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Implications of industry 4.0 (I4.0) for sustainable development have gained widespread attention from the perspectives of the circular economy, triple bottom line and sustainable supply chain. Evaluation of I4.0 enabling technologies to achieve digital transformation in the photovoltaic supply chain (PVSC) considers several aspects of sustainability and uncertain information. Therefore, the present work aims to develop a new decision-making framework for identifying I4.0 enablers as the ways to achieve digital transformation in the PVSC. The present framework is developed based on the combination of generalized Dombi operators, integrated objective-subjective weighting model and the weighted sum product method under interval-valued Pythagorean fuzzy (IVPF) environment. For this purpose, firstly some generalized weighted Dombi operators and their properties are introduced to aggregate the IVPF information. Second, an integrated weighting procedure is developed by combining the objective weights through proposed interval-valued Pythagorean fuzzy entropy-based formula and subjective weights through IVPF-Pivot Pairwise relative Criteria Importance Assessment model. Further, the practicability and effectiveness of the proposed model is tested on a case study of I4.0 enablers to achieve digital transformation in the PVSC from sustainability perspective. The result shows the significance degrees of social, environmental and economic dimensions are 0.2258, 0.4947 and 0.2795, respectively and the big data and data analytics should be chosen as the most suitable choice among others for given data. At last, sensitivity and comparative analyses are discussed to illustrate the reliability and robustness of the obtained result. The study emphasizes the practical consequences of the role and use of the triple bottom line in I4.0 implementation in PVSC sectors. The findings of this study help the policymakers and managers to achieve digital transformation in the photovoltaic sustainable supply chain through I4.0 technologies. [ABSTRACT FROM AUTHOR]

The present work proposes a new decision support tool for assessing the sustainable suppliers in the healthcare supply chain. For this purpose, the classical Measurement of Alternatives and Ranking according to Compromise Solution (MARCOS) model is integrated with the Sugeno–Weber weighted averaging operators, modified symmetry point of criterion (SPC) model, rank sum (RS) tool and Fermatean fuzzy sets (FFSs), and named as the 'FF-SPC-RS-MARCOS' framework. The developed model firstly determines the decision experts' weights through RS model. Second, novel Sugeno–Weber weighted operators are introduced to combine the experts' opinions. Third, a unified weighting procedure is presented based on the combination of modified SPC approach for objective weight and RS method for subjective weight of attributes. To this aim, a novel distance measure is introduced for FFSs and further applied to compute the distance between aggregated Fermatean fuzzy numbers and symmetry point value of an attribute in the modified SPC approach. Further, a hybrid FF-SPC-RS-MARCOS approach is proposed to tackle the decision-making problems on FFSs setting. To elucidate the efficacy of the developed method, it is applied to a case study of sustainable supplier selection problem in the healthcare supply chain. The paper further conducts sensitivity investigation and comparison with existent approaches to test the stability and robustness of the ranking outcomes. This study shows how the proposed MARCOS method in combination with SPC and RS models can be used to prioritize the alternative suppliers in the healthcare supply chain. The introduced work provides a new methodology, which can help the practitioners and academics to evaluate suppliers with uncertain information and can also be employed to other areas facing similar types of decision-making problems. [ABSTRACT FROM AUTHOR]

Due to intensified sensitivity towards environmental protection and social responsibility, the concept of sustainable development has been widely mentioned in various industries. Circular economy has received great attention as it meets environmental and social requirements. It contributes to better resource efficiency and a more sustainable economic development by means of its principles to gain strategic advantages. Choosing suitable supplier in view of the circular and sustainability aspects are of great importance for all firms. Thus, the purpose of this study is to integrate the Pythagorean fuzzy information-based fairly aggregation operators, the CRiteria Importance Through Intercriteria Correlation (CRITIC), the PIvot Pairwise RElative Criteria Importance Assessment (PIPRECIA) and the Measurement of Alternatives and Ranking based on COmpromise Solution (MARCOS) methods to assess and rank the sustainable suppliers in circular supply chains. The proposed study classified into four phases. First, some fairly aggregation operators for Pythagorean fuzzy numbers (PFNs) are introduced that include the concept of proportional distribution to achieve a fair treatment to the membership and non-membership degrees of PFNs. Second, a combination of PF-CRITIC and PF-PIPRECIA-based weight-determining formula is introduced to compute the relative significances of the considered sustainability indicators. Third, the PF-MARCOS based on proposed PF-fairly aggregation operator and combined weight-determining tool is proposed to rank the sustainable circular suppliers (SCSs). Further, an illustrative case study of SCS selection is discussed to prove the practicability and effectiveness of the PF-MARCOS method. For this purpose, this study considers an inclusive set of four key criteria and 25 sub-criteria in the related literature concerning SCS selection process. The assessment criteria are categorized into economic, circular, environmental and social dimensions based on the expert's opinions. The result shows the significance degrees of economic, circular, environmental and social dimensions are 0.1964, 0.277, 0.3237 and 0.203, respectively and the SCS-4 (M4) should be chosen as the most suitable choice among others for the given data. The reliability and robustness of the presented methodology are examined by means of the comparative and sensitivity analyses. The findings of this study make a significant contribution to the SCS process by providing a novel decision support system from uncertainty perspective. [ABSTRACT FROM AUTHOR]

