Abstract
The assessment of the corporate environmental conduct in the context of social responsibility is a complex decision-making (DM) problem because of the contradictory evaluation criteria, qualitative judgments, and enormous uncertainties in the professional evaluation. The current methods of assessment do not capture expert hesitation well as well as fail to give balanced and transparent ranking of corporate environmental performance. To overcome these drawbacks, this paper will propose a problem-focused hybrid DM framework by combining the Pythagorean Fuzzy (PF) Analytic hierarchy Process (AHP) with Multi-Attribute Ideal-Real Comparative Analysis (MAIRCA) system.The expressive weaknesses of classical and intuitionistic fuzzy environments will be overcome by using pythagorean fuzzy sets (PFS). PF-AHP method is applied to obtain credible and uniform weights of social responsibility-based environmental criteria, and the MAIRCA methodology provides an objective and balanced ranking of corporate options by comparing ideal and real performances profile. Hypothetical case study is performed on six corporations with six evaluation criteria to demonstrate the relevance and usefulness of the proposed framework to decision support. The findings demonstrate that the proposed model of PF-AHP-MAIRCA has a higher level of discriminative power, transparency, and realistic decision support than any of the currently applicable fuzzy MCDM methods. The framework can provide useful information to corporate managers and policymakers who want to understand and compare corporate environmental behavior and improve it in accordance with the goals of social responsibility and sustainable development.
Keywords: AHP-MAIRCA, Behavior, Corporate, Environmental, Dimensions, Decision-making, Pythagorean fuzzy set, Social responsibility
Subject terms: Environmental social sciences, Mathematics and computing
Introduction
The more recent trend in business practices has made corporate environmental behavior highly prominent due to the alarming issues that societies are facing, including climate change, eroding natural resources, and the growing population pressure of sustainable development1. Business organizations are not only rated on their financial reports but also on the way they balance their operations with social responsibility and environmental stewardship. Corporate Social Responsibility (CSR) then provides a much-needed outlook through which ecological practices could be gauged and therefore organizations could give back to society in a positive manner yet cause minimal harm to the ecology2. In this respect, it is not only a managerial need, but also a social need to test the corporate environmental behavior3. This area of DM is complex and the stakeholders such as managers and investors, regulating or community bodies, are likely to hold different opinions and the aspects of evaluation are qualitative and quantitative. Traditional evaluation methods cannot capture the complexity and uncertainty inherent in human judgment. In order to address these weaknesses, the fuzzy set (FS) theory has been applied more in multi-criteria decision-making (MCDM)4. Among the various extensions, there is the PFS, which is particularly beneficial as it allows decision makers to consider more flexibility with respect to uncertainty, reluctance, and vagueness compared to classical or intuitionistic fuzzy sets (IFS). Systematic identification of the weight of the criteria, considering the uncertainty present in expert judgment about the dimensions of CSR, including environmental protection, regulatory compliance, energy efficiency5, and stakeholder engagement6, can be achieved using the PF-AHP7 Combined, this hybrid method ensures both rigor and flexibility, making it well-suited for real-world applications. The framework offers significant implications for practice and policy. It provides managers with a way to diagnose corporate environmental behavior by identifying strengths and weaknesses in their sustainability practices, assists policymakers by facilitating responsible corporate governance5, and enhances the level of trust in the community by improving accountability. Moreover, it enables institutions to reach their planning objectives in tandem with the overall goals of sustainable development, thus leading to conservation of the environment and sustainable long-term social welfare. To conclude, the present paper proposes a novel hybrid model PF- AHP-MAIRCA that would enable an assessment of corporate environmental behavior in terms of social responsibility. The framework is not only contribution to the methodological advancment of MCDM, but also offers viable information towards establishing a culture of sustainability and responsibility in corporate systems.
Although the role of corporate environmental responsibility is gradually increasing, the assessment of corporate environmental behavior is still a difficult task because of the discrepancy in evaluation parameters and the ambiguity of the expert judgments. Current CSR based assessment techniques tend to be based on crisp or restricted fuzzy models and do not sufficiently reflect expert uncertainty and can lead to unstable or biased rankings. This drawback shows the necessity of the systematic and uncertainty-conscious decision-making model that would offer valid and transparent assessment results.
Problem statement
Corporate environmental behavior is critical towards the attainment of sustainable development yet measurement is sometimes complicated. The reactions of companies to social responsibility vary significantly, and their environmental activities depend on a range of factors. To gain this diversity, organizations should be rated on several significant criteria, including:
Regulatory compliance (conformity to environmental laws and regulations).
Energy and material and resource efficiency.
Reducing pollution (waste management and reduction of emissions).
Green innovation (investment in environmentally friendly technologies).
Stakeholder involvement (responsiveness to communitarian and customer issues).
Transparency and reporting (disclosure of environmental information).
