Risk assessment approach for analyzing risk factors to overcome pandemic using interval-valued q-rung orthopair fuzzy decision making method

Abstract

The process of developing and implementing sustainable strategies to prevent spread of COVID-19 for society typically requires integrating all social, technological, economic, governmental aspects in a systematic way. Since the clear understanding of risk factors contribute to the success of the strategies applied against COVID-19, a risk assessment procedure is applied in this study to properly evaluate risk factors cause to spread of pandemic as a multi-complex decision problem. Therefore, due to the evaluation of risk factors, which often involves uncertain information, the model is constructed based on interval-valued q-rung orthopair fuzzy-COmplex PRoportional ASsessment (IVq-ROF-COPRAS) method. While the developed framework is efficient to enhance the quality of decisions by implementing more realistic, precise, and effective application procedure under uncertain environment, it has capability to help governments for developing comprehensive strategies and responses. According to the results of the proposed risk analysis model, the top three risk factors are “The Approach that Prioritizes the Economy in Policies”, “Insufficient Process Control in Normalization” and “Lack of Epidemic Management Culture in Individuals and Businesses”. Lastly, to show applicability and efficiency of the model sensitivity and comparative analysis were conducted at the end of the study.

1. Introduction

COVID-19 first announced in Wuhan, China on December 19, 2019, and the disease was spread to other countries in a short time with the impact of globalization. COVID-19 was reported with the definition of “unspecified lung disease” by WHO and declared as a global pandemic on January 30, 2020 [1]. Currently (15 May 2022), the number of confirmed cases worldwide has reached 521 million and the number of deaths has reached 6.3 million [2]. WHO explained that the spread of the virus can be ended with a successful system for early diagnosis, isolation, rapid treatment, and monitoring of contacted individuals [1]. To reduce the mobility of the virus, while country borders and cities are partially or completely closed all over the world, education and office works turned to be conducted from home, using masks, and applying hygiene rules have been implemented. Among these measures, the most recommended measures have been the use of masks, cleaning of contact surfaces with disinfectant and social distance [3]. While some countries such as China have taken more drastic measures, some countries such as Sweden have followed softer strategies by trying the herd immunity method. Most of the countries, on the other hand, have started to take measures quickly since the WHO declared the pandemic and has started to work to get over this process with minimal damage. In February, flights from China were cancelled, citizens come from other countries were quarantined for 14 days and education activities were turned to distance learning. In addition, places where citizens can be found collectively (cafes, gyms, theaters, etc.) were closed, and as of April, intercity travel and curfews began to be implemented on weekends [4]. As given in Table 1, with the measures taken in the first phase of the epidemic, some countries have successfully come to the fore among European countries with its fast and effective measures against the COVID-19 pandemic [5].

Table 1.

Measures taken in the first phase of the epidemic [5].

Country	Emergence of first case	School closure	Closing public places	Restriction of public events	Extensive travel and transport restrictions
Italy	31st of January	10th of March (After 39 days)	12nd Of March (After 41 Days)	10th Of March (After 39 Days)	10th of March (After 39 Days)
Spain	31st of January	11st of March (After 40 Days)	14th of March (After 43 Days)	11th of March (After 40 Days)	14th of March (After 43 Days)
England	31st of January	18th of March (After 47 Days)	20th of March (After 49 Days)	13rd of March (After 42 Days)	24th of March (After 53 Days)
Germany	27th of January	17th of March (After 50 Days)	16th of March (After 49 Days)	13rd of March (After 46 Days)	17th of March (After 40 Days)
France	24th of January	13rd of March (After 49 Days)	14th of March (After 50 Days)	13rd of March (After 48 Days)	17th of March (After 53 Days)
Turkey	10th of March	12nd of March (After 2 Days)	15th of March (After 5 Days)	12nd of March (After 2 Days)	13rd of March (After 3 Days)

As a result of the different measures taken by different countries, the pandemic process also varied from country to country. While the center of the pandemic was initially China, it was replaced by other countries over time. As presented in Table 2, the United States, Brazil, and India are among the countries with a poor pandemic progress. Considering Turkey’s struggle against COVID-19, the “Pandemic Influenza National Preparation Plan” was successfully implemented in June 2020, as a result, the number of possible cases and deaths decreased with this plan. With the revival of social life, second wave of pandemic process existed as of November 30, 2020, and the number of daily cases and deaths started to increase [6]. While the restrictions continued until March 1, 2021, the course of the pandemic started to move positively and with the vaccination-controlled normalization process started again. In this stage, four groups of countries with high, very high, medium and low-level risks are identified, and restrictions have been gradually lifted accordingly [7].

Table 2.

Number of cases and deaths of countries [2].

Country	Number of cases (Ranking)	Number of deaths (Rank)
United States of America	37.5 million (1)	626 thousand (1)
India	32.0 million (2)	429 thousand (3)
Brazil	20.5 million (3)	573 thousand (2)
Russia	6.68 million (4)	174 thousand (4)
France	6.56 million (5)	113 thousand (11)
United Kingdom	6.39 million (6)	131 thousand (7)
Turkey	6.16 million (7)	54 thousand (18)
Argentina	5.12 million (8)	110 thousand (12)
Colombia	4.88 million (9)	124 thousand (9)
Spain	4.76 million (10)	83 thousand (15)

However, as a result of both the socialization brought about by normalization and the mutations of the virus has undergone, the number of cases has reached its peak in the whole of the process since the first day. Because of the rapid decrease in the number of cases, thanks to the full closure and vaccination campaigns, all restrictions other than wearing masks and social distance have been lifted across the country as of July 1, 2021 [8]. The course of the pandemic, which was stable for a while, started to show a remarkable negative increase as of July 26, 2021. During this process, the minimum and maximum daily case numbers for Turkey are given in Table 3. Ongoing restrictions, increasing number of cases, and ongoing vaccinations not producing a complete solution create uncertainties in the course of the epidemic and the management of the process.

Table 3.

The minimum and maximum daily case numbers for Turkey [9].

Date	Daily number of cases
11nd of April 2020	13.976
4$\mathrm{th}$ of December 2020	32.736
14$\mathrm{rd}$ of April 2021	62.797
16$\mathrm{st}$ of April 2021	63.082
01$\mathrm{st}$ of February 2022	102.601
08$\mathrm{st}$ of February 2022	111.096

Since the COVID-19 pandemic has negatively affected all countries socially and economically, governments have explored various strategies to prevent the spread of the epidemic [10]. The pandemic we are in will only be terminated by handling and coping with the risk factors in front of it. Thus, these risk factors need to be understood correctly, and a clear understanding of the risk levels will contribute to the success of the strategies applied against COVID-19. Hence, the clear understanding of risk factors is important to contribute to the success of the strategies that prevent the spread of COVID-19 pandemic. A new risk assessment model is applied in this study to properly evaluate risk factors determined based on social, technological, government and economic aspects under uncertain information. Due to limited knowledge or data obtained in a short period of time for COVID-19, there may be hesitation and uncertainty with respect to experts’ evaluation information. According to the complexity of problem, this research adopts IVq-ROF-COPRAS to determine the most important risk factors based on people, technology, government and economic conditions to deal with COVID-19 pandemic by considering maximizing and minimizing attributes simultaneously.

Thus, since interval-valued q-rung fuzzy concept is very flexible to capture the uncertainty and incompleteness of information, interval-valued q-rung orthopair fuzzy-COmplex PRoportional ASsessment (IVq-ROF-COPRAS) method is established. In addition to its logical concepts to make risk assessment more effectively, this method has been selected for the purpose of providing more flexibility to professionals in stating their judgments about the ambiguity and imprecision of the considered problem than other fuzzy extensions. Thus, considering four important attributes available in traditional occupational health and safety (OHS) for risk evaluation, the risk factors cause COVID-19 pandemic spread in a society are evaluated to develop strategies by government and health agencies.

The main contributions of this paper are as follows.

