR152	0.204208	35	0.191244	20	0.19543	25
VR153	0.223499	28	0.225006	11	0.225006	15
VR154	0.135979	81	0.021653	146	0.077449	121
VR155	0.090155	116	0.055889	107	0.110329	93
VR156	0.112545	103	0.093842	79	0.093842	103
VR157	0.112545	103	-0.067522	209	0.093842	103
VR158	0.234962	19	0.232047	10	0.232047	13
VR159	0.009875	185	-0.028156	180	-0.001368	180
VR160	0.011569	182	-0.021662	177	0.002985	178
VR161	0.009875	185	-0.028156	180	-0.001368	180
VR162	0.144676	76	0.182427	25	0.148427	59
VR163	-0.122682	280	-0.142507	250	-0.266085	287
VR164	-0.083814	250	-0.177565	269	-0.12517	258
VR165	0.041802	156	0.021653	146	0.038175	157
VR166	-0.153987	291	-0.177565	269	-0.32457	293
VR167	-0.006952	197	-0.103442	220	-0.009754	187
VR168	0.122206	95	0.112617	66	0.125686	75
VR169	0.021653	176	0.05642	103	0.013643	174
VR170	0.019105	179	0.036947	121	0.036947	160
VR171	0.200002	36	0.133451	42	0.098155	100
VR172	0.128272	89	0.112545	67	0.112545	88
VR173	0.126144	92	0.067139	97	0.117716	84
VR174	0.031105	166	0.022797	128	-0.028913	200
VR175	0.234962	19	0.150465	37	0.232047	13
VR176	0.195614	43	0.09949	71	0.150465	54
VR177	0.124841	93	0.09949	71	0.150465	54
VR178	0.12096	96	0.105188	68	0.105188	94
VR179	0.166607	57	0.160044	32	0.160044	41
VR180	0.055889	137	0.022797	128	0.088602	107
VR181	0.047593	154	0.033499	123	0.049313	143
VR182	0.197748	37	0.113047	62	0.124841	76
VR183	0.120137	98	0.113047	62	0.124841	76
VR184	0.058036	135	0.055889	107	0.055889	139
VR185	0.072285	120	0.022797	128	0.088602	107
VR186	0.055889	137	0.022797	128	0.046937	145
VR187	-0.122682	280	-0.142507	250	-0.266085	287
VR188	-0.085508	267	-0.103442	220	-0.215221	278
VR189	0.242132	18	0.232048	9	0.269528	6
VR190	-0.153987	291	-0.177565	269	-0.32457	293
VR191	-0.032113	213	-0.103442	220	-0.061492	223
VR192	-0.083814	250	-0.177565	269	-0.12517	258
VR193	-0.122682	280	-0.142507	250	-0.142507	271
VR194	0.024535	175	0.021653	146	-0.002328	184
VR195	-0.053512	234	-0.177565	269	-0.067522	233
VR196	0.151472	72	0.09712	78	0.143445	62
VR197	0.232225	22	0.05642	103	0.160044	41
VR198	-0.083814	250	-0.177565	269	-0.12517	258
VR199	-0.032113	213	-0.103442	220	-0.061492	223
VR200	0.113594	102	0.067139	97	0.080903	119
VR201	0.114829	101	0.103486	69	0.117406	85
VR202	0.195614	43	0.09949	71	0.150465	54
VR203	-0.036637	222	-0.042656	193	0.105188	94
VR204	0.031105	166	0.022797	128	0.022797	167
VR205	-0.153987	291	-0.177565	269	-0.32457	293
VR206	0.277131	5	0.242132	8	0.24104	11
VR207	-0.032113	213	-0.103442	220	-0.061492	223
VR208	-0.063665	242	-0.142507	250	-0.096914	247
VR209	-0.153987	291	-0.177565	269	-0.32457	293
VR210	-0.083814	250	-0.177565	269	-0.12517	258
VR211	-0.063665	242	-0.042656	193	-0.096914	247
VR212	0.055889	137	0.022797	128	0.046937	145
VR213	-0.085508	267	-0.103442	220	-0.215221	278
VR214	0.069961	127	-0.001603	163	0.060523	135
VR215	0.246755	16	0.208843	13	0.208843	19
VR216	0.13586	83	0.12096	55	0.008955	175
VR217	0.150189	73	0.128381	46	0.171822	37
VR218	0.102881	111	0.09949	71	0.07847	120
VR219	0.259701	12	0.199483	17	0.197575	22
VR220	-0.085508	267	-0.103442	220	-0.215221	278
VR221	0.322101	2	0.314996	2	0.348174	2
VR222	-0.063665	242	-0.142507	250	-0.096914	247
VR223	0.204458	34	0.191244	20	0.232465	12
VR224	0.161032	66	0.031652	124	0.047112	144
VR225	-0.085508	267	-0.103442	220	-0.215221	278
VR226	0.032143	163	-0.028898	188	0.028443	163
VR227	-0.083814	250	-0.177565	269	-0.12517	258
VR228	0.223499	28	0.21509	12	0.223499	16
VR229	-0.153987	291	-0.177565	269	-0.32457	293
VR230	0.166607	57	0.160044	32	0.160044	41
VR231	0.135221	86	0.075874	92	0.126829	73
VR232	0.296486	4	0.117716	58	0.199421	21
VR233	-0.053512	234	-0.177565	269	-0.067522	233
VR234	0.051631	148	-0.001603	163	0.019105	169
VR235	0.267577	9	0.259985	7	0.267577	8
VR236	-0.085508	267	-0.103442	220	-0.103442	255
VR237	0.184639	48	0.080538	88	0.063601	134
VR238	-0.063665	242	-0.142507	250	-0.096914	247
VR239	0.067139	128	0.048069	110	0.063698	128
VR240	-0.085508	267	-0.103442	220	-0.103442	255
VR241	0.1275	91	0.113047	62	0.124841	76
VR242	0.25841	13	0.169819	30	0.163709	40
VR243	-0.122682	280	-0.142507	250	-0.266085	287
VR244	0.048069	151	0.019086	150	0.041485	153
VR245	0.197118	39	0.190354	22	0.190354	27
VR246	0.233753	21	0.1275	47	0.120137	82
VR247	0.053582	147	-0.053512	203	0.034886	162
VR248	-0.002328	192	-0.010365	171	-0.060375	221
VR249	-0.073273	249	-0.063665	205	-0.122682	257
VR250	-0.085508	267	-0.103442	220	-0.215221	278
VR251	0.169819	55	0.1275	47	0.138376	64
VR252	-0.083814	250	-0.177565	269	-0.067522	233
VR253	-0.053512	234	-0.177565	269	-0.067522	233
VR254	0.067139	128	0.048069	110	0.063698	128
VR255	0.244024	17	0.141148	39	0.150782	52
VR256	0.031105	166	0.022797	128	-0.028913	200
VR257	0.072285	120	0.022797	128	0.088602	107
VR258	-0.016088	206	-0.052802	202	0.0187	173
VR259	-0.083814	250	-0.177565	269	-0.12517	258
VR260	0.197118	39	0.088602	82	0.190354	27
VR261	-0.085508	267	-0.103442	220	-0.215221	278
VR262	0.041802	156	0.077449	91	0.038175	157
VR263	-0.083814	250	-0.067522	209	-0.12517	258
VR264	0.055889	137	0.022797	128	0.046937	145
VR265	0.080034	119	0.072211	93	0.072211	125
VR266	0.147716	74	0.048069	110	0.063698	128
VR267	-0.036637	222	-0.142507	250	-0.042656	210
VR268	0.038175	160	-0.010365	171	0.05642	137
VR269	-0.153987	291	-0.177565	269	-0.32457	293
VR270	0.031105	166	0.022797	128	-0.028913	200
VR271	-0.097486	279	-0.083814	214	-0.153987	275
VR272	0.072285	120	0.088602	82	0.088602	107