These criteria have been extensively utilized in the literature on corporate social responsibility and environmental sustainability to represent the regulatory compliance, efficiency in its operations, its capability to innovate, its interactions with its stakeholders, and its transparency, which are typical dimensions of CSR assessment systems. When different corporations (six in the present study) are rated against these six criterion, the decision makers are at bay. To begin with, the criteria are usually conflicting a company may be very active in the field of green innovations but not in compliance and transparency. Second, there is uncertainty and indecisiveness in the professional opinions about the corporate practices. The traditional evaluation measures have failed to capture this uncertainty and this can result into biased or incomplete rankings. We must address these issues by having a good DM model that would be able to deal with uncertainty in expert judgment and provide a balanced systematic ranking of corporations. Thus, the current research uses a hybrid PF-AHP-MAIRCA DM model to formally deal with uncertainty in professional decision making and offer a moderate ranking of corporate environmental performance.The PF-AHP helps in the establishment of the weight relative to the six criteria which also include expert hesitation and the MAIRCA method offers an impartial classification of the six corporations according to their overall environmental conduct. Through the framework, the research not only determines the best corporations in regards to environmental responsibility but it also informs the managers, policymakers and stakeholders on how to reinforce the practices of corporations to the advantage of the society and the environment.
Objectives and contribution
In this section we will discuss the Objectives and Contribution of this study.
The primary aim of the study is to come up with a logically consistent and uncertainty-conscious decision-making framework to assess the corporate environmental behavior within the social responsibility considerations. To be more precise, the study will focus on: (i) the identification of the important social responsibility-based environmental evaluation criteria; (ii) modeling the expert uncertainty and hesitation with the help of the Pythagorean fuzzy sets; (iii) the determination of the reliable criteria weights with the help of the PF-AHP method; and (iv) the objective ranking of the corporate alternatives with the help of the MAIRCA approach.
The study has the following Contributions.
This study contributes to the practice and research in a number of ways. Firstly, it introduces something novel to the PF-AHP-MAIRCA methodology of measuring the environmental behavior of companies. This combination has received little literature studies. Second, it adds to the usage of FS extensions, which proves that PFS may be more effective as the tool of expressing hesitation and uncertainty in DM in relation to CSR. Third, the study provides a clear picture of differences between corporations in environmental practices, in form of a Hypothetical case study, educating managers and policymakers to come up with more sustainable practices. Finally, the framework will be included in the wider corporate social responsibility agenda since it will offer a more open and versatile tool that can be implemented in industries to improve accountability, sustainability and long-term social gains.
Research question and motivation
In this section we will discuss the research questions and motivation of this study.
The research question that the study attempts to address is as follows: How can corporate environmental behavior be assessed in an organized and obscurity-conscious way through the social responsibility factor by a hybrid Pythagorean fuzzy DM model?
The study has the following Motivation:
This study is motivated by the growing need on businesses to be responsible to the environment and society. Business companies are not evaluated solely on their profits anymore but also on the sphere of sustainability and social responsibility. Nevertheless, it is a complicated process to assess corporate actions in the environmental field; therefore, numerous criteria can be used, such as compliance, innovativeness, resource productivity, and transparency, and the issue of subjectivity of the assessor expertise. The measurement mechanisms used at the moment are more likely to be incapable of dealing with this complexity on a comprehensive level, and generate data that are not always a fair reflection of reality. By providing a strict and adaptable framework, the given research will provide a blend of PF-AHP-MAIRCA, which will allow decision makers, policy makers and the stake holders to possess a reliable tool to evaluate and compare the behaviour of corporations in the environmental spheres. The long-term objective will be to assist organizations to adopt sustainable practices that will have an impact that is positive to the society and environment.