• •Risk assessment for the pandemic is a crucial undertaking to increase consciousness and conduct safety measures for controlling the disease. Managing epidemics need critical strategic decisions to handle due to its vital consequences on people and society. Therefore, an extensive risk analysis framework is conducted.
• •For this aim, a new risk assessment model considering uncertainty and incompleteness of information in decision making process has been presented to determine the risk levels of the risk factors that cause spreading of COVID-19 pandemics in a society. The methodology is constructed based on interval-valued q-rung orthopair fuzzy-COmplex PRoportional ASsessment (IVq-ROF-COPRAS) method. Thus, the constructed model is appropriate for enhancing the quality of decisions by offering capability to represent complex and vague information.
• •To the best knowledge of authors, in the literature there are only a few studies to evaluate and rank risk factors for the spread of the COVID-19 epidemic in general, specifically using Fuzzy MCDM models [11], [12], [13]. Thus, there are very few studies in the literature that can help governments in this regard. By the study, the most important risk factors are determined and highlighted for managers and governments to fight against COVID-19 pandemic. Consequently, the contribution of this study to the existing literature is to develop a decision support model to evaluate the risk factors causing the spread of the pandemic for the development of strategies against the COVID-19 pandemic. Using technique and information in this study decision makers will be able to create better strategies to prevent pandemics.
• •The framework is capable of determining risk factors against COVID-19 in any country given that the region-specific data is updated. Furthermore, the proposed model may be used or developed to fight other pandemics and different types of disasters.

The study continues as follows: In Section 2, a literature review that examines the Multi-Criteria-Decision Making (MCDM) applications related to COVID-19 and the applications that make use of MCDM methods in risk analysis is presented. Section 3 is the preliminary section in which information about the methods used in the study is presented. Section 4 includes the methodology of the study, Section 5 includes the real case study is performed and sensitivity and comparative analyses are conducted to demonstrate the efficiency of the proposed method, and finally Section 6 includes the results of the implementation and the controversial analysis of the results.

2. Literature review

Although the cause and exact solution are not known, the number of studies related to an epidemic as serious as COVID-19 has increased continuously in a short time. The epidemic did not only affect health globally, but also had an impact on many areas from economy to sports, from tourism to politics and brought life to a standstill. In this process, while scientists tried to overcome the disease, social scientists investigated the economic, social and political effects of the work [14]. The literature review in this study consists of two parts. In the first part, MCDM practices on the COVID-19 pandemic were summarized, and in the second part, risk analysis practices made by MCDM methods were summarized.

Shrestha et al. [15] examined the influence of COVID-19 in potential global health based on calculated pandemic vulnerability index (PVI) using the Technique for order performance by similarity to ideal solution (TOPSIS) method. The objective was to develop and implement strategies in required countries to help ease emerging burden. The results showed that in Africa; more vulnerable countries were South Africa and Egypt, in Europe; Russia, Germany, and Italy; in Asia and Oceania; India, Iran, Pakistan, Saudi Arabia, and Turkey, and for the Americas; Brazil, USA, Chile, Mexico, and Peru.  Maqbool and Khan [16] divided the risk factors in the execution of the measures taken against the COVID-19 in India into 10 titles and analyzed them with a decision-making trial and evaluation laboratory (DEMATEL) method. As a result of the analysis, while lack of resources was found to be the most influential barrier, it was found that the successful implementation of the measures depends on medical equipment and financial resources. Yüksel et al. [17] applied the DEMATEL to analyze which factors were prioritized in determining the most optimal economic recovery package for COVID-19 and concluded that the interest-free loan option was the most important factor. Albahri et al. [18] established a joined Analytic hierarchy Process (AHP) and VIse KriterijumsaOptimiz acija I Kompromisno Resenje (VIKOR) methodology to compare Artificial Intelligence (AI) practices used in the discovery and categorization of COVID-19 examination illustrations in terms of assessment and benchmarking. AHP was used to assess the evaluation factors, and VIKOR was applied for benchmarking AI classification techniques. Ocampo and Yamagishi [19] applied the fuzzy-DEMATEL in determining the most important criteria in the transition of the Philippine government for COVID-19 normalization protocols and determined the exact cause groups as: compliance with the standards, limited mobility of people, 50% capacity, non-operating places such as hotels, industries being closed, and collective meetings were prohibited. Results showed that compliance of community well-being standards, restricted movement of people, postponement of physical courses, the prevention of mass meetings, non-operation of type IV businesses, and non-operation of resorts or like businesses are the most critical properties for developing strategies in the governments to distribute resources and apply measures for developing mitigation efforts. Altuntaş and Gök [20] used DEMATEL to analyze the effect of quarantine decisions on domestic tourism. The objective was to diminish the negative effect of a pandemic on the hospitality industry. The results showed that Istanbul has significant influence on Turkey’s rest. The results also showed that the DEMATEL method produced appropriate solutions for quarantine decisions in a pandemic to prepare the hospitality industry and the method applied also is convenient for similar pandemic. Alkan and Kahraman [13] developed two q-ROF TOPSIS methodologies to evaluate the strategies implemented by governments against the COVID-19. The goal of the research is to identify and analyze the risks or obstacles to control the negative consequences of COVID-19 systematically that may arise from the uncertainties. As a result of the riskanalysis, the risk factors with the highest risk level are identified and measures related to these risk factors to deal with COVID-19 are determined systematically.

In almost all risk assessment techniques, the factors that create the risk are determined, the risks are graded and measures are determined in order of importance. In addition to classical risk assessment techniques, the risk levels of risk factors can be listed with MCDM Techniques, which are used to determine the degree of importance of certain alternatives under certain criteria [21]. However, due to risk factors often involves uncertain information, fuzzy MCDM applications were effectively used in the literature [21], [22].

For example, Yazdani et al. [22] developed a fuzzy COPRAS methodology to perform risk analysis of critical infrastructures and compared it with Risk Analysis and Management for Critical Asset Protection (RAMCAP), one of the traditional risk analysis methods, to analyze the accuracy of the results. As a result of the comparison, it was determined that the proposed methodology has the capability to provide more accurate results for ranking the risk of critical infrastructures. Jin et al. [23] used IV-q-ROF, stating that the traditional Failure Mode and Effect Analysis (FMEA) methodology is insufficient in the risk assessment process of tool changing manipulators. To ensure experts’ assessments more reliable, a stable review and process is applied and experts’ opinions are integrated by IVq-ROF weighted average (IVq-ROFWG) operator and IVq-ROF weighted Maclaurin symmetric mean (IVq-ROFWMSM) operator. IVq-ROF-ARAS method applied and sufficient, adequate and precise outcomes were obtained in positioning failure modes. Wan and Zhou [24] combines CRITIC-WASPAS under uncertainty for group decision making. To deal with the uncertainty Interval-valued q-rung orthogonal sets were used. The objective was to evaluate early warning management of hypertension risk diseases. Since the proposed method was adaptable and effective, the results were consistent with decision-makers’ opinions. Cheng et al. [25] used VIKOR (VlseKriterijumska Optimizacija Kompromisno Resenje) approach under q-rung orthopair fuzzy set (q-ROFSs) to identify and assess Enterprise Risk Management (ERM) in the universal appeal under the sustainability platform includes 29 sub-criteria considering social, environmental, technological, and economic issues. The results demonstrated that technological appropriateness was the significant risk aspect followed by technical improvement, work-related protection and well-being, merchandise and services concern, (advantage) anti-corruption labor force applies, and industrial practicality. The results of the study revealed that the suggested technique was effective and successful to evaluate risk factors of sustainable ERM in the Small and Mid-Size Enterprises.

The pandemic we are in will only be terminated by handling and coping with the risk factors in front of it. Thus, these risk factors need to be understood correctly, and a clear understanding of the risk levels will contribute to the success of the strategies applied against COVID-19. According to the complexity of problem, this research adopts IVq-ROF-COPRAS to determine the most important risk factors based on people, technology, government and economic conditions to deal with COVID-19 pandemic by considering maximizing and minimizing attributes simultaneously.

Due to uncertain and vague information of decision makers (DMs) derived from the information obtained in a short period of time for COVID-19, the model is implemented under an uncertain environment. Thus, since DMs can express their judgement more accurately in IVq-ROF format, the proposed risk assessment methodology become more robust to evaluate risk factors affecting the spread of COVID-19. Different from the literature, this study presents a useful method for risk assessment with simplified calculations, which provide reasonable and practical solutions to DMs.