VR273	0.026426	173	-0.072514	213	-0.028744	199
VR274	0.268401	8	0.268401	4	0.276048	5
VR275	0.063698	130	0.019086	150	0.082724	115
VR276	0.232225	22	0.05642	103	0.160044	41
VR277	0.158107	69	0.036947	121	0.143859	60
VR278	-0.002328	192	-0.010365	171	-0.060375	221
VR279	-0.083814	250	-0.177565	269	-0.12517	258
VR280	0.100659	113	0.067139	97	0.051502	142
VR281	0.352528	1	0.352906	1	0.352528	1
VR282	0.231929	24	0.139746	40	0.139746	63
VR283	0.179921	49	0.1275	47	0.172169	34
VR284	0.179921	49	0.1275	47	0.172169	34
VR285	-0.153987	291	-0.177565	269	-0.32457	293
VR286	0.167349	56	0.174735	28	0.167349	39
VR287	0.055889	137	0.022797	128	0.046937	145
VR288	0.179921	49	0.172169	29	0.245264	9
VR289	-0.038933	229	-0.047565	201	-0.022158	198
VR290	-0.083814	250	-0.177565	269	-0.12517	258
VR291	-0.122682	280	-0.142507	250	-0.266085	287
VR292	0.187776	46	0.181817	26	0.181817	31
VR293	-0.053512	234	-0.177565	269	-0.067522	233
VR294	-0.036637	222	-0.142507	250	-0.042656	210
VR295	-0.053512	234	-0.177565	269	-0.067522	233
VR296	-0.032113	213	-0.103442	220	-0.061492	223
VR297	0.21509	31	0.113594	61	0.126144	74
VR298	-0.006952	197	-0.009754	169	-0.009754	187
VR299	0.055889	137	0.022797	128	0.046937	145
VR300	0.055889	137	0.022797	128	0.046937	145
q = 10
Alternatives	Expert 1		Expert 2		Expert 3
	Score	final rank	Score	final rank	Score	final rank
VR1	0.00956	189	-0.059204	248	-0.024363	216
VR2	0.050663	113	0.02489	113	0.046543	113
VR3	0.088206	84	0.082568	49	0.082568	71
VR4	0.013559	174	-0.047112	217	-0.014532	207
VR5	0.000597	198	-0.022901	206	0.01409	166
VR6	0.043713	117	0.037974	93	0.037974	124
VR7	-0.016359	234	-0.093189	269	-0.024363	216
VR8	-0.011633	222	-0.075758	250	-0.014532	207
VR9	0.040108	118	0.051437	80	0.127586	24
VR10	-0.029006	249	-0.093189	269	-0.024363	216
VR11	0.113437	44	0.109707	28	0.1126	34
VR12	0.062565	103	0.052421	73	0.080104	75
VR13	0.02389	152	0.009127	154	0.019136	157
VR14	0.013026	180	-0.003436	171	0.032174	131
VR15	0.06947	99	0.073822	55	0.070056	85
VR16	0.00956	189	-0.059204	248	-0.024363	216
VR17	0.013559	174	-0.047112	217	-0.014532	207
VR18	0.154199	21	0.107277	29	0.105514	44
VR19	0.099484	61	-0.000283	169	0.095292	51
VR20	0.083493	90	0.05829	70	0.080104	75
VR21	0.014134	173	0.009127	154	0.009127	178
VR22	-0.071408	291	-0.093189	269	-0.229116	293
VR23	-0.029006	249	-0.093189	269	-0.024363	216
VR24	0.181392	7	0.136471	13	0.139072	17
VR25	0.000873	196	-0.093189	269	-0.013292	205
VR26	0.031572	143	0.027452	108	0.032308	130
VR27	0.010113	182	-0.009763	178	0.002751	180
VR28	0.076949	95	-0.003436	171	0.040884	119
VR29	-0.022612	242	-0.014532	194	-0.047112	247
VR30	-0.0046	207	0.00956	153	0.088206	61
VR31	0.028997	147	0.009127	154	0.043322	114
VR32	0.047415	114	0.037974	93	0.065593	90
VR33	0.108654	53	-0.014532	194	0.10719	37
VR34	0.006032	192	-0.011608	189	-0.00016	185
VR35	0.137601	31	0.112355	27	0.112355	35
VR36	0.019585	169	0.016026	127	0.00956	176
VR37	0.034543	126	0.02389	114	0.051134	110
VR38	-0.009834	213	-0.05749	220	-0.031528	235
VR39	-0.011633	222	-0.014532	194	0.085236	66
VR40	0.025905	150	0.021294	120	0.02489	151
VR41	0.028997	147	0.009127	154	0.043322	114
VR42	0.000287	199	-0.05749	220	-0.000283	187
VR43	0.088206	84	0.082568	49	0.082568	71
VR44	0.110477	50	0.042049	89	0.109968	36
VR45	0.087644	89	0.05829	70	0.083493	70
VR46	0.107277	58	0.105514	34	0.105514	44
VR47	0.172794	11	0.172862	5	0.172862	6
VR48	-0.009834	213	-0.05749	220	-0.031528	235
VR49	0.000287	199	-0.05749	220	-0.000283	187
VR50	0.033584	141	0.03416	96	0.03416	127
VR51	0.01309	178	0.006032	162	0.028997	135
VR52	-0.009834	213	-0.05749	220	-0.031528	235
VR53	-0.057723	280	-0.022612	203	-0.047112	247
VR54	-0.041318	268	-0.05749	220	-0.031528	235
VR55	0.009779	188	-0.009763	178	0.016026	163
VR56	-0.011633	222	-0.075758	250	-0.014532	207
VR57	-0.005057	209	0.01409	128	-0.011322	202
VR58	0.013559	174	-0.047112	217	-0.014532	207
VR59	0.022502	156	-0.011633	192	0.013559	169
VR60	0.092751	75	-0.024363	207	0.088206	61
VR61	-0.057723	280	-0.075758	250	-0.075758	272
VR62	0.035524	125	0.002081	168	0.02902	134
VR63	0.020552	159	0.013566	129	-0.030023	230
VR64	0.000287	199	-0.05749	220	-0.000283	187
VR65	0.136471	32	0.136471	13	0.139072	17
VR66	-0.041318	268	-0.05749	220	-0.158403	278
VR67	0.099484	61	0.095292	36	0.095292	51
VR68	0.089909	78	-0.014532	194	0.085236	66
VR69	-0.022612	242	-0.014532	194	-0.047112	247
VR70	0.0723	98	0.010113	151	0.091972	55
VR71	0.088682	81	0.113437	26	0.066958	87
VR72	-0.041318	268	-0.05749	220	-0.158403	278
VR73	0.034017	138	0.00278	164	0.009962	173
VR74	0.000873	196	-0.013292	193	-0.013292	205
VR75	0.051134	112	0.019136	122	0.043322	114
VR76	0.066697	101	-0.003436	171	-0.003436	196
VR77	0.099484	61	0.095292	36	0.095292	51
VR78	0.112786	47	0.058811	65	0.054586	101
VR79	0.110345	51	0.106948	33	0.129547	21
VR80	0.094271	69	0.089909	41	0.089909	57
VR81	0.129411	37	0.051437	80	0.127586	24
VR82	0.017565	172	0.010113	151	0.016026	163
VR83	-0.022612	242	-0.075758	250	-0.047112	247
VR84	-0.029006	249	-0.093189	269	-0.024363	216
VR85	0.056912	109	0.025905	110	0.050663	112
VR86	0.08347	91	0.051134	84	0.028997	135
VR87	0.06757	100	0.04111	91	0.063525	92
VR88	0.099484	61	0.095292	36	0.095292	51
VR89	0.040108	118	0.013566	129	0.051437	103
VR90	-0.009834	213	-0.05749	220	-0.031528	235
VR91	-0.029006	249	-0.093189	269	-0.059204	258
VR92	-0.041318	268	-0.05749	220	-0.158403	278
VR93	0.21123	3	0.211265	3	0.211265	4