Literature review
The phenomenon of corporate environmental behavior (CEB)6 is extensively analyzed as one of the components of Corporate Social Responsibility (CSR) and environmental social and governance (ESG)8 programs. Past research has evaluated the approaches used by firms to control emissions, minimize energy consumption, optimize resources, promote green innovation, and comply with environmental regulations. Most standard methods are based on indices based on ISO 14,001 certifications, GRI-based disclosures, or industry benchmarks or indicators related to stakeholders, such as community impact and supply chain practices. To a large extent, methodologically, most studies are divided into three streams: disclosure and scoring models, which translate voluntary reports into quantifiable indices; econometric and panel studies9, which relate environmental practices with financial or social results; and MCDM models10, which compare various criteria. Some of these methods, including AHP11, TOPSIS12, VIKOR13, PROMETHEE14, EDAS15, WASPAS16, and MARCOS17, have received broad applications in sustainability18, CSR, green supplier evaluation19, energy planning20, and ESG decision analytics. Although successful in other settings, conventional MCDM techniques presuppose accurate judgments and full information which is not always the case given the uncertainty of expert judgments or the incompleteness of corporate disclosure. To address these shortcomings, investigators have increasingly resorted to fuzzy methods. The fuzzy sets21 of Zadeh were used to describe linguistic terms like the high or moderate performance and make the evaluation less strict in the early work. With the increasing complexity of CSR assessments, IFS22 were developed to explicitly represent membership, non-membership and hesitation, to be able to express the doubt more fully. AHP and TOPSIS approaches based on IFS started to be used commonly in CSR assessment, to minimize overconfidence in one-point ratings. Based on these advances, PFS23 were proposed as a more generalized counterpart. In contrast to IFS, where the sum of membership degree MD and non-membership degree NMD is constrained to one, PFS is quadratic in nature, i.e., the sum of the squares of the membership and the squares of the non-membership degrees is not more than one. This maturity framework provides DM with additional room to articulate indecisiveness and nuanced entitlement. It comes in handy in a sustainability and CSR setting, where data is diffuse and the levels of specialist conviction differ. Research has indicated that PFS-based techniques tend to give more consistent and discriminating outputs, particularly when dealing with a group DM process wherein the views are not homogeneous. Ranking methods have also been developed in conjunction with FS. MAIRCA24 is a method used to rank alternatives based on a comparison with ideal-real profile. Compared to approaches that only focus on proximity to an ideal, MAIRCA not only focuses on the best possible case but also examines the realistic distribution of preferences, which minimizes the likelihood of one criterion with a heavy weight dominating the result. Although MAIRCA has been utilized in other areas like energy planning, selection of suppliers and assessment of infrastructure, it has not been extensively used in the context of CSR-inspired corporate environmental behavior. In areas where it has been used, the approach has demonstrated a high potential of optimization in trade-offs between compliance, efficiency, and innovation. These advances notwithstanding, several research gaps remain. Even various CSR assessments continue to use sharp or simple fuzzy methods, which do not adequately reflect the uncertainty and uncertainty as to expert judgments moreover, deriving weights and ranking alternatives usually are done separately, which restricts methodological consistency. There is also a lack of sensitivity analyses, which reduces transparency and complicates the comprehension of how the results could vary in the event of different assumptions. Lastly, certain current frameworks adopt comprehensive criteria that combine environmental and governance variables, and it becomes more challenging to derive results that are uniquely applicable in terms of corporate environmental behavior. Against these gaps, one can evidently see a necessity of a framework that incorporates sound fuzzy weighting and ranking techniques and targets explicitly the CSR-based dimensions of the environment, including compliance, eco-efficiency, circularity, pollution prevention, stakeholder engagement, and green innovation. This paper addresses that need and provides a powerful instrument to evaluate corporate environmental behavior in the prism of social responsibility by implementing a PF-AHP-based criteria weighting process and the MAIRCA-based method of ranking.
Despite the fact that other researchers have applied different MCDM methods to the CSR and environmental performance assessment, most of them use crisp or basic fuzzy models and do not combine criteria weighting and ranking of alternatives. In addition, little has been done to explicitly model expert hesitation in an integrated CSR-oriented DM framework. The research fills these gaps by integrating Pythagorean fuzzy logic with a single PF-AHP-MAIRCA model, giving the research greater theoretical conformity and a methodological fit.
Preliminaries
In this section we will define some basic concepts of Fuzzy sets (FS), and Intuitionistic Fuzzy set (IFS) Pythagorean fuzzy set (PFS) and its Score function.
Definition 1
21: Let 
be a universal set. Then a FS 
on 
is defined as:
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1 |
Definition 2
22: Consider a fixed universe
, then an intuitionistic fuzzy set (IFS)
on 
is defined as:
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2 |
where
represents the MD 
represents the NMD. These degrees satisfy the following condition:
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3 |
Where the hesitancy degree is 
.
Definition 3
23: Consider a fixed universe
, then a Pythagorean fuzzy set (PFS)
on 
is defined as:
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4 |
where
represents the MD
represents the NMD. These degrees satisfy the following condition:
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5 |
Where the hesitancy degree is 
.
Definition 4
25: The score function for PFS is defined as:
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6 |
Pythagorean Fuzzy AHP-MAIRCA method
This study employs the MAIRCA24 method combined with the AHP approach to solve an MCDM problem involving PFS uncertainty. To address these challenges, an effective decision-making technique is introduced. The main goal of any MCDM26 The problem is to rank alternatives based on the given criteria. This section outlines the formulation of the MAIRCA method, integrated with PFS, for analyzing Decision Strategy for Understanding Consumer Value Perspectives in Purchasing. Let us consider 
a set of m alternatives and
. To address the complexities and uncertainties affecting decision-making reliability, the hybrid AHP-MAIRCA method combines two contrasting MCDM techniques for optimal results. MAIRCA emphasizes logical comparison of ideal and actual alternatives, supporting transparent and preference-driven ranking. Meanwhile, AHP objectively assigns weights to evaluation criteria by evaluating their contrast and conflict levels. This integration offers a balanced approach that considers decision-makers’ preferences through MAIRCA and leverages data-driven weighting with AHP, making it particularly effective for uncertain, multi-criteria scenarios, such as evaluating the Consumer value of a purchasing strategy.