3. Preliminaries

3.1. Interval-valued Q-rung orthopair fuzzy sets

Q-rung orthopair fuzzy sets (q-ROFSs) first launched by Yager  [26]. q-ROFSs are characterized with degree of membership and non-membership. In this method, q-ROFSs, the summation of the q$\mathrm{th}$ power of the membership and non-membership values should be at one. Some definitions for q-ROFSs and IVq-ROFSs are as follows:

Definition 1

A q-ROFS $\tilde{Q}$ in a finite universe of discourse X is specified as following by Yager [26].

$$\tilde{Q}=\left\{\left(\left(x,{\mu }_{\tilde{Q}}\left(x\right),v_{\tilde{Q}}\left(x\right)\right)|xϵX\right)\right\}$$ (1)

where ${\mu }_{\tilde{Q}}:X\to \left[0,1\right]$ and $v_{\tilde{Q}}:X\to \left[0,1\right]$ are the degree of membership and non-membership, respectively. q-ROFS must satisfy the condition of

$$0\le {\left({\mu }_{\tilde{Q}}\left(x\right)\right)}^q+{\left(v_{\tilde{Q}}\left(x\right)\right)}^q\le 1(\mathrm{q}\ge 1)$$ (2)

The degree of indeterminacy:

$${\pi }_{\tilde{Q}}\left(x\right)=\sqrt[q]{1-{\mu }_{\tilde{Q}}{\left(x\right)}^q-v_{\tilde{Q}}{\left(x\right)}^q}\text{where q}\ge 1$$ (3)

q-ROFSs offers more wide scale for DMs  [27], [28] to prompt ambiguous info comparing to Pythagorean fuzzy sets (PFSs) and intuitionistic fuzzy sets (IFSs).1̑-gul-regular20 20The differences IFNs, PFNs, and q-ROFNs are seen in Fig. 1. It is clearly seen that the IFS and PFS can be deduce under the restricted domains $\mu \in \left[0,1\right],\vartheta \in [0,1]$, $\mu +\vartheta <1$ and ${\mu }^2+{\vartheta }^2<1$ by setting q $=$ 1 and q $=$ 2, respectively. In the idea of q-ROFSs, we see that $\mu +\vartheta$   $\nleqq$  1 and ${\mu }^2+{\vartheta }^2$   $\nleqq$  1 but ${\mu }^{\mathrm{q}}+{\vartheta }^{\mathrm{q}}$ $\le$ 1 by setting $2<$ q $<\mathrm{\infty }$  [29], [30]. Some preliminaries used through this paper for q-ROFSs and IVq-ROFSs are shown in the following. These operations for q-ROFSs are preferred in this study, since they broadly employed by the scholars to solve real-world MCDM problems in the literature.

Fig. 1.

Geometric space range of IFS, PFS, and q-ROFS [31].

In many real-life problems, it is complicated for the DMs to express the degree of membership and non-membership with a single value. To solve this problem, Joshi et al. [32] introduced IVq-ROFS notion whose main feature is to express membership and non-membership function rates in intervals instead of exact values.

Definition 2 [33] —

Let X be a non-empty and limited set, a IVq-ROFS $\tilde{P}$ on X is given as:

$$\tilde{P}=\left\{\left|〈x,{\mu }_{\tilde{P}}\left(x\right),v_{\tilde{P}}\left(x\right)〉\right|xϵX\right\}$$ (4)

where the function ${\tilde{\mu }}_{\tilde{P}}\left(x\right)=\left[{\mu }_{\tilde{P}}^L\left(x\right),{\mu }_{\tilde{P}}^U\left(x\right)\right]:X\to \left[0,1\right]$ and ${\tilde{v}}_{\tilde{P}}\left(x\right)=\left[v_{\tilde{P}}^L\left(x\right),v_{\tilde{P}}^U\left(x\right)\right]:X\to \left[0,1\right]$ are intervals representing the membership and non-membership degrees of the element $x$ $\in$ X to the set $\tilde{P}$, correspondingly, which satisfies the condition of

$${\left({\mu }_{\tilde{P}}^U\left(x\right)\right)}^q+{\left(v_{\tilde{P}}^U\left(x\right)\right)}^q\le 1,q\ge 1$$ (5)

The degree of indeterminacy is expressed as:

$$\begin{array}{c}{\pi }_{\tilde{p}}\left(x\right)=\left[{\pi }_{\tilde{p}}^L\left(x\right),{\pi }_{\tilde{p}}^U\left(x\right)\right]\hfill \\ =\left[\sqrt[q]{1-{\left({\mu }_{\tilde{P}}^U\left(x\right)\right)}^q+{\left(v_{\tilde{P}}^U\left(x\right)\right)}^q},\sqrt[q]{1-{\left({\mu }_{\tilde{P}}^L\left(x\right)\right)}^q+{\left(v_{\tilde{P}}^L\left(x\right)\right)}^q}\right]\hfill \end{array}$$ (6)

While $q=1$, IVq-ROFS reduces to interval-valued intuitionistic fuzzy set (IVIFS), q $=$ 2, IVq-ROFS reduces to interval-valued pythagorean fuzzy set (IVPFS).

Definition 3 [33] —

For a IVq-ROFN $\tilde{p}=\left[{\mu }_{\tilde{p}}^L,{\mu }_{\tilde{p}}^U\right],\left[v_{\tilde{p}}^L,v_{\tilde{p}}^U\right]$, the score function $s\left(\tilde{p}\right)$ and the accuracy function $H\left(\tilde{p}\right)$ of $\tilde{p}$ are calculated as follows:

$$\begin{array}{c}s\left(\tilde{p}\right)=\frac{1}{4}\left[(1+{\left({\mu }_{\tilde{p}}^L\right)}^q-{\left(v_{\tilde{p}}^L\right)}^q)+(1+{\left({\mu }_{\tilde{p}}^U\right)}^q-{\left(v_{\tilde{p}}^U\right)}^q)\right],\hfill \\ s\left(\tilde{p}\right)\in \left[0,1\right].\hfill \end{array}$$ (7)

$$H\left(\tilde{p}\right)=\frac{{\left({\mu }_{\tilde{p}}^L\right)}^q+{\left(v_{\tilde{p}}^L\right)}^q+{\left({\mu }_{\tilde{p}}^U\right)}^q+{\left(v_{\tilde{p}}^U\right)}^q}{2},H\left(\tilde{p}\right)\in \left[0,1\right].$$ (8)

Definition 4 [34] —

${\tilde{p}}_1=\left(\left[{\mu }_{{\tilde{p}}_1}^L,{\mu }_{{\tilde{p}}_1}^U\right],\left[v_{{\tilde{p}}_1}^L,v_{{\tilde{p}}_1}^U\right]\right)and{\tilde{p}}_2=\left(\left[{\mu }_{{\tilde{p}}_2}^L,{\mu }_{{\tilde{p}}_2}^U\right],\left[v_{{\tilde{p}}_2}^L,v_{{\tilde{p}}_2}^U\right]\right)$ are two IVq-ROFNs. Some arithmetic operations of the IVq-ROFNs are defined as follows and the result of each operation is an IVq-ROFN:

$${\tilde{p}}_1\oplus {\tilde{p}}_2=$$

$$\left[\sqrt[q]{{\left({\mu }_{{\tilde{p}}_1}^L\right)}^q+{\left({\mu }_{{\tilde{p}}_2}^L\right)}^q-{\left({\mu }_{{\tilde{p}}_1}^L\right)}^q{\left({\mu }_{{\tilde{p}}_2}^L\right)}^q},\right)\left(\sqrt[q]{{\left({\mu }_{{\tilde{p}}_1}^U\right)}^q+{\left({\mu }_{{\tilde{p}}_2}^U\right)}^q-{\left({\mu }_{{\tilde{p}}_1}^U\right)}^q{\left({\mu }_{{\tilde{p}}_2}^U\right)}^q}\right],\left[v_{{\tilde{p}}_1}^L{v}_{{\tilde{p}}_2}^L,v_{{\tilde{p}}_1}^U{v}_{{\tilde{p}}_2}^U\right]$$ (9)

$${\tilde{p}}_1\otimes {\tilde{p}}_2=\left[\left[{\mu }_{{\tilde{p}}_1}^L{\mu }_{{\tilde{p}}_2}^L,{\mu }_{{\tilde{p}}_1}^U{\mu }_{{\tilde{p}}_2}^U\right],\right)\sqrt[q]{{\left(v_{{\tilde{p}}_1}^L\right)}^q+{\left(v_{{\tilde{p}}_2}^L\right)}^q-{\left(v_{{\tilde{p}}_1}^L\right)}^q{\left(v_{{\tilde{p}}_2}^L\right)}^q},\left(\sqrt[q]{{\left(v_{{\tilde{p}}_1}^U\right)}^q+{\left(v_{{\tilde{p}}_2}^U\right)}^q-{\left(v_{{\tilde{p}}_1}^U\right)}^q{\left(v_{{\tilde{p}}_2}^U\right)}^q}\right]$$ (10)

$$\begin{array}{c}\lambda \tilde{p}=\left(\left[\sqrt[q]{1-{(1-{\left({\mu }^L\right)}^q)}^{\lambda }},\sqrt[q]{1-{(1-{\left({\mu }^U\right)}^q)}^{\lambda }}\right],\right)\hfill \\ \left(\left[{\left(v^L\right)}^{\lambda },{\left(v^U\right)}^{\lambda }\right]\right),\lambda >0;\hfill \end{array}$$ (11)

$$\begin{array}{c}{\left(\tilde{p}\right)}^{\lambda }=\left(\left[{\left({\mu }_{\tilde{p}}^L\right)}^{\lambda },{\left({\mu }_{\tilde{p}}^U\right)}^{\lambda }\right],\left[\sqrt[q]{1-(1-{\left(v_{\tilde{p}}^L\right)}^q}){}^{\lambda }\right],\right)\hfill \\ \left(\left[\sqrt[q]{1-(1-{\left(v_{\tilde{p}}^U\right)}^q}){}^{\lambda }\right]\right),\lambda >0\hfill \end{array}$$ (12)