Healthcare waste management has been an extensively attractive topic recently since it is one of the key concerns regarding both environment and public health, predominantly in developing nations. The optimization of the treatment procedure for healthcare waste is indeed a complex "multi-criteria decision-making (MCDM)" problem that involves contradictory and interweaved critical criteria. To successfully handle this issue, this study extends the original method, named the "double normalization-based multi-aggregation (DNMA)" approach, with "interval-valued intuitionistic fuzzy sets (IVIFSs)" for decision-making problems taking criteria in terms of benefit or cost types. This method involves two target-based normalizations and three subordinate utility models. To estimate the criteria weights, we propose a new parametric divergence measure and discuss the feasibility of the developed divergence measure based on existing divergence measures for IVIFSs. Further, the developed framework is implemented to elucidate the "healthcare waste treatment (HCWT)" problem. The comparative and sensitivity analyses of the outcomes indicate that the proposed approach efficiently tackles the problem of HCWT selection. The outcomes show that steam sterilization (0.462) is the optimal one for HCWT. The prioritization options, obtained by presented approach, are dependable and suitable, which are steam sterilization ≻ microwave ≻ incineration ≻ landfilling. [ABSTRACT FROM AUTHOR]

The development opportunities and high-performance capacity of offshore wind energy project depends on the selection of the suitable offshore wind power station (OWPS) location. The present study aims to introduce a decision-making model for assessing the locations for OWPS from multiple criteria and uncertainty perspectives. In this regard, the concept of interval-valued intuitionistic fuzzy set (IVIFS) is utilized to express uncertain information. To quantify the degree of difference between IVIFSs, an improved distance measure is proposed and further utilized for deriving the objective weights of criteria. Numerical examples are discussed to illustrate the usefulness of introduced IVIF-distance measure. The RANking COMparison (RANCOM) based on interval-valued intuitionistic fuzzy information is presented to determine the subjective weights of criteria. With the combination of objective and subjective weights of criteria, an integrated weighting tool is presented to find the numeric weights of criteria under IVIFS environment. Further, a hybrid interval-valued intuitionistic fuzzy Weighted integrated Sum Product (WISP) approach is developed to prioritize the OWPS locations from multiple criteria and uncertainty perspectives. This approach combines the benefits of two normalization tools and four utility measures, which approves the effect of beneficial and non-beneficial criteria by means of weighted sum and weighted product measures. Further, the developed approach is applied to the OWPS location selection problem of Gujarat, India. Sensitivity and comparative analyses are presented to confirm the robustness and stability of the present WISP approach. This study provides an innovative decision analysis framework, which makes a significant contribution to the OWPS locations assessment problem under uncertain environment. [ABSTRACT FROM AUTHOR]

This study aims to propose a new group multi-attribute decision-analysis (MADA) model to prioritize the renewable energy sources (RESs) from sustainability perspectives. The selection of RESs can be considered as a MADA problem due to considering the numerous conflicting sustainability indicators/factors. In this regard, we propose an integrated decision-making framework with the "criteria importance through inter-criteria correlation (CRITIC)", the "rank sum (RS)" and the "Vlse Kriterijumska Optimizacija Kompromisno Resenje (VIKOR)" approaches with intuitionistic fuzzy information called the "IF-CRITIC-RS-VIKOR" model. In the developed model, the CRITIC is applied to derive the objective weights, while the RS model is used to compute the subjective weights of the considered sustainability indicators. Further, an incorporated weight-determining formula is presented by combining the CRITIC and RS models under intuitionistic fuzzy environment. Moreover, the VIKOR method is employed to rank the candidate RESs by means of several sustainability indicators. In this line, new intuitionistic fuzzy distance measures are proposed to calculate the "group utility (GU)" and "individual regret (IR)" degrees of candidate RESs. Based on the obtained results, the most significant factors for RESs assessment are impact on ecosystem, technology cost and efficiency, respectively. The assessment outcomes show that the wind energy can serve as an effective RES followed by the solar energy, biomass energy and small hydel energy. Furthermore, comparative study and sensitivity analysis are discussed to show the utility and reasonability of the proposed method. [ABSTRACT FROM AUTHOR]