The AHP-MAIRCA has following steps:
This section presents an algorithm for MADM within the AHP framework based on PFS. We first generate a decision matrix using PF value and then use it to find the CI, after which we can generate the WVs. Thereafter, the following is the process involved in this procedure:
Weight vector calculation:
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i.
Construct the fuzzy Decision matrix by taking the Experts’ Opinion. Since we are in the PF framework, we shall take membership degree (MD) and non-membership degree (NMD) against each of the criteria in the form of:
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After the Decision matrix is formed, in the next step we will defuzzify the matrix by using this formula:
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Where 
.
Step 1
We construct a PF value-based decision matrix and perform pairwise comparisons of the available options.
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9 |
Where 
shows the relative significance of standard 
.
Where 
.
Step 7
To obtain weight vectors (WVs), The decision matrix is normalized to bring the criteria values on a comparative scale. The normalization takes into consideration the kind of each criterion (benefit or cost) following the MAIRCA procedure. In the case of benefits criteria, an increased defuzzifed score is favorable. On cost criteria, a lower score would be desirable, and this is taken care of in normalization process. The normalized value 
of alternative i under criterion j is obtained by dividing its defuzzifed score with the sum total of the absolute values of all alternatives scores on the criterion. This method normalizes the scale and as it was discovered later in the case study could lead to normalized values that are either positive or negative, which are performance-based on the type of criterion.
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Step 8
Check the confidence interval (CI) of the calculated value using the formula below. The value of CI of the computed 
is checked using the assistance of the following formula.
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Where,
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And 
is the alternative number.
Where 
must belongs to 
.
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ii.
In this step, we will use the normalized obtained from Eq. 10 to find the theoretical Assessment matrix. The formula use to find the theoretical assessment matrix is:
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Where 
is number of elements of weights.
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iii.
After the theoretical Assessment matrix find Absolute difference matrix by using the equation given below:
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iv.
In these steps we will calculate the deviations degrees using the formula given below. After that we will use deviation degrees to find the rankings of Alternatives:
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v.
Rank the Alternatives in ascending Order.
Here is visual representation of AHP-MAIRCA method steps and given in Fig. 1.
Fig. 1.
Steps of the PF-AHP-MAIRCA approach.
Case study
The presented case study is a simulation of a CSR-based environmental assessment of six companies operating in the energy, chemical, technology, agriculture, construction, and retail sectors. The choice of these sectors was based on the fact that their environmental impacts and CSR requirements differ substantially. In the case study, modeling expert hesitation and uncertainty using PF evaluations, combined with PF-AHP and MAIRCA, yields transparent weights and consistent rankings. To demonstrate the feasibility of this PF-AHP-MAIRCA framework, we develop a hypothetical case study that assesses the environmental behavior of corporations through the lens of social responsibility. The case study is based on six criteria 
and six alternatives 
. We will use these criteria to choose a suitable alternative from the given. In this case study, we will apply our proposed methodology, utilizing the AHP method to calculate weights and the MAIRCA method to rank alternatives.The evaluation criteria adopted in this case study is based on existing literature regarding corporate social responsibility and environmental sustainability. These dimensions have the regulatory, operational, environmental, innovation-driven, stakeholder-oriented, and disclosure-related factors that together constitute the corporate environmental behavior within a CSR framework. The Description of criteria and alternatives is given in Tables 1 and 2.
Table 1.
Description table of criteria.
| Criteria | Name | Description |
|---|---|---|
|
Regulatory Compliance | How far a company lives up to the environment laws, standards and policies. |
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Resource Efficiency | Utilizing energy, water and raw materials efficiently to minimize waste and expenses. |
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Pollution Control | Actions taken to curb air, water and soil pollution. |
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Green Innovation | Commitment in sustainable processes, technologies, and products that are environmentally friendly. |
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Stakeholder Engagement | The extent to which the company engages and reacts to customers, employees and communities in matters related to the environment. |
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Transparency & Reporting | The good and clear environmental reporting, disclosure and sustainability reports. |
Table 2.