Definition 5 [35] —

Interval-valued q-rung orthopair fuzzy weighted geometric (IVq-ROFWG) operator: Suppose ${\tilde{P}}_i=\left[{\mu }_{{\tilde{P}}_i}^L,{\mu }_{{\tilde{P}}_i}^U\right],\left[v_{{\tilde{P}}_i}^L,v_{{\tilde{P}}_i}^U\right]$ (i $=$ 1,2,…,n) is a collection IVq-ROFNs then Interval-valued q-rung orthopair fuzzy weighted geometric (IVq-ROFWG) operator is defined as follows and the result is an IVq-ROFN :

$$\text{IVq-ROFWG}({\tilde{P}}_1,{\tilde{P}}_2,\dots ,{\tilde{P}}_n)=$$

$$\left[\prod _{i=1}^n{\left({\mu }_{{\tilde{P}}_i}^L\right)}^{w_i},\prod _{i=1}^n{\left({\mu }_{{\tilde{P}}_i}^U\right)}^{w_i}\right]\left[\sqrt[q]{1-\prod _{i=1}^n{(1-v_{{\tilde{P}}_i}^L)}^{w_i}},\right)\left(\sqrt[q]{1-\prod _{i=1}^n{(1-v_{{\tilde{P}}_i}^U)}^{w_i}}\right]$$ (13)

where

$w_j={(w_1,w_2,\dots ,w_n)}^T$ thereby satisfying $w_j\in [0,1]$ and ${\sum }_{j=1}^n{w}_j=1$

A comparative examination of the proposed approach with other state-of-the-art methods under both q-ROFS and IVq-ROFS context considering theoretical and numerical factors is represented in Table 4.

A large amount of uncertainties may occur in risk analysis, IVq-ROFSs have an distinctive benefit in coping with the uncertainty and vagueness of DMs’ assessment information and provide a efficient aggregation operators such as IVq-ROFWG and q-rung interval-valued orthopair fuzzy weighted Hamy mean (q-RIVOFWHM) operator. IVq-ROFWG is well suited for calculating the relative weights of four main attributes available in proposed risk assessment process. IVq-ROF COPRAS method easy-use and comprehensible steps, which can produce rational, satisfactory and relatively accurate results in ranking of risk factors.

Table 4.

Characteristic investigation of proposed and different models under q-ROFS and IVq-ROFS context.

	Proposed method	[34]	[35]	[29]	[30]
Context
Data	IVq-ROFNs	IVq-ROFNs	IVq-ROFNs	q-ROFNs	q-ROFNs
Decision-making type	Group decision-making	Group decision-making	Group decision-making	Group decision-making	Group decision-making
Attributes’ weight calculation	IVq-ROFWG operator	q-rung interval-valued orthopair fuzzy weighted Hamy mean (q-RIVOFWHM) operator		Gini index	SV method
Aggregation operator	IVq-ROFWG	Hamy mean (HM) operator, weighted HM (WHM) operator, dual HM (DHM) operator, and the dual-weighted HM (WDHM)	IVq-ROFWA, Vq-ROFOWA, GIVq-ROFHA	Muirhead mean	q-ROFGMSM
Prioritization methods	COPRAS	q-RIVOFWHM	IVq-ROFWA, IVq-ROFOWA,GIVq-ROFWA, GIVq-ROFOWA, IVq-ROFHA, and GIVq-ROFHA	TODIM	VIKOR

3.2. COPRAS method

The main steps of COPRAS are summarized as follows (Zavadskas et al. [36]):

Step 1: Definition of the problem: Considering the problem, determine the sets of alternatives and measures.

Step 2: Construction of the decision-matrix: Specialists assess the determined alternatives taking into consideration the criteria. Accordingly, construct the decision-matrix as:

$${\left[x_{ij}\right]}_{nxm}=\left[\begin{array}{ccc}\hfill x_{11}{x}_{12}\hfill & \hfill \cdots \hfill & \hfill x_{1m}\hfill \\ \hfill ⋮\hfill & \hfill \ddots \hfill & \hfill ⋮\hfill \\ \hfill x_{n1}{x}_{n2}\hfill & \hfill \cdots \hfill & \hfill x_{nm}\hfill \end{array}\right]$$ (14)

where $x_{ij}$ represents the performance value of $i$th {i $\in$ 1,2,…, n} alternative associated with the criterion j, j $\in${1,2,…, m}.

Step 3: Normalize decision-matrix. The normalized matrix is created by employing normalization process as in Eq. (15).

$$n_{ij}=\frac{x_{ij}}{\sum _{i=1}^n{x}_{ij}}$$ (15)

where i $\in${1,2,…, n} and j $\in${1,2,…, m}

Step 4: Establish the weighted normalizes-matrix. This matrix is created by performing Eq. (16).

$$r_{ij}=w_j{n}_{ij}$$ (16)

where i $\in${1,2,…, n}, j $\in${1,2,…, m} and ${\sum }_{j=1}^n{w}_j=1$.

Step 5: For each alternative, compute the summation of maximizing and minimizing criteria: Alternatives are rated considering the maximizing ${\mathit{P}}_i$(benefit) and minimizing ${\mathit{R}}_i$, (cost) features. The summation of both types of criteria are calculated by employing Eqs. (17), (18) correspondingly. k represents the number of criteria to be maximized while there are n criteria;

$$P_i=\sum _{i=1}^k{r}_{ij}$$ (17)

$$R_i=\sum _{i=k+1}^n{r}_{ij}$$ (18)

Step 6: Calculate $R_{i_{min}}$, the minimal value of $R_i$:

$$R_{i_{min}}=mi{n}_i{R}_i$$ (19)

Step 7: Obtain the relative weights associated with each alternative (Qi) by performing Eqs. (20)–(21):

$$Q_i=P_i+\frac{R_{i_{min}}\sum _{i=1}^n{R}_i}{R_i\sum _{i=1}^n\frac{R_{i_{min}}}{R_i}}i\in 1,2,\dots ,n$$ (20)

$Q_i$ can be simplified as:

$$Q_i=P_i+\left(\frac{\sum _{i=1}^n{R}_i}{R_i\sum _{i=1}^{n}1/R_i}\right)i\in 1,2,\dots ,n$$ (21)

Step 8: Obtain the alternative with the highest value of $Q_i$:

$$Q_{max}=\underset{i}{max}{Q}_{i}i\in 1,2,\dots ,n$$ (22)

Step 9: For each alternative, compute the utility-degree $-U_i$, which is used to rank the alternatives and obtained by applying the Eq. (23):

$$U_i=\frac{Q_i}{Q_{max}}$$ (23)

The priority of the alternatives is determined by the value of $U_i$. In other words, the greater $U_i$ the more priority.

4. Proposed methodology: IVq-ROF COPRAS method

The proposed methodology, which is used in risk assessment model for the risk factors to cope with the COVID-19 pandemic faced. The Interagency Security Committee (ISC) defines risk “as a function of threat, vulnerability, and impact values. The purpose of risk management is to create a protection scheme that reduces vulnerabilities and potential impacts against threats, thereby reducing the risk to an acceptable level. Various mathematical models are available to calculate risk and show the effect of increased protective measures on the risk equation [37]. The framework of the methodology followed in this study is shown in Fig. 2.

Fig. 2.