VR94	0.198335	4	0.195927	4	0.21593	3
VR95	0.03416	128	0.013566	129	0.026354	141
VR96	0.088682	81	0.063607	57	0.066958	87
VR97	0.019841	166	0.013026	147	0.018419	160
VR98	-0.015873	231	-0.009834	186	-0.009834	199
VR99	0.094271	69	0.089909	41	0.089909	57
VR100	0.133099	33	0.129411	18	0.129411	22
VR101	0.024908	151	-0.031528	215	-0.000283	187
VR102	-0.071408	291	-0.093189	269	-0.093189	276
VR103	-0.029006	249	-0.093189	269	-0.059204	258
VR104	0.034017	138	0.00278	164	0.009962	173
VR105	0.119139	42	0.022969	119	0.051958	102
VR106	0.020552	159	0.013566	129	0.013566	167
VR107	0.039919	124	0.037974	93	0.037974	124
VR108	-0.009834	213	-0.05749	220	-0.031528	235
VR109	0.06233	106	0.026354	109	0.051437	103
VR110	0.108654	53	0.10719	30	0.10719	37
VR111	0.010113	182	-0.009763	178	0.002751	180
VR112	0.020552	159	0.013566	129	-0.030023	230
VR113	0.03416	128	0.052421	73	0.026354	141
VR114	-0.015873	231	0.02389	114	-0.009834	199
VR115	-0.071408	291	-0.009763	178	-0.093189	276
VR116	0.03416	128	0.052421	73	0.051437	103
VR117	0.108654	53	0.032174	99	0.10719	37
VR118	0.022116	157	0.019503	121	0.01584	165
VR119	0.009962	186	-0.009834	186	0.024908	149
VR120	0.088682	81	0.063607	57	0.063607	91
VR121	0.079235	93	0.009127	154	0.100877	47
VR122	0.006179	191	0.006032	162	0.028997	135
VR123	-0.016359	234	-0.093189	269	-0.024363	216
VR124	0.097431	67	0.017565	124	0.070311	84
VR125	0.183837	6	0.136471	13	0.157974	9
VR126	0.177751	9	0.046647	86	0.050784	111
VR127	0.109707	52	0.061867	63	0.05829	99
VR128	0.019503	170	-0.009763	178	0.019539	156
VR129	-0.029006	249	-0.009763	178	-0.059204	258
VR130	0.154199	21	0.028221	107	0.105514	44
VR131	-0.0046	207	-0.029006	212	0.00956	176
VR132	0.02389	152	0.009127	154	0.019136	157
VR133	0.000287	199	-0.05749	220	-0.000283	187
VR134	0.000287	199	-0.05749	220	-0.000283	187
VR135	0.155903	17	0.074786	53	0.072568	82
VR136	-0.057723	280	-0.075758	250	-0.075758	272
VR137	-0.008944	212	-0.022612	203	-0.011633	204
VR138	-0.057723	280	-0.075758	250	-0.188303	287
VR139	-0.057723	280	-0.075758	250	-0.075758	272
VR140	-0.015873	231	-0.009834	186	-0.009834	199
VR141	0.120326	41	0.116817	24	0.11953	30
VR142	-0.005624	211	-0.011608	189	-0.011608	203
VR143	0.16413	15	0.043322	88	0.116585	31
VR144	0.10372	59	0.099484	35	0.099484	49
VR145	0.046173	116	0.018419	123	0.040884	119
VR146	-0.016359	234	-0.093189	269	-0.024363	216
VR147	-0.029006	249	-0.024363	207	-0.059204	258
VR148	-0.011633	222	-0.075758	250	-0.014532	207
VR149	0.000287	199	-0.05749	220	-0.000283	187
VR150	-0.057723	280	-0.075758	250	-0.188303	287
VR151	-0.013292	230	-0.029006	212	-0.016359	215
VR152	0.131659	35	0.127677	19	0.128478	23
VR153	0.145244	26	0.145379	10	0.145379	15
VR154	0.076949	95	0.013026	147	0.040884	119
VR155	0.046324	115	0.03416	96	0.06233	97
VR156	0.088206	84	0.082568	49	0.082568	71
VR157	0.088206	84	-0.024363	207	0.082568	71
VR158	0.146537	24	0.145955	9	0.145955	13
VR159	0.010113	182	-0.009763	178	0.002751	180
VR160	0.006032	192	-0.011608	189	-0.00016	185
VR161	0.010113	182	-0.009763	178	0.002751	180
VR162	0.099115	65	0.120896	23	0.100842	48
VR163	-0.057723	280	-0.075758	250	-0.188303	287
VR164	-0.029006	249	-0.093189	269	-0.059204	258
VR165	0.019841	166	0.013026	147	0.018419	160
VR166	-0.071408	291	-0.093189	269	-0.229116	293
VR167	0.000287	199	-0.05749	220	-0.000283	187
VR168	0.089649	80	0.087621	46	0.091297	56
VR169	0.013026	180	0.032174	99	0.007424	179
VR170	0.009962	186	0.024908	111	0.024908	149
VR171	0.112837	46	0.060506	64	0.03929	122
VR172	0.092751	75	0.088206	44	0.088206	61
VR173	0.062519	105	0.030352	104	0.056219	100
VR174	0.020552	159	0.013566	129	-0.030023	230
VR175	0.146537	24	0.080104	52	0.145955	13
VR176	0.1126	48	0.052421	73	0.080104	75
VR177	0.062565	103	0.052421	73	0.080104	75
VR178	0.089909	78	0.085236	48	0.085236	66
VR179	0.108654	53	0.10719	30	0.10719	37
VR180	0.03416	128	0.013566	129	0.051437	103
VR181	0.021294	158	0.016702	126	0.021816	155
VR182	0.113437	44	0.058811	65	0.062565	93
VR183	0.061096	107	0.058811	65	0.062565	93
VR184	0.033584	141	0.03416	96	0.03416	127
VR185	0.040108	118	0.013566	129	0.051437	103
VR186	0.03416	128	0.013566	129	0.026354	141
VR187	-0.057723	280	-0.075758	250	-0.188303	287
VR188	-0.041318	268	-0.05749	220	-0.158403	278
VR189	0.148651	23	0.14531	11	0.166602	8
VR190	-0.071408	291	-0.093189	269	-0.229116	293
VR191	-0.009834	213	-0.05749	220	-0.031528	235
VR192	-0.029006	249	-0.093189	269	-0.059204	258
VR193	-0.057723	280	-0.075758	250	-0.075758	272
VR194	0.013391	177	0.013026	147	0.002148	184
VR195	-0.016359	234	-0.093189	269	-0.024363	216
VR196	0.078898	94	0.048448	85	0.072784	81
VR197	0.15541	19	0.032174	99	0.10719	37
VR198	-0.029006	249	-0.093189	269	-0.059204	258
VR199	-0.009834	213	-0.05749	220	-0.031528	235
VR200	0.058753	108	0.030352	104	0.034543	126
VR201	0.088193	88	0.085749	47	0.08963	59
VR202	0.1126	48	0.052421	73	0.080104	75
VR203	-0.011633	222	-0.014532	194	0.085236	66
VR204	0.020552	159	0.013566	129	0.013566	167
VR205	-0.071408	291	-0.093189	269	-0.229116	293
VR206	0.172705	13	0.148651	8	0.148538	12
VR207	-0.009834	213	-0.05749	220	-0.031528	235
VR208	-0.022612	242	-0.075758	250	-0.047112	247
VR209	-0.071408	291	-0.093189	269	-0.229116	293
VR210	-0.029006	249	-0.093189	269	-0.059204	258
VR211	-0.022612	242	-0.014532	194	-0.047112	247
VR212	0.03416	128	0.013566	129	0.026354	141
VR213	-0.041318	268	-0.05749	220	-0.158403	278
VR214	0.040006	123	0.00278	164	0.033276	129