Description table of alternatives.
| Alternative Code | Corporation | Description |
|---|---|---|
|
EcoEnergy Ltd. | Good emphasis on the use of renewable energy but little in the community. |
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GreenChem Corp. | A company which has superior pollution control systems and has lower standards of reporting. |
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FutureTech Inc. | Green-based technology company with the focus on green innovation and environmentally-friendly product design. |
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AgroSustain Pvt. | Farming-based company with resources efficiency and compliance but might not be very active in the field of innovation. |
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UrbanBuild Co. | Construction firm that has had a good stakeholder interaction but lacks in the control of pollution. |
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GlobalRetailers | High transparency but low resource efficiency MNC retail chain with high reporting transparency and low resource efficiency. |
The chosen corporate options are the companies that have different environmental plans and performance characterization. This diversity will allow giving an important comparison and accentuate the effects of differences between the CSR dimensions on the overall environmental ratings.
Numerical evaluation
The steps that are followed are the implementation of the PF-AHP-MAIRCA framework where each stage is made to rectify uncertainty in the expert judgments and the smooth progression of the criteria weighting stage to alternative ranking stage.
Step 1. Construct the fuzzy Decision matrix by taking the Experts’ Opinion. As we are working in PF frame work we will take a MD and NMD against each criterion as shown in Table 3:
Table 3.
PF-Decision matrix.
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Where 
are MD and NMD and must belongs to 
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Step 2. After the Decision matrix is formed, in the next step we will defuzzify (Score) the matrix by using this formula as shown in Table 4.
Table 4.
Defuzzification of matrix.
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Where 
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Step 3. In this step, we will normalize the decision matrix. Normalization is based on Cost and Benefit type criterion. For cost type criterion Normalization is needed. Divide all the entries in a column by the sum of the column The Normalized matrix is shown in Table 5.
Table 5.
Normalized matrix.
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Step 4. After normalization, the next step is to calculate the criteria weights that we will use to rank the alternatives after applying the MAIRCA approach. An average normalized values of each row gives weight. The weights are calculated as the average of normalized values of each criterion (column) The weights from Normalized matrix are given in Table 6.
Table 6.
Criteria weights.
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It can be noted that the negative values in the normalized and weight matrices can be attributed to the reverse normalization of cost-type measures where smaller numerical values indicate superior performance and it does not necessarily mean poor performance.
Step 5. In this step we will use the normalized obtained from Eq. 8 to find the theoretical Assessment matrix. The formula use to find the theoretical assessment matrix is shown in Table 7.
Table 7.
Theoretical assessment matrix.
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Where 
is number of elements of weights.
Step 6. After theoretical Assessment matrix find Absolute difference matrix by using the equation given below in Table 8.
Table 8.
Absolute difference matrix.
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Step 7. In these steps we will calculate the deviations degrees using the formula given below. After that we will use deviation degrees to find the rankings of alternatives: rank the alternatives in ascending order as shown in Table 9.
Table 9.
Ranking of alternatives.
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Step 8. The graphical representation of ranking is given in Fig. 2.
Fig. 2.
Ranking of alternatives.
Result discussion
The findings of the recommended PF-AHP-MAIRCA framework were presented in the table above, in which six corporate options were compared with six social responsibility-based environmental standards. The ranking results show that 
scored the best and got the first position followed by 
in the second position and 
in the third position. 
and 
held the medium positions whereas 
had the lowest score and was ranked last. These results imply that 
is doing well in most of the dimensions of environmental behavior especially when it comes to compliance, resource efficiency, and innovation. Conversely, 
is performing behind because it is not performing well in several parameters and this shows areas that should be improved. The balanced ranking also demonstrates that some businesses can be good in terms of innovation or reporting, however, their performance can be weak in terms of pollution control or stakeholder engagement which influences their overall results. The ultimate advantage of the study is that the PF-AHP-MAIRCA method is much better than the conventional methods, such as the classical AHP-TOPSIS method or the IF MCDM method. Firstly, by using the Pythagorean fuzzy sets, the decision makers can express hesitation and uncertainty more adequately, and this is quite common with CSR evaluations, where judgment is subjective and incomplete. In contrast to IFS, PFS offers a greater range of membership and non-membership, and therefore, it is a more accurate model of expert judgments. Second, AHP quantitatively identifies the relative importance of the CSR criteria, and MAIRCA quantitatively ranks them by comparing actual performance to an ideal-real profile. This prevents favoritism to one overruling criterion and creates less discriminative and more balanced rankings. All in all, the findings prove that the given framework is not only practical but also stronger, more sensitive and transparent than others. It provides managers and policymakers a better understanding of corporate environmental behavior, reveals the strengths and weaknesses of the practices carried out in the organizations and asks the firms to engage in strategies that are more aligned to the objectives of social responsibility and sustainability. The ranking variance also shows that good results in one dimension of CSR cannot be used to gain a high ranking. The companies with balanced results in terms of compliance, efficiency, innovation, and stakeholder engagement will be ranked higher, but the weaknesses in terms of pollution control or transparency will be rated as a major setback. This shows that the proposed framework is sensitive to detect trade-offs between the dimensions of CSR and is applicable in diagnosing certain areas that need improvement.