Framework of the methodology proposed.

Considering the complication of the decision-making process and the uncertain information during decision making process, this study implements IVq-ROF-COPRAS to define the most significant risk factors to cope with COVID-19 pandemic spread by considering maximizing and minimizing criteria concurrently.

COPRAS, as one of the well-known and easy to apply method  [38], [39], is preferred in assessing the risks. Because of IVq-ROFSs’s ability to handle a wider range of uncertainty of information in the real-world decision-making processes and providing freedom degree to DMs’ assessments, an extension of COPRAS, which is named as IVq-ROF COPRAS, is developed as a risk assessment framework for assessing risk factors against COVID-19 pandemic spread, in the following steps:

Step 1. Create a DM group to determine risk factors cause of spreading COVID-19 and determine attributes with respect to risk assessment to evaluate risk factors. The members of this group determine the risk factors cause spreading of COVID- 19 pandemic.

Step 2. Determine the weights of attributes: The DMs opinions regarded to attributes are represented in the form of IVq-ROFNs based on linguistic expressions given in Table 5. The aggregation operator $\mathrm{IV\; q}-\text{ROFWG}$, which is given in Eq. (13), is applied once the weights given by experts are assigned.

Table 5.

Linguistic expressions and correspondence IVq-ROFNs to evaluate attributes [40].

Linguistic expression	${\mathrm{\mu }}^U$	${\mathrm{\mu }}^U$	$v^L$	$v^U$
Extremely High Important (EHI)	0.80	0.95	0.00	0.15
Very High Important (VHI)	0.70	0.80	0.15	0.25
High Important (HI)	0.55	0.70	0.25	0.40
Medium Important (MI)	0.45	0.55	0.40	0.55
Low Important (LI)	0.30	0.45	0.55	0.70
Very Low Important (VLI)	0.20	0.30	0.70	0.80
Extremely Low Important (ELI)	0.00	0.20	0.80	0.95

$w_j^k=〈\left[a_{ij},b_{ij}\right],\left[c_{ij},d_{ij}\right]〉$ represents the $k$th ($k=1,2,\dots ,K$) DM’s weights assigned to $j$th ($j=1,2,n$) attribute.

Step 3. Create the decision matrix X, which is the IVq-ROF evaluation matrix: In the X, ${\check{x}}_{ij}^k=〈\left[a_{ij}^k,b_{ij}^k\right],\left[c_{ij}^k,d_{ij}^k\right]〉$ designates the IVq-ROF ranking value of $i$th ($i=1,2,\dots m$) risk factors taking into account the attribute j, ($j=1,2,n$) for the $k$th ($k=1,2,\dots r$) DM. Once judgments are provided by the DMs linguistically to evaluate risk factors for overcoming COVID-19 pandemic, they are transformed into IVq-ROFNs via linguistic measures provided in Table 6.

$$\tilde{X}={\left[{\tilde{x}}_{ij}^k\right]}_{nxm}=\left[\begin{array}{ccc}\hfill {\tilde{x}}_{11}^k{\tilde{x}}_{12}^k\hfill & \hfill \cdots \hfill & \hfill {\tilde{x}}_{1m}^k\hfill \\ \hfill ⋮\hfill & \hfill \ddots \hfill & \hfill ⋮\hfill \\ \hfill {\tilde{x}}_{n1}^k{\tilde{x}}_{n2}^k\hfill & \hfill \cdots \hfill & \hfill {\tilde{x}}_{nm}^k\hfill \end{array}\right]$$ (24)

where ${\tilde{x}}_{ij}^k\ge 0$ and ${\tilde{x}}_{ij}^k=〈\left[a_{ij}^k,b_{ij}^k\right],\left[c_{ij}^k,d_{ij}^k\right]〉$ and $0\le {\left(b_{ij}^k\right)}^q+{\left(d_{ij}^k\right)}^q\le 1$.

Table 6.

Linguistic expressions and correspondence IVq-ROFNs to evaluate risk factors [33].

Linguistic expression	${\mathrm{\mu }}^L$	${\mathrm{\mu }}^U$	$v^L$	$v^U$
Extremely High (EH)	0.90	0.95	0.10	0.15
Very High (VH)	0.80	0.85	0.20	0.25
High (H)	0.70	0.75	0.30	0.35
Medium High (MH)	0.60	0.65	0.40	0.45
Medium (M)	0.50	0.55	0.50	0.55
Medium Low (ML)	0.40	0.45	0.60	0.65
Low (L)	0.30	0.35	0.70	0.75
Very Low (VL)	0.20	0.25	0.80	0.85
Extremely Low (EL)	0.10	0.15	0.90	0.95

Step 4. Create the aggregated IVq-ROF decision-matrix considering the opinions of DMs: In this step, previously created individual decision-matrices are combined in this matrix. To determine the overall expert opinions, IVq-ROFWG operator is conducted, which is provided in Eq. (13) and known as aggregation operator. Accordingly, ${\tilde{X}}^A$ matrix is constructed.

Step 5. Normalization of the aggregated IVq-ROF decision matrix: The matrix created in the previous step is normalized by using Equations given in Eqs. (25)–(26).

$${\tilde{N}}_{ij}=\left({\tilde{n}}_{ij}\right)$$ (25)

$${\tilde{n}}_{ij}=\left(\begin{array}{c}\left(\left[c_{ij},d_{ij}\right],\left[a_{ij},b_{ij}\right]\right)\text{for cost attribute}\hfill \\ \left[a_{ij},b_{ij}\right],\left[c_{ij},d_{ij}\right]\text{for benefit attribute}\hfill \end{array}\right)$$ (26)

Step 6. Determine the IVq-ROF weighted normalized matrix: The weights of criteria are multiplied by the normalized values.

$$\tilde{R}={\left[{\tilde{r}}_{ij}\right]}_{nxm}$$ (27)

$${\tilde{r}}_{ij}={\tilde{w}}_j\otimes {\tilde{n}}_{ij}$$ (28)

Step 7. Compute sum of weights, which is gathered through Eq. (29), for cost (minimized or non-beneficial) attributes:

$$P_i=\sum _{i=1}^k{\tilde{r}}_{ij}$$ (29)

Step 8. Compute sum of weights, which is gathered through Eq. (30), for beneficial-(maximized) attributes.

$$R_i=\sum _{i=k+1}^n{\tilde{r}}_{ij}$$ (30)

Step 9. In this step, the relative weight of each risk factor (Qi) is calculated: The priorities (relative weights) of risk factors are determined via Equations given in Eqs. (31)–(32). The score functions of $P_i$ and $R_i$ are shown by s($P_i)$ and s($R_i)$ and they are calculated using Eq. (7) respectively.

$$Q_i=s\left(P_i\right)+\left(s\left(R_{i_{min}}\right)\sum _{i=1}^{n}s\left(R_i\right)\right)/\left(s\left(R_i\right)\left(\sum _{i=1}^{n}s\left(R_{i_{min}}\right)/s\left(R_i\right)\right)\right)$$ (31)

$$Q_i=s\left(P_i\right)+\left(\sum _{i=1}^{n}s\left(R_i\right)/s\left(R_i\right)\sum _{i=1}^{n}1/s\left(R_i\right)\right)$$ (32)

where ${\mathit{R}}_{{\mathit{i}}_{\mathit{min}}}$ shows the min. value of ${\mathit{R}}_{\mathit{i}}$.

Step 10. Select the highest $Q_i$ and the risk factor that belongs to by using Equation given in Eq. (33).

$$Q_{max}=\underset{i}{max}{Q}_i$$ (33)

Step 11. Using the Equation given in (34) calculate the utilities, which represents the priority of the risk factors:

$$U_i=\frac{Q_i}{Q_{max}}$$ (34)

5. Application

5.1. Problem definition

Although it has been almost 2 years since the declaration of a global pandemic on January 30, 2020, and vaccination continues to be widespread, COVID-19 pandemic, which has affected the whole world continued to appear. While some countries have successfully dealt with the pandemic, the situation is still bad in many countries such as in America, India, and Brazil. For this aim, in this part of the study, it is aimed to prioritize the risk factors that prevent countries to overcome the COVID-19 pandemic according to risk levels and in turn presenting strategic precautions that can be applied.

5.2. Factors preventing societies from overcoming the covid-19 pandemic

Risk factors in dealing with the COVID-19 pandemic spread are represented under four factors as in Fig. 3 considering the literature and opinions of expert on the field.

Fig. 3.