VR215	0.157779	16	0.133099	17	0.133099	20
VR216	0.094271	69	0.089909	41	0.013559	169
VR217	0.097417	68	0.090971	39	0.113746	33
VR218	0.054586	110	0.052421	73	0.038921	123
VR219	0.180188	8	0.13525	16	0.135075	19
VR220	-0.041318	268	-0.05749	220	-0.158403	278
VR221	0.221723	2	0.219395	2	0.238801	2
VR222	-0.022612	242	-0.075758	250	-0.047112	247
VR223	0.13119	36	0.127677	19	0.149862	11
VR224	0.098906	66	0.017565	124	0.022246	154
VR225	-0.041318	268	-0.05749	220	-0.158403	278
VR226	0.01309	178	-0.008393	177	0.011622	172
VR227	-0.029006	249	-0.093189	269	-0.059204	258
VR228	0.145244	26	0.142645	12	0.145244	16
VR229	-0.071408	291	-0.093189	269	-0.229116	293
VR230	0.108654	53	0.10719	30	0.10719	37
VR231	0.074209	97	0.041651	90	0.067936	86
VR232	0.19103	5	0.056219	72	0.121539	29
VR233	-0.016359	234	-0.093189	269	-0.024363	216
VR234	0.034017	138	0.00278	164	0.009962	173
VR235	0.172794	11	0.170326	7	0.172794	7
VR236	-0.041318	268	-0.05749	220	-0.05749	255
VR237	0.131837	34	0.046647	86	0.04089	118
VR238	-0.022612	242	-0.075758	250	-0.047112	247
VR239	0.030352	144	0.02389	114	0.028997	135
VR240	-0.041318	268	-0.05749	220	-0.05749	255
VR241	0.063607	102	0.058811	65	0.062565	93
VR242	0.170128	14	0.090542	40	0.088682	60
VR243	-0.057723	280	-0.075758	250	-0.188303	287
VR244	0.02389	152	0.009127	154	0.019136	157
VR245	0.129411	37	0.127586	21	0.127586	24
VR246	0.138177	30	0.063607	57	0.061096	98
VR247	0.02902	146	-0.016359	201	0.02353	153
VR248	0.002148	194	-0.003436	171	-0.038267	245
VR249	-0.029745	266	-0.022612	203	-0.057723	257
VR250	-0.041318	268	-0.05749	220	-0.158403	278
VR251	0.090542	77	0.063607	57	0.066958	87
VR252	-0.029006	249	-0.093189	269	-0.024363	216
VR253	-0.016359	234	-0.093189	269	-0.024363	216
VR254	0.030352	144	0.02389	114	0.028997	135
VR255	0.141285	29	0.067597	56	0.070531	83
VR256	0.020552	159	0.013566	129	-0.030023	230
VR257	0.040108	118	0.013566	129	0.051437	103
VR258	-0.005155	210	-0.024825	211	0.013399	171
VR259	-0.029006	249	-0.093189	269	-0.059204	258
VR260	0.129411	37	0.051437	80	0.127586	24
VR261	-0.041318	268	-0.05749	220	-0.158403	278
VR262	0.019841	166	0.040884	92	0.018419	160
VR263	-0.029006	249	-0.024363	207	-0.059204	258
VR264	0.03416	128	0.013566	129	0.026354	141
VR265	0.034434	127	0.031572	103	0.031572	133
VR266	0.08347	91	0.02389	114	0.028997	135
VR267	-0.011633	222	-0.075758	250	-0.014532	207
VR268	0.018419	171	-0.003436	171	0.032174	131
VR269	-0.071408	291	-0.093189	269	-0.229116	293
VR270	0.020552	159	0.013566	129	-0.030023	230
VR271	-0.03841	267	-0.029006	212	-0.071408	271
VR272	0.040108	118	0.051437	80	0.051437	103
VR273	0.02279	155	-0.032144	216	-0.009462	198
VR274	0.172862	10	0.172862	5	0.175337	5
VR275	0.028997	147	0.009127	154	0.043322	114
VR276	0.15541	19	0.032174	99	0.10719	37
VR277	0.10372	59	0.024908	111	0.099484	49
VR278	0.002148	194	-0.003436	171	-0.038267	245
VR279	-0.029006	249	-0.093189	269	-0.059204	258
VR280	0.054474	111	0.030352	104	0.024567	152
VR281	0.244441	1	0.244465	1	0.244441	1
VR282	0.155903	17	0.074786	53	0.074786	80
VR283	0.093666	72	0.063607	57	0.087644	64
VR284	0.093666	72	0.063607	57	0.087644	64
VR285	-0.071408	291	-0.093189	269	-0.229116	293
VR286	0.124014	40	0.125373	22	0.124014	28
VR287	0.03416	128	0.013566	129	0.026354	141
VR288	0.093666	72	0.087644	45	0.149931	10
VR289	-0.012047	229	-0.017059	202	-0.006966	197
VR290	-0.029006	249	-0.093189	269	-0.059204	258
VR291	-0.057723	280	-0.075758	250	-0.188303	287
VR292	0.1179	43	0.116585	25	0.116585	31
VR293	-0.016359	234	-0.093189	269	-0.024363	216
VR294	-0.011633	222	-0.075758	250	-0.014532	207
VR295	-0.016359	234	-0.093189	269	-0.024363	216
VR296	-0.009834	213	-0.05749	220	-0.031528	235
VR297	0.142645	28	0.058753	69	0.062519	96
VR298	0.000287	199	-0.000283	169	-0.000283	187
VR299	0.03416	128	0.013566	129	0.026354	141
VR300	0.03416	128	0.013566	129	0.026354	141

Table A2.

Group results of q-ROFDOSM.

Alternatives	q = 1		q = 3		q = 5		q = 7		q = 10
	Score	Final rank	Score	Final rank	Score	Final rank	Score	Final rank	Score	Final rank
VR1	-0.2879969	234	-0.2298837	234	-0.1262594	228	-0.0662891	226	-0.02466931	217
VR2	0.1861822	53	0.2183817	68	0.1475219	86	0.0894377	101	0.04069889	114
VR3	-0.0807016	166	0.0355225	141	0.0920117	118	0.100076	91	0.0844476	63
VR4	-0.2056802	210	-0.1557731	210	-0.0836673	210	-0.0435386	212	-0.01602858	206
VR5	-0.2013731	209	-0.1306485	198	-0.0583542	198	-0.0217009	196	-0.00273792	194
VR6	0.0247994	116	0.1111214	108	0.0991704	114	0.0723318	116	0.03988728	115
VR7	-0.3478996	258	-0.2922598	258	-0.1726611	249	-0.0995332	245	-0.04463694	243
VR8	-0.2605366	228	-0.214181	228	-0.1267636	230	-0.0739335	231	-0.03397462	232
VR9	0.0669532	95	0.1643745	84	0.1518465	82	0.1170806	80	0.07304372	80
VR10	-0.379279	270	-0.3206686	266	-0.1901438	257	-0.1096338	257	-0.04885261	256
VR11	0.3095055	19	0.3632172	22	0.2745458	22	0.1932362	25	0.1119145	31
VR12	0.1592543	65	0.2351317	60	0.1836005	67	0.1249318	74	0.06502967	87
VR13	-0.0142952	131	0.0441067	136	0.0501061	139	0.0362134	149	0.01738409	155
VR14	-0.0540078	147	0.0003042	158	0.023225	160	0.0225692	167	0.01392129	169
VR15	0.1277663	73	0.1903929	76	0.159286	76	0.1170176	81	0.07111569	82
VR16	-0.2879969	234	-0.2298837	234	-0.1262594	228	-0.0662891	226	-0.02466931	217
VR17	-0.2056802	210	-0.1557731	210	-0.0836673	210	-0.0435386	212	-0.01602858	206
VR18	0.1801295	54	0.2634994	51	0.2287674	39	0.1796898	30	0.12233021	25