Qualitative comparative analysis
In this section We will now make a comparative analysis of this study and some of the existing frameworks and methods in this section. This comparison will contribute in proving the better quality of this study as compared to the current ones. In a bid to highlight the advantage of the proposed model of the PF-AHP-MAIRCA, the proposed method will be contrasted to the existing methodologies, including classical Fuzzy AHP and IF-AHP. The four major aspects in which the comparison is carried out are the coping with uncertainty, the description of hesitation, ranking transparency, and DM strength. The Table 10 illustrates a trait comparative analysis of this work.
Table 10.
Characteristic Comparative Analysis.
| Feature | Fuzzy AHP | IF- AHP | PF- AHP–MAIRCA |
|---|---|---|---|
| Handles uncertainty effectively | ✓ | ✓ | ✓ |
| Captures hesitation clearly | ✗ | ✓ | ✓✓ (more flexible) |
| Balanced and transparent ranking | ✗ | ✗ | ✓ |
| Robustness in complex CSR issues | ✗ | Partial | ✓ |
| Practical applicability | ✓ | ✓ | ✓✓ (stronger) |
The given comparison proves that the Fuzzy AHP and IF-AHP can be useful due to their capability to offer a valuable weighting mechanism, yet, they do not provide the ability to capture a more subtle hesitation and offer balanced ranking mechanisms to overall CSR evaluations. PF-AHP-MAIRCA, by contrast, provides greater flexibility than IFS in representing hesitation and expert uncertainty, thereby allowing more realistic reflection. In addition, when used with MAIRCA, it allows constructing transparent and objective rankings of what is achieved in comparison with an ideal-real profile, which deemphasizes bias in one and the most dominant criterion. This not only makes the suggested framework methodologically stronger but also more realistic in the context of practical application on the subject of the determination of corporate environmental behavior under the conditions of social responsibility.
Sensitivity analysis
In this section Table 11 shows the sensitivity analysis for this study by changing the weights.
Table 11.
Sensitivity Analysis under Weight Perturbation.
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The sensitivity analysis was done to test the stability and strength of the proposed decision-making outcomes, in case of a potential change in the importance of the criteria. In particular, the weight of the strongest criteria (
and 
) was incrementally added by 
The weight of the criteria was proportionally changes to ensure that the overall weight was equal to 1, however 0.20 was used. The ultimate performance scores of options were re-calculated in each case. The findings indicate that the ranking pattern is very much stable with an overall ranking pattern of 
constantly takes the first place, then,
and there are slight variations between mid-ranked alternatives in some few instances only. That this finding confirms that the acquired ranking is not particular to moderate weight changes, which proves the reliability, consistency and strength of the proposed model in assessing the corporate environmental conduct in terms of social responsibility dimensions. The graphical representation of the sensitivity analysis is shown in Fig. 3.
Fig. 3.
Sensitivity analysis by changing weights.
Advantages of study
In this section we will discuss the advantages of this study.
There are several strengths associated with the current study. First, it provides a full-fledged evaluation system, thus, combining weighting (PF-AHP) with ranking (MAIRCA), in such a way that the decisions will be systematic and balanced. Second, the framework can more effectively model hesitation and uncertainty in expert judgments than classical or IF approaches as it makes use of PFS. This makes the outcomes more believable and valid. Third, the addition of the CSR compliance, innovation and stakeholder engagement dimensions ensures that the corporate environmental behavior can be assessed not only with the help of technical perspective but also with the help of its social responsibility that is one of the contemporary global concerns. Fourth, the applicability of the framework to practical application is manifested in the case study because it shows that corporations can be equitably and transparently compared. Finally, the framework is flexible and general i.e. it may be applied to other sectors, regions or the policy environment as a guideline that can enable managers, policymakers and other individuals within a society to be more sustainable and responsible.
Limitations and future direction
In this section, we will discuss the Limitations and future directions of this study.
The research has limitations even though this study is original and practical. The case study is based on hypothetical information and limited number of criteria and decisions that may not be representative of the reality of the actual corporate environmental practices. Its framework is also premised on the opinion of experts, which, despite being run on PFS, can result in subjectivity of the assessment process. The paper is also devoted to six aspects; practically the impacts of the supply chain or lifecycle analysis are the possible aspects and industry-dependent considerations that the supply chain of corporations can rely on. Such limitations mean that the given model is powerful, whereas the outcomes should be viewed as illustrative and not final.
The study has following Future Directions.