Risk factors cause COVID-19 pandemic spread.

The hierarchical structure consists of two levels under target objective. The first and second level are the main and sub-risk factors that can cause spreading of COVID-19. Accordingly, in this paper, the risk factors cause COVID-19 pandemic spread in society are ranked for developing strategies by governments.

5.2.1. People

Insufficient Isolation at Home (R1)

Once the virus-carrying people are identified, they must be quarantined. The people who contact with them must be also identified after they subjected to the necessary tests and quarantined according to the test result. At the beginning of the pandemic, all individuals at risk of COVID-19 were quarantined for 14 days in designated areas outside the hospital [41]. Further, the units where they can be quarantined outside the hospital for individuals who stated that they could not provide isolation at home were determined on the basis of provinces, but in the following process, implementation was insufficient. People who have tested positive for COVID-19 stayed at home by stating that they could provide isolation [42]. However, most of these individuals could not meet sufficient distance and cleaning measures with family members, and as a result of this contact, all households were infected.

Lack of Pandemic Management Culture in Individuals and Businesses (R2)

The increase of COVID-19 cases is closely related to the society’s compliance with measures such as social distance, hand hygiene and use of masks. Precautions and policies were not sufficient to prevent the spread of COVID-19 in their workplace for employers [43]. In addition, it was not enough to close the coffee shops or restaurants etc., where people could hang out in groups. Individuals continued to contact each other at home, on beaches, wedding ceremonies etc. instead of reducing contact with each other to the required level. Furthermore, many citizens do not maintain social distance and wear masks properly. As a result, most people got infected with COVID-19 and they cause to spread of virus throughout the community. Applying only the measures taken by government the pandemic will increase the number of cases and deaths if the necessary measures are not taken individually [37].

Lack of Health Literacy (R3)

During the pandemic process, communication network established between the society and responsible institutions to share information for COVID-19 pandemic. Thus, thanks to communication network, individuals should clearly know the importance of hygiene and distance measures and the possible consequences that may arise as a result of the implementation or non-application of these measures. In the current pandemic process, due to limited and inadequate health literacy, negative information bias leads to catastrophic thinking in the society, while positive information bias leads to unrealistic optimism [44]. In addition, for example, while citizens agree for vaccination, individuals who refuse to be vaccinated endanger not only their own health but also the public health based on adequate.

5.2.2. Technology

Efficiency of Tracking Applications (R4)

Through the Tracking Applications, the user codes that are checked at the entrance to the public areas are strictly followed by the officials. However, it is a matter of debate that the public uses the application regularly and correctly to manage the application data correctly. It is known that thousands of people are infected every day and, since people do not use the application sufficiently before it turns out to be positive, it cannot be determined with whom they exceeded the social distance, and the application cannot achieve its purpose. For this reason, the promotion and operation of the Tracking Applications should be made more widely and effectively [45].

Patients who want to get a vaccine appointment over the phone face problems such as line preoccupation, Tracking Applications is not functional in some areas, and most patients over the age of 60 are having hard times using the internet. In the mobile application, it is emphasized that technical problems caused the delay and sometimes inability to vaccinate [46].

Lack of Medical Technologies in diagnosis and treatment (R5)

A strong health technology infrastructure is one of the factors that facilitates the fight against pandemic. Many countries have assigned and supported experts in their fields for treatment and vaccination studies. Behind the success of countries such as Germany, South Korea, and China, which are among the successful examples of combating pandemics, is the high number of laboratories and high testing capacity [47].

If samples are taken from the contact persons for 5–7 days and are negative, the isolation periods are terminated on the 7th day. However, this period is insufficient considering the situations where people who have contact with one of their families live in the same house with positive patients during the isolation process. Because there is no 100% reliable method for diagnosis yet swab tests can give ‘false negative’ results [48]. In addition, it is known that a significant portion of the cases experience the process asymptomatically and these people are sometimes not tested because they do not show symptoms. These people cause the disease to spread without realizing that they are sick [49].

In some countries, the fact that a successful vaccine has not been developed, there is no COVID-19 treatment standard in practice, and the tests used are not yet 100% reliable, show that medical technologies are inadequate.

Lack of Infrastructure in Carrying out Mandatory Activities (R6)

Technological infrastructure is an important element for activities that should be carried out in educational institutions, businesses, etc. in combating the pandemic. Due to the lack of this infrastructure, many business employees could not switch to work from home and multiple cases have emerged in businesses. In addition, the disrupted educational activities have also created negative psychological effects on the people’s adoption of the pandemic culture.

5.2.3. Government

Lack of Strict Restrictions (R7)

During the coronavirus epidemic process, many countries had to take restrictive measures in unprecedented levels. The aim of the governments’ objective was to apply restrictions such as social distancing, curfew, travel etc. to reduce the spread of the virus [50]. However, public measures taken to control individuals’ compliance with the precautions have been insufficient. The uncertainty in business life and the suspension of the activities in many workplaces and schools accelerated the mobility and this caused the spread of virus in society [51].

Lack of Process Control in Normalization (R8)

The purpose of the normalization process should be to maintain life as close to normal as possible while keeping the number of diseases and deaths in the society as low as possible. WHO recommends that restrictions on travel and curfews be gradually lifted. Following the steps to be taken to reduce restrictions, their effects should be controlled. Experts state that the number of tests should be increased and contact tracking should be done strictly to control the epidemic rather than lifting the restrictions.

WHO recommends allowing activities gradually during the normalization period. However, before decision taken predictive models should be developed, tested, and the use of public spaces should be categorized. On the other hand, the normalization process in some countries was not realized as stated, and priority was given to normalization in areas such as “tourism”, where at the measures will be very difficult to apply.

Based on the statistics, it can be concluded that there was a serious decrease in the number of cases and patients during the curfews. The sudden reopening of the public areas, which enabled the crowds to coexist together, caused people who were closed at home for a period to perceive that the “virus danger has passed” or decreased and behave irresponsibly [45].

Flow of Information and Communication/ Trust in Institutions (R9)

King states that “information flow, trust in government and trust in institutions are important” to ensure people comply with restrictive measures [52]. The uncertainty of the messages given by the government or health authorities can cause confusion and fear in the public, which may make people to behave uncontrolled because they tend to take measures to secure themselves. For example, in the first days of the epidemic, people emptied the shelves in markets, and cash withdrawal queues were formed in front of ATMs. The closure that will start at 24:00 in Turkey was announced only two hours in advance, which caused a similar confusion. This type of confusion causes the disease to spread. Thus, citizens should be warned about fake news and false information, and information should be shared with the public in a timely and accurate manner.

Another of the most important elements in this process is the communication. Proper communication between health authorities, government, leaders, and public will encourage individuals to be conscious about the pandemic and take suitable actions to prevent its spread [53].

5.2.4. Economy

Insufficient Economic Resources Against Economic Anxiety (R10)

The strength of people to comply with their calls to stay at home is proportional to their jobs and economic situations. Poverty has become the key in determining the more sensitive segments of societies to restrictions [37]. While individuals with high income are trying to protect themselves from the epidemic by living in isolation in their homes in the outside world, those with low income and those who must work outside are more likely to get the disease [53].

The government, tried to help people in economic difficulties by announcing support packages. Various aid campaigns (such as “We Are Enough for Us”, “Pay the Bill For Others”) have been carried out for those who are unemployed or who are in poor financial situation after the decision of staying at home, and a large participation in them has been achieved. However, it is very difficult for governments as well as individuals to bear the economic difficulties caused by restrictions. For this reason, sometimes the economic resources required to implement public health and social measures may be insufficient [54], [55], [56].

Lack of Medical Facilities and Staff (R11)

The COVID-19 pandemic has increased the need for medical supply, healthcare facilities and healthcare professionals to a much higher than before [57]. With the onset of the pandemic, it is known that despite the rapid construction of emergency hospitals and the increase in healthcare worker employment, polyclinics are now evacuated and converted into COVID-19 services, and intensive care occupancy rates have reached high values in some provinces [58], [59], [60].

Approach in Policies that Prioritize the Economy (R12)

While taking precautions during the pandemic process, first, gathering of big groups such as stadiums and concerts should be prevented. If this measure is insufficient afterwards, measures such as medium-sized weddings, funerals, and if it continues, measures should be taken to prevent 10 people from coming together. The opposite should be followed when the measures are loosened [55]. However, in this process, the first loosened environments in some countries have been environments where thousands of people can coexist. This situation indicates that the pandemic management process has an approach that prioritizes the economy.