VR19	-0.0097874	128	0.0805052	125	0.0986898	115	0.0878914	103	0.064831	89
VR20	0.1935764	51	0.2707227	47	0.2084137	51	0.1414337	61	0.07396224	76
VR21	-0.0613609	153	0.0013317	157	0.0244658	159	0.02151	168	0.01079629	172
VR22	-0.5104426	293	-0.4683455	293	-0.3195247	293	-0.2187072	293	-0.1312375	293
VR23	-0.379279	270	-0.3206686	266	-0.1901438	257	-0.1096338	257	-0.04885261	256
VR24	0.3776349	10	0.4033188	12	0.3072183	12	0.2280596	12	0.15231181	11
VR25	-0.3285027	246	-0.2825857	246	-0.1576862	241	-0.0853794	238	-0.03520271	237
VR26	0.0938197	86	0.1506887	90	0.1101942	104	0.0686886	119	0.03044413	131
VR27	-0.1466017	186	-0.0872613	191	-0.0285181	188	-0.0065496	186	0.0010339	184
VR28	0.0626389	99	0.1101696	110	0.0946709	117	0.0676875	120	0.0381323	117
VR29	-0.2582641	225	-0.2105812	224	-0.1213712	225	-0.0677453	228	-0.02808577	219
VR30	-0.1271966	180	-0.0626527	182	0.0042316	171	0.0279059	159	0.03105537	130
VR31	0.024852	113	0.0864484	120	0.0793915	125	0.0551694	133	0.02714879	134
VR32	0.0849529	89	0.1677712	83	0.1351936	89	0.094129	97	0.05032737	101
VR33	0.0503824	106	0.1209599	101	0.1158347	102	0.0946649	96	0.06710367	84
VR34	-0.0765703	164	-0.0318228	170	-0.0075344	180	-0.0023691	184	-0.00191194	191
VR35	0.2891864	24	0.3433579	24	0.2653159	27	0.1917715	28	0.12077062	26
VR36	-0.1083775	172	-0.0580868	180	-0.0032653	177	0.0143767	171	0.01505685	167
VR37	0.1016574	83	0.1484004	91	0.1173866	99	0.0769138	112	0.03652234	120
VR38	-0.2381774	214	-0.1869896	214	-0.1095815	216	-0.0656824	217	-0.03295054	223
VR39	-0.1462024	184	-0.0781582	187	-0.0175812	183	0.0086315	174	0.0196903	151
VR40	0.1171402	78	0.1432547	95	0.096491	116	0.0569181	129	0.02402952	146
VR41	0.024852	113	0.0864484	120	0.0793915	125	0.0551694	133	0.02714879	134
VR42	-0.1882942	198	-0.1338241	199	-0.0714821	200	-0.0400495	204	-0.0191617	209
VR43	-0.0807016	166	0.0355225	141	0.0920117	118	0.100076	91	0.0844476	63
VR44	0.1652573	61	0.2376996	59	0.1905496	64	0.1399364	64	0.08749786	61
VR45	0.2335792	34	0.2984121	38	0.2230174	41	0.1486684	52	0.0764755	73
VR46	0.115932	79	0.2095353	70	0.1933667	63	0.1548639	47	0.10610197	38
VR47	0.4405608	4	0.4768894	5	0.3639994	5	0.2681267	6	0.17283946	6
VR48	-0.2381774	214	-0.1869896	214	-0.1095815	216	-0.0656824	217	-0.03295054	223
VR49	-0.1882942	198	-0.1338241	199	-0.0714821	200	-0.0400495	204	-0.0191617	209
VR50	-0.0306289	140	0.0492368	131	0.0680755	132	0.0566049	130	0.0339679	126
VR51	0.0271573	112	0.0608647	130	0.0542948	136	0.0358036	152	0.01603962	160
VR52	-0.2381774	214	-0.1869896	214	-0.1095815	216	-0.0656824	217	-0.03295054	223
VR53	-0.3094664	240	-0.2680909	241	-0.1615178	242	-0.0944206	242	-0.04248275	241
VR54	-0.2677166	233	-0.2182454	233	-0.1338982	236	-0.0834807	237	-0.04344517	242
VR55	-0.1132338	174	-0.0613461	181	-0.0113574	182	0.0035872	182	0.00534742	178
VR56	-0.2605366	228	-0.214181	228	-0.1267636	230	-0.0739335	231	-0.03397462	232
VR57	-0.1991949	207	-0.1277636	197	-0.0548218	197	-0.0185101	194	-0.00076298	190
VR58	-0.2056802	210	-0.1557731	210	-0.0836673	210	-0.0435386	212	-0.01602858	206
VR59	-0.1106886	173	-0.0681929	183	-0.0176059	185	0.0021362	183	0.00814256	176
VR60	-0.0861884	169	-0.0045604	159	0.0461466	152	0.0577649	128	0.05219797	100
VR61	-0.3771719	266	-0.3343531	271	-0.2150157	272	-0.1358989	282	-0.06974667	273
VR62	-0.0234308	135	0.0225604	153	0.0428211	154	0.037884	147	0.02220829	147
VR63	-0.1466854	190	-0.0459123	172	0.0009616	172	0.0083296	176	0.00136486	179
VR64	-0.1882942	198	-0.1338241	199	-0.0714821	200	-0.0400495	204	-0.0191617	209
VR65	0.3457063	14	0.3727912	17	0.2830491	19	0.2079147	18	0.13733836	17
VR66	-0.328521	247	-0.2862959	247	-0.1931369	261	-0.1347237	273	-0.08573704	277
VR67	0.0448562	107	0.151357	86	0.1580434	78	0.1343327	67	0.09668906	47
VR68	-0.0694526	162	0.0147157	155	0.054218	137	0.061164	125	0.05353772	99
VR69	-0.2582641	225	-0.2105812	224	-0.1213712	225	-0.0677453	228	-0.02808577	219
VR70	0.0594526	101	0.1200148	102	0.1180089	97	0.0929053	99	0.05812843	96
VR71	0.2703296	29	0.3246309	31	0.2447984	31	0.1666109	37	0.08969236	56
VR72	-0.328521	247	-0.2862959	247	-0.1931369	261	-0.1347237	273	-0.08573704	277
VR73	-0.0563894	149	-0.0158369	164	0.0186987	165	0.0230447	164	0.01558651	164
VR74	-0.253127	224	-0.2122483	227	-0.1003893	215	-0.0419008	211	-0.0085704	198
VR75	0.0643743	98	0.1297094	98	0.1099081	105	0.0753262	113	0.03786374	118
VR76	-0.0711672	163	-0.0056604	160	0.024971	158	0.0274317	160	0.01994193	148
VR77	0.0448562	107	0.151357	86	0.1580434	78	0.1343327	67	0.09668906	47
VR78	0.1756524	56	0.245901	57	0.1957804	61	0.1369865	66	0.07539432	75
VR79	0.2253908	39	0.3162352	33	0.2440498	32	0.1792855	31	0.11561329	30
VR80	0.0681459	92	0.1482657	92	0.1494853	83	0.1259269	72	0.09136294	53
VR81	0.1290753	71	0.2326073	65	0.2051695	54	0.1586914	44	0.10281123	39
VR82	-0.0557352	148	-0.0122723	163	0.0203616	164	0.0230937	163	0.01456795	168
VR83	-0.3149314	241	-0.2710774	242	-0.1671839	245	-0.1010289	253	-0.04849439	252
VR84	-0.379279	270	-0.3206686	266	-0.1901438	257	-0.1096338	257	-0.04885261	256
VR85	0.2113865	44	0.2378351	58	0.1610836	74	0.0976928	95	0.04449319	111
VR86	0.146903	68	0.1983288	74	0.1545932	81	0.1043944	89	0.05453393	98
VR87	0.1456796	69	0.212038	69	0.1623577	73	0.1095229	87	0.05740182	97
VR88	0.0448562	107	0.151357	86	0.1580434	78	0.1343327	67	0.09668906	47
VR89	-0.0253101	136	0.0663172	127	0.077499	128	0.0612279	122	0.03503686	123