Future research can be continued in this work through several avenues. To assess the effectiveness of the framework, one can first refer to it in real case studies involving larger datasets and actual corporate performance measures. Second it is possible to add more criteria and sub-criteria to capture industry specifics of the environmental behavior e.g. carbon footprint, practices of a circular economy or biodiversity impact. Third, the model can be further extended with other more complex extensions of FS such as q-rung orthopair fuzzy sets (QROFS)27 or spherical fuzzy sets (SFS)28 in order to be more aspective of uncertainty. Finally, comparative studies can be considered in future research, taking advantage of the given framework to apply it to either industries or various countries, which would provide valuable data on international trends in corporate social responsibility and environmental friendliness.
Conclusion
This paper has come up with a new hybrid PF-AHP-MAIRCA model to assess the corporate behavior on environment amid the issue of social responsibility. The uncertainty and reluctance to take decisive action of expert judgment inherent in the model is dealt with by the use of the expressive power of PFS in a logically consistent weighting and ranking process. A hypothetical case study showed the efficiency of the framework. It affirmed that high overall performance involves balanced strength in various dimensions of CSR - regulatory compliance, green innovation, and stakeholder engagement as opposed to excellence in one dimension. This result answers the main research question directly and in a structured, uncertainty-aware way, which offers a comparative corporate evaluation approach. Three major contributions are made by the research. In theory, it is a step towards improving fuzzy MCDM through a meaningful combination of PFS and AHP-MAIRCA hybrid in CSR-based assessments. In practice, it provides a diagnostic resource to managers to detect the strengths and weaknesses of environmental practices. To policymakers, it aids in the design of transparent and multi-criteria and evaluation systems which should encourage accountability and sustainable development within corporations, even though its shortcomings such as the use of hypothetical information are also recognized in Sect. 4.5. The future research would incorporate the model into real-life data and investigate how it can be extended to other sophisticated fuzzy sets representations to make the model more general.
Author contributions
Qing Sun contributed fully in this study.
Data availability
The data used in the given study is hypothetical and is generated synthetically to test its methods. All evaluation data and decision matrices are completely outlined in the manuscript.
Code availability
The computational framework and calculation workflow used to generate the results are provided as a structured Microsoft Excel file and are publicly available via Zenodo at 10.5281/zenodo.19402095. The file contains all intermediate steps, formula-based computations, and ranking procedures required to reproduce the analysis.
Declarations
Competing interests
The authors declare no competing interests.
Footnotes
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
References
- 1.Wang, X., He, T., Wang, S. & Zhao, H. The impact of artificial intelligence on economic growth from the perspective of population external system. Soc. Sci. Comput. Rev.43(1), 129–147. 10.1177/08944393241246100 (2025). [Google Scholar]
- 2.Alamandi, M. Sustainable innovation management: Balancing economic growth and environmental responsibility. Sustainability17(10), 4362. 10.3390/su17104362 (2025). [Google Scholar]
- 3.Aktaş, N. & Demirel, N. A hybrid framework for evaluating corporate sustainability using multi-criteria decision making. Environ. Dev. Sustain.23(10), 15591–15618. 10.1007/s10668-021-01311-5 (2021). [Google Scholar]
- 4.Mahmood, T., Ullah, K., Khan, Q. & Jan, N. An approach toward decision-making and medical diagnosis problems using the concept of spherical fuzzy sets. Neural Comput & Applic31(11), 7041–7053. 10.1007/s00521-018-3521-2 (2019). [Google Scholar]
- 5.Abbasi, S. Environmental impact assessment with rapid impact assessment matrix method during the COVID-19 pandemic: A case study in Tehran, (2023).