5.3. Attribute evaluation

Four main attributes available in risk assessment process are determined as evaluation criteria to evaluate risk factors shown in Fig. 3. The attributes and related explanations are shown in Fig. 4. Due to the nature of the COPRAS method, while “Likelihood of threat”, “Vulnerability” and “Impact or Severity” are determined as cost attributes, “Precaution” is determined as benefit attribute. While the cost attribute should be as low as possible, the benefit attribute should be as high as possible maximized.

Fig. 4.

Proposed risk assessment model.

Since q-ROFSs can be used to describe larger and more complex fuzzy information [61], [62] we developed a new risk assessment approach based on IVq-ROFS including maximization of the chance and outcomes of positive trials and minimization of the chance and outcomes of undesirable consequences. Accordingly, four attributes are evaluated by DMs using Table 5 and then, the importance weights of attributes are determined using IVq-ROFWG operator, which is given in Eq. (13).

First of all, the DM group (DM1, DM2, DM3, DM4 and DM5) consist of academicians in training and research hospitals and the member of medical and public health agencies are invited. Five DMs evaluated risk factors based on four important attributes using linguistic variables presented in Table 6. For example, DM1 rated the probability of “Insufficient Isolation at Home” risk occur as medium (M), the impact and vulnerability of this risk as medium high (MH) and high (H), respectively. The measures taken for this risk in society is evaluated as medium (M) by DM1. The evaluations made by other DMs are reported in Table 7.

Table 7.

The evaluations of DMs for risk factors considering risk factors.

DM1	R1	R2	R3	R4	R5	R6	R7	R8	R9	R10	R11	R12
Likelihood	M	MH	M	MH	MH	M	MH	H	M	MH	MH	H
Impact	MH	H	M	H	H	M	MH	VH	MH	H	H	VH
Vulnerability	H	H	M	H	VH	M	M	H	MH	MH	H	H
Precautions	M	MH	MH	MH	H	M	MH	VH	M	H	MH	VH
DM2	R1	R2	R3	R4	R5	R6	R7	R8	R9	R10	R11	R12
Likelihood	MH	H	MH	MH	H	MH	MH	H	MH	H	VH	H
Impact	MH	VH	M	H	MH	M	MH	VH	H	VH	H	H
Vulnerability	H	VH	MH	VH	H	M	MH	VH	MH	MH	H	H
Precautions	VH	MH	H	H	VH	MH	MH	VH	MH	H	H	VH
DM3	R1	R2	R3	R4	R5	R6	R7	R8	R9	R10	R11	R12
Likelihood	M	VH	H	MH	H	H	H	VH	MH	H	VH	VH
Impact	MH	VH	M	H	MH	M	MH	VH	MH	VH	EH	H
Vulnerability	H	VH	H	VH	H	H	H	VH	H	MH	VH	VH
Precautions	H	H	H	VH	VH	H	MH	H	H	VH	H	VH
DM4	R1	R2	R3	R4	R5	R6	R7	R8	R9	R10	R11	R12
Likelihood	MH	MH	L	M	L	M	MH	M	MH	M	M	MH
Impact	MH	H	M	MH	M	M	M	M	M	MH	M	MH
Vulnerability	M	H	ML	MH	ML	M	M	M	M	M	M	MH
Precautions	MH	MH	L	M	L	M	MH	M	MH	M	M	MH
DM5	R1	R2	R3	R4	R5	R6	R7	R8	R9	R10	R11	R12
Likelihood	M	M	M	MH	ML	M	M	MH	MH	MH	M	MH
Impact	L	MH	ML	MH	ML	M	MH	M	MH	M	MH	MH
Vulnerability	L	MH	ML	MH	ML	M	MH	M	MH	M	MH	MH
Precautions	M	M	M	MH	ML	M	M	MH	MH	MH	M	MH

The decision matrices are aggregated in one decision matrix using IVq-ROFWG operator. The results are given in Table 8.

Table 8.

Aggregated decision matrix.

Risk	Likelihood				Impact				Vulnerability				Precautions
	${\mu }^{-}$	${\mu }^{+}$	$v^{-}$	$v^{+}$	${\mu }^{-}$	${\mu }^{+}$	$v^{-}$	$v^{+}$	${\mu }^{-}$	${\mu }^{+}$	$v^{-}$	$v^{+}$	${\mu }^{-}$	${\mu }^{+}$	$v^{-}$	$v^{+}$
R1	0.538	0.588	0.470	0.519	0.522	0.574	0.536	0.582	0.552	0.605	0.535	0.580	0.609	0.660	0.433	0.479
R2	0.632	0.683	0.405	0.452	0.716	0.766	0.316	0.362	0.716	0.766	0.316	0.362	0.597	0.647	0.419	0.460
R3	0.501	0.553	0.551	0.598	0.478	0.528	0.527	0.577	0.507	0.558	0.526	0.574	0.536	0.588	0.538	0.502
R4	0.579	0.629	0.429	0.478	0.658	0.708	0.354	0.402	0.694	0.745	0.343	0.389	0.632	0.683	0.405	0.404
R5	0.512	0.565	0.559	0.605	0.550	0.601	0.485	0.532	0.575	0.627	0.505	0.550	0.557	0.611	0.554	0.529
R6	0.555	0.605	0.463	0.512	0.500	0.550	0.500	0.550	0.535	0.585	0.480	0.529	0.555	0.605	0.463	0.500
R7	0.597	0.647	0.419	0.467	0.579	0.629	0.429	0.478	0.575	0.626	0.443	0.492	0.579	0.629	0.429	0.471
R8	0.652	0.702	0.393	0.439	0.663	0.714	0.418	0.462	0.645	0.697	0.421	0.465	0.669	0.720	0.390	0.409
R9	0.579	0.629	0.429	0.478	0.597	0.647	0.419	0.467	0.597	0.647	0.419	0.467	0.597	0.647	0.419	0.460
R10	0.615	0.666	0.408	0.456	0.669	0.720	0.390	0.434	0.558	0.608	0.451	0.500	0.652	0.702	0.393	0.415
R11	0.626	0.677	0.430	0.476	0.667	0.718	0.393	0.438	0.652	0.702	0.393	0.439	0.593	0.644	0.435	0.448
R12	0.676	0.726	0.349	0.396	0.676	0.726	0.349	0.396	0.676	0.726	0.349	0.396	0.713	0.764	0.336	0.364

Once the aggregated decision matrix is normalized using Eqs. (25)–(26) the weights of attributes are multiplied by normalized decision matrix using Eqs. (27)–(28). The results are reported in Table 9.

Table 9.

Weighted normalized matrix.

	Likelihood				Impact				Vulnerability				Precautions
	${\mu }^{-}$	${\mu }^{+}$	$v^{-}$	$v^{+}$	${\mu }^{-}$	${\mu }^{+}$	$v^{-}$	$v^{+}$	${\mu }^{-}$	${\mu }^{+}$	$v^{-}$	$v^{+}$	${\mu }^{-}$	${\mu }^{+}$	$v^{-}$	$v^{+}$
R1	0.342	0.446	0.451	0.493	0.358	0.463	0.517	0.549	0.389	0.505	0.518	0.548	0.346	0.455	0.609	0.639
R2	0.402	0.518	0.391	0.438	0.491	0.618	0.308	0.360	0.504	0.639	0.308	0.357	0.335	0.437	0.597	0.626
R3	0.318	0.419	0.528	0.561	0.328	0.426	0.509	0.545	0.357	0.466	0.510	0.543	0.431	0.477	0.536	0.569
R4	0.368	0.477	0.412	0.459	0.451	0.571	0.343	0.392	0.488	0.621	0.333	0.378	0.324	0.383	0.632	0.661
R5	0.326	0.429	0.536	0.567	0.377	0.485	0.468	0.504	0.404	0.523	0.489	0.521	0.443	0.503	0.557	0.592
R6	0.353	0.459	0.445	0.487	0.343	0.443	0.483	0.520	0.376	0.488	0.465	0.502	0.371	0.475	0.555	0.586
R7	0.379	0.491	0.403	0.450	0.396	0.507	0.415	0.456	0.405	0.522	0.430	0.468	0.343	0.448	0.579	0.609
R8	0.414	0.533	0.379	0.428	0.454	0.576	0.405	0.442	0.454	0.581	0.408	0.445	0.312	0.389	0.669	0.697
R9	0.368	0.477	0.412	0.459	0.409	0.521	0.405	0.446	0.420	0.540	0.406	0.446	0.335	0.437	0.597	0.626
R10	0.391	0.505	0.393	0.441	0.459	0.581	0.377	0.418	0.392	0.507	0.437	0.476	0.315	0.394	0.652	0.680
R11	0.398	0.513	0.414	0.457	0.457	0.579	0.380	0.421	0.459	0.586	0.382	0.421	0.348	0.426	0.593	0.623
R12	0.430	0.551	0.338	0.398	0.463	0.585	0.338	0.386	0.476	0.606	0.339	0.384	0.269	0.345	0.713	0.739

Once the score functions of $P_i$ and $R_i$ are calculated, the relative weight of each risk factor Q is calculated. The priorities of risk factors are calculated using Equations given in Eqs. (31)–(32). The risk factors with the highest value is determined using Eq. (34) and the results are given in Table 10.