VR90	-0.2381774	214	-0.1869896	214	-0.1095815	216	-0.0656824	217	-0.03295054	223
VR91	-0.4073165	276	-0.3529597	276	-0.2159625	276	-0.1288497	263	-0.06046627	263
VR92	-0.328521	247	-0.2862959	247	-0.1931369	261	-0.1347237	273	-0.08573704	277
VR93	0.4233344	5	0.4809144	4	0.3811576	3	0.2972496	3	0.21125332	3
VR94	0.3570667	11	0.4292712	9	0.3513243	8	0.2796798	4	0.20339749	4
VR95	-0.0686621	155	0.0231444	146	0.0479946	143	0.0418742	140	0.02469324	139
VR96	0.233045	35	0.2868943	40	0.2153947	43	0.143195	59	0.07308227	79
VR97	0.0110561	122	0.0445113	134	0.0469313	150	0.0338767	153	0.01709534	158
VR98	-0.1940662	205	-0.1482508	208	-0.0727083	207	-0.0347216	200	-0.01184713	200
VR99	0.0681459	92	0.1482657	92	0.1494853	83	0.1259269	72	0.09136294	53
VR100	0.2411547	32	0.3247047	30	0.2662041	26	0.2010262	21	0.13064019	19
VR101	-0.1379673	182	-0.079231	190	-0.0309244	192	-0.011433	192	-0.00230075	193
VR102	-0.4743332	292	-0.4218022	292	-0.2701798	292	-0.1697055	286	-0.08592856	286
VR103	-0.4073165	276	-0.3529597	276	-0.2159625	276	-0.1288497	263	-0.06046627	263
VR104	-0.0563894	149	-0.0158369	164	0.0186987	165	0.0230447	164	0.01558651	164
VR105	0.0310923	111	0.0796892	126	0.1016602	112	0.0907045	100	0.06468865	90
VR106	-0.1189583	175	-0.0195184	168	0.021731	162	0.0255659	161	0.01589445	161
VR107	0.0020294	126	0.095505	115	0.0916072	121	0.0686947	118	0.03862249	116
VR108	-0.2381774	214	-0.1869896	214	-0.1095815	216	-0.0656824	217	-0.03295054	223
VR109	0.0184227	119	0.110382	109	0.1082776	107	0.0819558	108	0.04670697	107
VR110	0.1703459	58	0.2526418	53	0.2125304	48	0.1622316	38	0.10767775	34
VR111	-0.1466017	186	-0.0872613	191	-0.0285181	188	-0.0065496	186	0.0010339	184
VR112	-0.1466854	190	-0.0459123	172	0.0009616	172	0.0083296	176	0.00136486	179
VR113	-0.0005581	127	0.086093	123	0.0889007	124	0.0674388	121	0.03764495	119
VR114	-0.1214242	178	-0.0763008	184	-0.026732	186	-0.0079941	190	-0.00060585	189
VR115	-0.382727	274	-0.3264067	270	-0.1988528	270	-0.1199025	262	-0.05811975	262
VR116	0.0197743	118	0.1096987	111	0.10769	108	0.0813274	109	0.04600574	109
VR117	0.1227774	76	0.1966634	75	0.1682387	72	0.1276901	71	0.08267247	66
VR118	-0.0108064	129	0.0404453	140	0.0485563	142	0.0371681	148	0.01915302	153
VR119	-0.0944292	170	-0.0463154	178	-0.0042293	179	0.0079798	181	0.00834537	175
VR120	0.2165977	41	0.2724562	46	0.2077719	52	0.1395698	65	0.07196503	81
VR121	0.0957226	85	0.1721725	81	0.1484388	85	0.1084792	88	0.06307951	91
VR122	0.0031736	125	0.0405735	139	0.0430477	153	0.0298313	157	0.0137359	170
VR123	-0.3478996	258	-0.2922598	258	-0.1726611	249	-0.0995332	245	-0.04463694	243
VR124	0.0517571	105	0.118816	103	0.1246332	95	0.0992266	94	0.06176911	92
VR125	0.4006543	8	0.4286395	10	0.3255338	10	0.2407239	10	0.15942749	8
VR126	0.1566111	67	0.204271	73	0.1833076	69	0.1423659	60	0.09172727	52
VR127	0.1981892	47	0.2694267	49	0.2056092	53	0.1411365	62	0.07662147	72
VR128	-0.0662573	154	-0.0088363	162	0.0153989	168	0.0167159	169	0.00975992	173
VR129	-0.3157103	245	-0.2575642	239	-0.1446355	237	-0.0790467	236	-0.03265746	222
VR130	0.1051172	82	0.1884248	78	0.1747773	71	0.1406521	63	0.0959783	50
VR131	-0.241074	223	-0.1907035	223	-0.0898535	214	-0.0375471	203	-0.00801525	197
VR132	-0.0142952	131	0.0441067	136	0.0501061	139	0.0362134	149	0.01738409	155
VR133	-0.1882942	198	-0.1338241	199	-0.0714821	200	-0.0400495	204	-0.0191617	209
VR134	-0.1882942	198	-0.1338241	199	-0.0714821	200	-0.0400495	204	-0.0191617	209
VR135	0.2329082	36	0.2888403	39	0.2320211	37	0.1681456	36	0.10108581	42
VR136	-0.3771719	266	-0.3343531	271	-0.2150157	272	-0.1358989	282	-0.06974667	273
VR137	-0.210547	213	-0.173821	213	-0.0898234	213	-0.0437367	215	-0.01439655	205
VR138	-0.4111057	286	-0.3766457	286	-0.2577335	286	-0.1770915	287	-0.10726158	287
VR139	-0.3771719	266	-0.3343531	271	-0.2150157	272	-0.1358989	282	-0.06974667	273
VR140	-0.1940662	205	-0.1482508	208	-0.0727083	207	-0.0347216	200	-0.01184713	200
VR141	0.2976141	20	0.3683538	19	0.2719254	25	0.1924566	27	0.11889087	27
VR142	-0.1269254	179	-0.0776959	186	-0.0355907	193	-0.0188811	195	-0.00961308	199
VR143	0.2047183	46	0.2851469	42	0.2323142	36	0.1720132	33	0.10801204	33
VR144	0.120172	77	0.2058502	72	0.1876861	65	0.1486082	53	0.10089606	43
VR145	0.0893154	88	0.1293013	99	0.1040762	111	0.0699379	117	0.03515884	122
VR146	-0.3478996	258	-0.2922598	258	-0.1726611	249	-0.0995332	245	-0.04463694	243
VR147	-0.3454372	256	-0.2882917	256	-0.1664228	243	-0.0921689	240	-0.03752439	239
VR148	-0.2605366	228	-0.214181	228	-0.1267636	230	-0.0739335	231	-0.03397462	232
VR149	-0.1882942	198	-0.1338241	199	-0.0714821	200	-0.0400495	204	-0.0191617	209
VR150	-0.4111057	286	-0.3766457	286	-0.2577335	286	-0.1770915	287	-0.10726158	287
VR151	-0.2954114	236	-0.2468403	238	-0.1278657	235	-0.0614852	216	-0.01955206	216
VR152	0.2057277	45	0.3173922	32	0.2589223	28	0.1969608	24	0.12927144	20
VR153	0.3507173	12	0.3960987	13	0.3061319	13	0.2245037	13	0.14533362	14
VR154	0.0928716	87	0.134727	97	0.1112022	103	0.0783604	111	0.04361933	112
VR155	0.0557192	102	0.1278728	100	0.1164828	101	0.0854578	106	0.04760465	106
VR156	-0.0807016	166	0.0355225	141	0.0920117	118	0.100076	91	0.0844476	63
VR157	-0.1421119	183	-0.0462136	177	0.0227464	161	0.046288	137	0.04880374	103
VR158	0.3229666	16	0.4054703	11	0.3177518	11	0.2330187	11	0.1461488	13
VR159	-0.1466017	186	-0.0872613	191	-0.0285181	188	-0.0065496	186	0.0010339	184