- 6.Lee, H., Kurisu, K. & Hanaki, K. Influential factors on pro-environmental behaviors—a case study in Tokyo and Seoul. LCE04, 104–116. 10.4236/lce.2013.43011 (2013). [Google Scholar]
- 7.Buyukozkan, G. & Gocer, F. A novel approach integrating AHP and COPRAS under Pythagorean fuzzy sets for digital supply chain partner selection. IEEE Trans. Eng. Manag.68(5), 1486–1503 (2019). [Google Scholar]
- 8.Meng, X. & Shaikh, G. M. Evaluating environmental, social, and governance criteria and green finance investment strategies using fuzzy AHP and fuzzy WASPAS. Sustainability15(8), 6786 (2023). [Google Scholar]
- 9.Ullah, A. Entropy, divergence and distance measures with econometric applications. J. Stat. Plan. Inference49(1), 137–162. 10.1016/0378-3758(95)00034-8 (1996). [Google Scholar]
- 10.Ullah, K., Hussain, A., Yin, S. & Pamucar, D. Intuitionistic Fuzzy Information Aggregation Based on Sugeno-Weber Triangular Norms. In Intelligent and Fuzzy Systems Vol. 1089 (eds Kahraman, C. et al.) 783–791 (Springer Nature Switzerland, 2024). 10.1007/978-3-031-67195-1_86. [Google Scholar]
- 11.Akusta, E., Ari, A. & Cergibozan, R. Barriers to renewable energy investments in Turkiye: A fuzzy AHP approach. Renew. Energy240, 122161. 10.1016/j.renene.2024.122161 (2025). [Google Scholar]
- 12.Abdelhafeez, A., Shreyas, J. & Udayaprasad, P. K. A fuzzy TOPSIS method for assessment blockchain technology strategies. Information Sciences with Applications1, 1–9 (2024). [Google Scholar]
- 13.Akram, M., Kahraman, C. & Zahid, K. Group decision-making based on complex spherical fuzzy VIKOR approach. Knowl.-Based Syst.216, 106793 (2021). [Google Scholar]
- 14.Agrawal, N. Multi-criteria decision-making toward supplier selection: Exploration of PROMETHEE II method. Benchmarking Int. J.29(7), 2122–2146 (2022). [Google Scholar]
- 15.Ashraf, S. & others A circular spherical fuzzy EDAS approach for selection problems under uncertainty. IEEE Access.11, 23456–23472 (2023). [Google Scholar]
- 16.Albaity, M., Mahmood, T. & Ali, Z. Impact of machine learning and artificial intelligence in business based on intuitionistic fuzzy soft WASPAS method. Mathematics11(6), 6. 10.3390/math11061453 (2023). [Google Scholar]
- 17.Ali, J. A q-rung orthopair fuzzy MARCOS method using novel score function and its application to solid waste management. Appl. Intell.52(8), 8770–8792. 10.1007/s10489-021-02921-2 (2022). [Google Scholar]
- 18.Kaur, P., Verma, R. & Mahanti, N. C. Selection of vendor using analytical hierarchy process based on fuzzy preference programming. OPSEARCH47(1), 16–34. 10.1007/s12597-010-0002-5 (2010). [Google Scholar]
- 19.Kaur, P., Dutta, V., Pradhan, B. L., Haldar, S. & Chauhan, S. A pythagorean fuzzy approach for sustainable supplier selection using TODIM. Math. Probl. Eng.2021(1), 4254894. 10.1155/2021/4254894 (2021). [Google Scholar]
- 20.Kaur, P., Roy, S. & Kaur, G. Circular economy practices: A case with priority selection under multi-criteria decision-making. Circ. Econ. Sust.10.1007/s43615-025-00572-w (2025). [Google Scholar]
- 21.Zadeh, L. A. Fuzzy sets. Inf. Control8(3), 338–353 (1965). [Google Scholar]
- 22.Atanassov, K. T. Intuitionistic fuzzy sets. Fuzzy Sets Syst.20(1), 87–96. 10.1016/S0165-0114(86)80034-3 (1986). [Google Scholar]
- 23.Yager, R. R. Pythagorean fuzzy subsets, in 2013 joint IFSA world congress and NAFIPS annual meeting (IFSA/NAFIPS), IEEE, pp. 57–61. (2013).
- 24.Ecer, F. An extended MAIRCA method using intuitionistic fuzzy sets for coronavirus vaccine selection in the age of COVID-19. Neural Comput. Appl.34 (7), 5603–5623 (2022). [DOI] [PMC free article] [PubMed] [Google Scholar]
- 25.Yager, R. R. Pythagorean membership grades in multicriteria decision making. IEEE Trans. Fuzzy Syst.22(4), 958–965. 10.1109/TFUZZ.2013.2278989 (2014). [Google Scholar]
- 26.Alshamsi, A. M., El-Kassabi, H., Serhani, M. A. & Bouhaddioui, C. A multi-criteria decision-making (MCDM) approach for data-driven distance learning recommendations. Educ. Inf. Technol.28(8), 10421–10458. 10.1007/s10639-023-11589-9 (2023). [DOI] [PMC free article] [PubMed] [Google Scholar]
- 27.Qiyas, M., Naeem, M. & Khan, N. Confidence levels complex q-rung orthopair fuzzy aggregation operators and its application in decision making problem. Symmetry14(12), 2638 (2022). [Google Scholar]
- 28.Ajay, D. et al. Einstein exponential operation laws of spherical fuzzy sets and aggregation operators in decision making. Multimed. Tools Appl.82(27), 41767–41790. 10.1007/s11042-023-14532-9 (2023). [DOI] [PMC free article] [PubMed] [Google Scholar]
Associated Data
This section collects any data citations, data availability statements, or supplementary materials included in this article.
Data Availability Statement
The data used in the given study is hypothetical and is generated synthetically to test its methods. All evaluation data and decision matrices are completely outlined in the manuscript.
The computational framework and calculation workflow used to generate the results are provided as a structured Microsoft Excel file and are publicly available via Zenodo at 10.5281/zenodo.19402095. The file contains all intermediate steps, formula-based computations, and ranking procedures required to reproduce the analysis.