Table 10.

The relative weights and ranking of risk factors.

Risk factor	Q	U	Rank
R1	2.447	0.890	9
R2	2.599	0.945	3
R3	2.364	0.859	12
R4	2.590	0.941	4
R5	2.403	0.873	10
R6	2.393	0.870	11
R7	2.451	0.891	8
R8	2.634	0.958	2
R9	2.477	0.900	7
R10	2.568	0.934	5
R11	2.447	0.922	6
R12	2.568	1.000	1

5.4. Results

In normalization period “The Approach that Prioritizes the Economy in Policies”, “Insufficient Process Control in Normalization” and “Lack of Epidemic Management Culture in Individuals and Businesses” are detected as the most major factors to deal with COVID-19. It has been observed that these factors are frequently emphasized in the literature scanned at the beginning of the study and in the expert opinions. For this reason, it is possible to say that the results of the study reflect the truth.

It would be more accurate to consider the factors of “The Approach that Prioritizes the Economy in Policies” and “Insufficient Process Control in Normalization” together. These two factors are interrelated. WHO recommends the gradual lifting of restrictions such as travel and curfews. Modeling should be done and tested when deciding which measures should be mitigated first, and the use of public spaces as lower risk activities should be prioritized [45]. Thus, the effects of the alleviating of restrictions should be monitored in the social environment after 15 days, and decisions should be reconsidered at the end of this 15-day process.

In the normalization processes initiated in June 2020, March 2021 and July 2021, contrary to these recommendations, adequate control could not be achieved, and a rapid normalization process was experienced. First of all, the tourism sector returned to normal and public areas such as beaches, shopping malls, cafes, where the number of people and contact were high, were opened to public. This situation shows that there is an approach that prioritizes the economy in policies. The economic resources required to implement public health and social measures may be insufficient from time to time. Thus, it is possible to say that it is usual for the policies implemented to prioritize the economy at a certain level, and it would be more accurate to make strategy proposals specific to this factor by economists who are experts in the subject. However, whatever the reason may lie on the basis of the strategies applied, the practices must be ensured in order and control. Currently, pandemic restrictions have been lifted in countries, except for masks and social distance, and it is seen that the number of cases is increasing rapidly. It seems inevitable that the restrictions will be re-enacted in the future. However, serious strategies should be implemented to prevent the number of cases, which are predicted to decrease with the restrictions, from increasing as in previous times with the resumption of normalization. “Lack of Epidemic Management Culture in Individuals and Businesses” is actually interrelated with other factors. The increase in cases is closely related to the public’s compliance with measures such as social distance, hand cleaning and mask use, which are the measures that are not strictly complied by the public.

Recall the factors given in the application section and in line with the results, it can be said that the factors on the basis of “Human” and “Economy” rather than the factors on the basis of “Technology” and “Government”, are the most important factors to cope with the pandemic. Suggestions for what the authorities should consider to overcome these risk factors in the strategies to be implemented in the future are listed as follows:

• •The normalization process should be applied gradually and in a controlled manner, spreading over a long period of time. Entry/exit measures of environments where people can be found in groups should be increased. Businesses and individuals should be checked frequently for compliance with the measures taken by the government.
• •In order to comply with the maximum number of people determined within the framework of social distance rules for areas such as cafes, buses, shopping malls, and beaches, surveillance should be more frequent. However, due to these restrictions, updates should be made in fields such as bus times to prevent people from experiencing disability. Otherwise, the life of the people becomes difficult when the usage is restricted while the service remains at the same level.
• •Due to the lack of knowledge of individuals on this subject, clear, understandable, and detailed information should be provided to all households on how to provide isolation at the beginning of quarantine to infected individuals and households in order to prevent the spread of the virus.
• •Increasing the trust of individuals towards institutions and information flow is an important step to ensure compliance with the measures taken. For this reason, efforts should be made to convince the public that public spaces, political/social groups, and people who are central in these groups comply with the measures taken.

5.5. Sensitivity and comparison analysis

To validate the robustness of the proposed risk assessment model in determining risk factors to cope with COVID-19, a sensitivity analysis is performed. To apply sensitivity analysis, the rung q, as the most significant feature of the proposed IVq-ROF concept, is changed slightly and the ranking results for risk factors are investigated. In this study, q is selected as 5 to handle the uncertain information better in the base case. The effect of changing q in the ranking of risk factors are shown in Fig. 5. Sensitivity analyses confirmed that the proposed model is stable and efficient due to slight changes in the ranking results.

Fig. 5.

Sensitivity analysis results.

To verify effectiveness and feasibility of the approach a comparison analysis is conducted. To do comparison analysis the results of proposed approach are compared with Interval valued q-rung orthopair fuzzy hybrid averaging (IVq-ROFHA) operator proposed by Ju et al. [35], IVIF TOPSIS conducted by Budak et al. [63] and IVPF-COPRAS introduced by Seker [64]. The comparison results are given in Fig. 6. The comparative analysis results reveal that there is high consistency between proposed approach and existing approaches since the ranking order of the 12 risk factors are parallel. The differences are derived from the use of different fuzzy extensions in the whole process.

Fig. 6.

Comparative analysis results.

The results of sensitivity and comparison analyses demonstrates that the proposed risk assessment model to cope with COVID-19 is stable and practical for DMs. In addition, the proposed model produces feasible results since the results coincides with the ones shown in existing approaches.

6. Conclusion

In the global pandemic announced by WHO on January 30, 2020, the number of confirmed cases worldwide has reached 521 million and the number of deaths has reached 6.3 million by May 16, 2022 [2]. Almost all countries of the world have adopted various strategies to apply to their own societies. Many measures have been taken since the beginning of the pandemic but the situation is not very promising at the moment. The virus has once again started to increase its effect rapidly. With the increasing of daily number of cases, many countries started to experience the 4th wave concern in the pandemic. Despite the various measures implemented since the beginning of the pandemic, the fact that the number of cases reaches peak points from time to time is an indication that the measures applied are insufficient. Based on the results gathered from this study, to be able to take clearer steps in the measures and strategies implemented, it is necessary to clearly understand the reasons that hinder in this fight. In line with this reason, the risk factors that cause the spread of the epidemic were determined based on an extensive literature research and expert judgments. Subsequently, the risk levels of these factors were determined by considering certain criteria using IVq-ROF- COPRAS method.

According to the results of the proposed risk analysis to determine risk factors against COVID-19 in countries, the top three factors were “The Approach that Prioritizes the Economy in Policies”, “Insufficient Process Control in Normalization” and “Lack of Epidemic Management Culture in Individuals and Businesses”. It has been observed that these factors are frequently emphasized in the literature, in the expert opinions, and in the news sources as the reasons for the inability to overcome the pandemic. For this reason, it is possible to say that the results of the study reflect the fact.

To check the validity and robustness of the developed methodology, the analysis was also carried out with two existing methods available in the literature, and a comparative analysis and sensitivity analysis were carried out. As a result of these analyses, the proposed methodology produces consistent and effective results. For future work, the proposed methodology can be improved for the new risk analysis problems faced in real life under uncertain environments.

CRediT authorship contribution statement

Sukran Seker: Conceptualization, Methodology, Formal analysis, Writing – review & editing. Fatma Betül Bağlan: Writing – original draft, Writing – review & editing, Visualization. Nezir Aydin: Software, Investigation, Data curation, Writing – review & editing. Muhammet Deveci: Validation, Investigation, Data curation, Writing – review & editing. Weiping Ding: Supervision, Project administration, Writing – review & editing.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability

No data was used for the research described in the article.