VR160	-0.0765703	164	-0.0318228	170	-0.0075344	180	-0.0023691	184	-0.00191194	191
VR161	-0.1466017	186	-0.0872613	191	-0.0285181	188	-0.0065496	186	0.0010339	184
VR162	0.110109	80	0.2323717	67	0.2020184	56	0.1585098	46	0.10695105	37
VR163	-0.4111057	286	-0.3766457	286	-0.2577335	286	-0.1770915	287	-0.10726158	287
VR164	-0.4073165	276	-0.3529597	276	-0.2159625	276	-0.1288497	263	-0.06046627	263
VR165	0.0110561	122	0.0445113	134	0.0469313	150	0.0338767	153	0.01709534	158
VR166	-0.5104426	293	-0.4683455	293	-0.3195247	293	-0.2187072	293	-0.1312375	293
VR167	-0.1882942	198	-0.1338241	199	-0.0714821	200	-0.0400495	204	-0.0191617	209
VR168	0.0167621	120	0.13729	96	0.138736	88	0.1201695	77	0.08952236	57
VR169	-0.0295136	139	0.0233399	145	0.0371873	155	0.0305721	156	0.01754104	154
VR170	-0.0462085	144	0.0048834	156	0.0313719	157	0.0309999	155	0.01992616	150
VR171	0.2900877	22	0.3283303	29	0.2276724	40	0.1438692	58	0.07087789	83
VR172	0.0048013	124	0.0985727	114	0.1277301	93	0.1177873	79	0.08972116	55
VR173	0.1641334	62	0.2089482	71	0.1595619	75	0.1036663	90	0.04969693	102
VR174	-0.1466854	190	-0.0459123	172	0.0009616	172	0.0083296	176	0.00136486	179
VR175	0.2840436	25	0.3655561	21	0.2855491	18	0.2058245	19	0.12419847	23
VR176	0.1969388	48	0.2730942	44	0.2132723	46	0.148523	54	0.08170802	67
VR177	0.1592543	65	0.2351317	60	0.1836005	67	0.1249318	74	0.06502967	87
VR178	-0.0117858	130	0.0902424	116	0.1175877	98	0.1104453	85	0.08679403	62
VR179	0.1703459	58	0.2526418	53	0.2125304	48	0.1622316	38	0.10767775	34
VR180	-0.0483298	145	0.0467501	133	0.066784	135	0.0557627	132	0.03305403	128
VR181	0.0413663	110	0.0891898	117	0.0680552	134	0.0434685	138	0.01993715	149
VR182	0.2316395	37	0.2843318	43	0.2134966	44	0.1452118	57	0.07827078	71
VR183	0.1747426	57	0.2337294	62	0.1785537	70	0.1193414	78	0.0608239	95
VR184	-0.0306289	140	0.0492368	131	0.0680755	132	0.0566049	130	0.0339679	126
VR185	-0.0253101	136	0.0663172	127	0.077499	128	0.0612279	122	0.03503686	123
VR186	-0.0686621	155	0.0231444	146	0.0479946	143	0.0418742	140	0.02469324	139
VR187	-0.4111057	286	-0.3766457	286	-0.2577335	286	-0.1770915	287	-0.10726158	287
VR188	-0.328521	247	-0.2862959	247	-0.1931369	261	-0.1347237	273	-0.08573704	277
VR189	0.4052603	6	0.4663732	7	0.345414	9	0.2479027	9	0.15352137	10
VR190	-0.5104426	293	-0.4683455	293	-0.3195247	293	-0.2187072	293	-0.1312375	293
VR191	-0.2381774	214	-0.1869896	214	-0.1095815	216	-0.0656824	217	-0.03295054	223
VR192	-0.4073165	276	-0.3529597	276	-0.2159625	276	-0.1288497	263	-0.06046627	263
VR193	-0.3771719	266	-0.3343531	271	-0.2150157	272	-0.1358989	282	-0.06974667	273
VR194	-0.0612813	152	-0.0188205	167	0.0110396	169	0.0146201	170	0.00952151	174
VR195	-0.3478996	258	-0.2922598	258	-0.1726611	249	-0.0995332	245	-0.04463694	243
VR196	0.217943	40	0.2705482	48	0.1982053	58	0.1306788	70	0.06670969	85
VR197	0.1601359	63	0.2333674	63	0.1960184	59	0.1495629	50	0.09825803	45
VR198	-0.4073165	276	-0.3529597	276	-0.2159625	276	-0.1288497	263	-0.06046627	263
VR199	-0.2381774	214	-0.1869896	214	-0.1095815	216	-0.0656824	217	-0.03295054	223
VR200	0.131677	70	0.1721987	80	0.1341097	90	0.0872122	104	0.0412162	113
VR201	-0.0506052	146	0.0870749	119	0.1166227	100	0.1119071	84	0.08785746	59
VR202	0.1969388	48	0.2730942	44	0.2132723	46	0.148523	54	0.08170802	67
VR203	-0.1462024	184	-0.0781582	187	-0.0175812	183	0.0086315	174	0.0196903	151
VR204	-0.1189583	175	-0.0195184	168	0.021731	162	0.0255659	161	0.01589445	161
VR205	-0.5104426	293	-0.4683455	293	-0.3195247	293	-0.2187072	293	-0.1312375	293
VR206	0.3954212	9	0.4673405	6	0.35182	7	0.2534343	8	0.15663151	9
VR207	-0.2381774	214	-0.1869896	214	-0.1095815	216	-0.0656824	217	-0.03295054	223
VR208	-0.3149314	241	-0.2710774	242	-0.1671839	245	-0.1010289	253	-0.04849439	252
VR209	-0.5104426	293	-0.4683455	293	-0.3195247	293	-0.2187072	293	-0.1312375	293
VR210	-0.4073165	276	-0.3529597	276	-0.2159625	276	-0.1288497	263	-0.06046627	263
VR211	-0.2582641	225	-0.2105812	224	-0.1213712	225	-0.0677453	228	-0.02808577	219
VR212	-0.0686621	155	0.0231444	146	0.0479946	143	0.0418742	140	0.02469324	139
VR213	-0.328521	247	-0.2862959	247	-0.1931369	261	-0.1347237	273	-0.08573704	277
VR214	-0.0151882	134	0.0298711	144	0.0501457	138	0.0429604	139	0.02535404	138
VR215	0.2954219	21	0.3711464	18	0.2977938	14	0.2214806	14	0.14132555	16
VR216	0.0151738	121	0.0836982	124	0.0993819	113	0.0885918	102	0.06591292	86
VR217	0.1933379	52	0.2601921	52	0.2009126	57	0.1501309	49	0.10071106	44
VR218	0.0616297	100	0.1507676	89	0.132389	91	0.0936137	98	0.04864283	104
VR219	0.2893776	23	0.3420734	25	0.2828279	20	0.2189195	16	0.1501708	12
VR220	-0.328521	247	-0.2862959	247	-0.1931369	261	-0.1347237		-0.08573704	277
VR221	0.4961161	2	0.5512576	2	0.4291956	2	0.3284237	2	0.22663972	2
VR222	-0.3149314	241	-0.2710774	242	-0.1671839	245	-0.1010289	253	-0.04849439	252
VR223	0.2312318	38	0.3452173	23	0.2774794	21	0.209389	17	0.13624296	18
VR224	0.0676133	94	0.111301	107	0.1062291	109	0.0799321	110	0.04623898	108
VR225	-0.328521	247	-0.2862959	247	-0.1931369	261	-0.1347237	273	-0.08573704	277
VR226	-0.0386765	143	-0.0080683	161	0.0105703	170	0.0105627	173	0.00543976	177
VR227	-0.4073165	276	-0.3529597	276	-0.2159625	276	-0.1288497	263	-0.06046627	263
VR228	0.3097341	18	0.3679051	20	0.2957312	15	0.220696	15	0.14437743	15
VR229	-0.5104426	293	-0.4683455	293	-0.3195247	293	-0.2187072	293	-0.1312375	293
VR230	0.1703459	58	0.2526418	53	0.2125304	48	0.1622316	38	0.10767775	34
VR231	0.1245348	75	0.1895822	77	0.158954	77	0.1126414	83	0.06126535	94
VR232	0.3181049	17	0.3755051	16	0.2878437	17	0.2045408	20	0.1229294	24
VR233	-0.3478996	258	-0.2922598	258	-0.1726611	249	-0.0995332	245	-0.04463694	243
VR234	-0.0563894	149	-0.0158369	164	0.0186987	165	0.0230447	164	0.01558651	164
VR235	0.4052289	7	0.4555222	8	0.3561761	6	0.2650467	7	0.17197117	7
VR236	-0.2963358	237	-0.246436	236	-0.1538522	239	-0.097464	243	-0.05209909	260
VR237	0.054694	103	0.114049	105	0.1303758	92	0.1095927	86	0.07312497	78
VR238	-0.3149314	241	-0.2710774	242	-0.1671839	245	-0.1010289	253	-0.04849439	252
VR239	0.0657862	96	0.1088623	112	0.0903379	122	0.0596355	126	0.02774644	132
VR240	-0.2963358	237	-0.246436	236	-0.1538522	239	-0.097464	243	-0.05209909	260
VR241	0.1943549	50	0.2465952	56	0.1840929	66	0.121796	76	0.06166069	93
VR242	0.2751449	28	0.3420028	26	0.2737251	23	0.1973128	23	0.11645062	29
VR243	-0.4111057	286	-0.3766457	286	-0.2577335	286	-0.1770915	287	-0.10726158	287
VR244	-0.0142952	131	0.0441067	136	0.0501061	139	0.0362134	149	0.01738409	155
VR245	0.1761613	55	0.2852717	41	0.2474179	30	0.1926088	26	0.12819438	21
VR246	0.234684	33	0.2984314	37	0.2319335	38	0.1604633	41	0.08762653	60
VR247	-0.1041331	171	-0.050566	179	-0.0035034	178	0.011652	172	0.01206393	171
VR248	-0.1521565	195	-0.0985187	195	-0.0458803	195	-0.0243561	197	-0.01318493	203
VR249	-0.2994327	239	-0.2631217	240	-0.1535827	238	-0.0865401	239	-0.03669348	238
VR250	-0.328521	247	-0.2862959	247	-0.1931369	261	-0.1347237	273	-0.08573704	277
VR251	0.2515532	31	0.2988548	36	0.2203014	42	0.1452317	56	0.07370213	77
VR252	-0.379279	270	-0.3206686	266	-0.1901438	257	-0.1096338	257	-0.04885261	256
VR253	-0.3478996	258	-0.2922598	258	-0.1726611	249	-0.0995332	245	-0.04463694	243
VR254	0.0657862	96	0.1088623	112	0.0903379	122	0.0596355	126	0.02774644	132
VR255	0.3480105	13	0.3866998	15	0.2725407	24	0.1786514	32	0.09313753	51
VR256	-0.1466854	190	-0.0459123	172	0.0009616	172	0.0083296	176	0.00136486	179
VR257	-0.0253101	136	0.0663172	127	0.077499	128	0.0612279	122	0.03503686	123
VR258	-0.1202467	177	-0.0791378	189	-0.0361542	194	-0.0167303	193	-0.00552676	195
VR259	-0.4073165	276	-0.3529597	276	-0.2159625	276	-0.1288497	263	-0.06046627	263
VR260	0.1290753	71	0.2326073	65	0.2051695	54	0.1586914	44	0.10281123	39
VR261	-0.328521	247	-0.2862959	247	-0.1931369	261	-0.1347237	273	-0.08573704	277
VR262	0.0522216	104	0.0884319	118	0.0764502	131	0.0524752	136	0.02638147	137
VR263	-0.3454372	256	-0.2882917	256	-0.1664228	243	-0.0921689	240	-0.03752439	239
VR264	-0.0686621	155	0.0231444	146	0.0479946	143	0.0418742	140	0.02469324	139
VR265	0.1263586	74	0.1706169	82	0.1219857	96	0.0748184	114	0.03252617	129
VR266	0.1090627	81	0.1573344	85	0.1265857	94	0.0864945	105	0.04545245	110
VR267	-0.2605366	228	-0.214181	228	-0.1267636	230	-0.0739335	231	-0.03397462	232
VR268	-0.0313232	142	0.0209355	154	0.0344578	156	0.0280765	158	0.01571927	163
VR269	-0.5104426	293	-0.4683455	293	-0.3195247	293	-0.2187072	293	-0.1312375	293
VR270	-0.1466854	190	-0.0459123	172	0.0009616	172	0.0083296	176	0.00136486	179
VR271	-0.3907092	275	-0.3442674	275	-0.2004282	271	-0.1117621	261	-0.04627449	251
VR272	0.0198672	117	0.1117101	106	0.1095981	106	0.0831632	107	0.04766056	105
VR273	-0.1805969	197	-0.1372569	206	-0.0603184	199	-0.0249444	199	-0.00627211	196
VR274	0.4655178	3	0.4923461	3	0.3705159	4	0.2709503	5	0.17368736	5
VR275	0.024852	113	0.0864484	120	0.0793915	125	0.0551694	133	0.02714879	134
VR276	0.1601359	63	0.2333674	63	0.1960184	59	0.1495629	50	0.09825803	45
VR277	0.070006	90	0.145335	94	0.1405273	87	0.112971	82	0.07603746	74
VR278	-0.1521565	195	-0.0985187	195	-0.0458803	195	-0.0243561	197	-0.01318493	203
VR279	-0.4073165	276	-0.3529597	276	-0.2159625	276	-0.1288497	263	-0.06046627	263
VR280	0.0684069	91	0.1177157	104	0.1053339	110	0.0731	115	0.03646415	121
VR281	0.5169436	1	0.5734171	1	0.4543916	1	0.3526536	1	0.24444907	1
VR282	0.2523543	30	0.301631	35	0.2374382	35	0.1704733	34	0.10182544	41
VR283	0.2797245	26	0.3295549	27	0.2420588	33	0.1598632	42	0.08163873	69
VR284	0.2797245	26	0.3295549	27	0.2420588	33	0.1598632	42	0.08163873	69
VR285	-0.5104426	293	-0.4683455	293	-0.3195247	293	-0.2187072	293	-0.1312375	293
VR286	0.0962651	84	0.1771154	79	0.1956424	62	0.1698115	35	0.12446706	22
VR287	-0.0686621	155	0.0231444	146	0.0479946	143	0.0418742	140	0.02469324	139
VR288	0.3426099	15	0.3941029	14	0.2917013	16	0.1991179	22	0.11041363	32
VR289	-0.2000514	208	-0.1392801	207	-0.0736538	209	-0.0362187	202	-0.01202402	202
VR290	-0.4073165	276	-0.3529597	276	-0.2159625	276	-0.1288497	263	-0.06046627	263
VR291	-0.4111057	286	-0.3766457	286	-0.2577335	286	-0.1770915	287	-0.10726158	287
VR292	0.2144575	43	0.3032885	34	0.2476315	29	0.1838035	29	0.11702324	28
VR293	-0.3478996	258	-0.2922598	258	-0.1726611	249	-0.0995332	245	-0.04463694	243
VR294	-0.2605366	228	-0.214181	228	-0.1267636	230	-0.0739335	231	-0.03397462	232
VR295	-0.3478996	258	-0.2922598	258	-0.1726611	249	-0.0995332	245	-0.04463694	243
VR296	-0.2381774	214	-0.1869896	214	-0.1095815	216	-0.0656824	217	-0.03295054	223
VR297	0.2154906	42	0.2654438	50	0.2133195	45	0.1516096	48	0.08797222	58
VR298	-0.1363048	181	-0.0772643	185	-0.0284263	187	-0.0088203	191	-9.2697E-05	188
VR299	-0.0686621	155	0.0231444	146	0.0479946	143	0.0418742	140	0.02469324	139
VR300	-0.0686621	155	0.0231444	146	0.0479946	143	0.0418742	140	0.02469324	139