In comparison to probabilistic linguistic term sets (PLTSs), dual probabilistic linguistic term sets (DPLTSs) reveal the complexity and uncertainty of this realistic world more accurately. The power average operator can mitigate the consequences of some decision-makers' strong biases while evaluating data. Additionally, the Dombi operators during the phase of aggregation are very adaptable with general parameter. Inspired by these topics, we propose some dual probabilistic linguistic Dombi power aggregation operators to aggregate the decision-making expert's preferences and various elegant properties of these proposed dual probabilistic linguistic (DPL)-aggregating operators. Further, we establish an integrated method with the combination of proposed DPL-aggregation operators, full consistency method (FUCOM) and additive ratio assessment (ARAS) model called the "DPL-FUCOM-ARAS" methodology for solving multi-criteria decision analysis problems under dual probabilistic linguistic environment. In this methodology, the FUCOM is applied to determine criteria weight, while the ARAS model is presented to prioritize the options from dual probabilistic linguistic perspective. We present a case study on the selection of a medical equipment supplier to highlight the applicability and show the usefulness of the proposed DPL-FUCOM-ARAS methodology. Further, we discuss the sensitivity investigation and comparative discussion to check the stability and robustness of the proposed DPL-FUCOM-ARAS methodology. [ABSTRACT FROM AUTHOR]

Bipolar complex fuzzy set (BCFS) is an enlargement of the bipolar fuzzy set and complex fuzzy set. A bipolar complex fuzzy number (BCFN) is used to represent both the bipolarity of ambiguity and bipolarity of periodicity semantics. This paper develops an integrated BCF–CRITIC–WASPAS methodology to elucidate the multi-criteria decision-making (MCDM) problems with bipolar complex fuzzy (BCF) data. Firstly, we propose the idea of cross-entropy of BCFSs followed by the introduction of some Archimedean operations between the BCFNs. Secondly, we discuss some BCF-Archimedean weighted aggregation operators with the proposed Archimedean aggregation operators that are generalizations of many renowned operators' namely algebraic operator, Einstein operator, Hamachar operator and Frank operator to combine the BCF information. Thirdly, a procedure is given to estimate the decision expert's weights using proposed cross-entropy measure of BCFSs. Since cross-entropy measure quantifies the degree of uncertain information and hence it reflects the influence of each expert. Fourthly, criteria weights are estimated through CRITIC (criteria importance through inter-criteria correlation) method which is a well-known objective method based on aggregated score values of options, intensity contrast of every criteria and conflict among attributes. Further, a green supplier selection (GSS) problem is taken to show the applicability of the developed methodology in real decision problems. We also exhibit a sensitivity investigation with diverse parameter values and criteria weights sets to examine the stability of proposed approach. Finally, we draw attention towards a comparison between the proposed approach and the extant methods to show its superiority. [ABSTRACT FROM AUTHOR]

The necessity and policy of eco-economy stimulate enterprises to attain sustainability by executing supply chain management. Generally, the evaluation process of sustainable recycling partner (SRP) selection is treated as a multi-criteria decision-making problem due to existence of numerous influencing aspects. To tackle the uncertain information during the process of SRP selection, the q-rung orthopair fuzzy sets have a good choice, which can refer to a broader range of uncertain decision-making information. Thus, this study presents a combined framework with the additive ratio assessment (ARAS) approach, notions of q-rung orthopair fuzzy set (q-ROFS) and information measures, and further implements to tackle the multi-criteria SRP selection problem with q-ROFSs setting. In this procedure, the criteria weights are evaluated with the integration of the subjective weights given by decision-experts and the objective weights obtain from the entropy and discrimination measures-based approach. For this, new entropy and discrimination measures are introduced for q-ROFSs and discussed the effectiveness of proposed measures. To elucidate the applicability of the present methodology, a case study related to sustainable recycling partner assessment is presented under q-ROFSs context. Sensitivity analysis is conducted over diverse set of criteria weights to verify the robustness of introduced framework. The results of the sensitivity analysis signify that the recycling partner SRP1 constantly secures the best rank and despites how sub-criteria weights differ. A comparison with extant methods is made to validate of the results of proposed one. The findings of the work verify that the developed framework is more valuable and well consistent with formerly proposed decision-making models. [ABSTRACT FROM AUTHOR]

In the past few years, the private sectors and industries have focused their attention on sustainable development goals to achieve the better and more sustainable future for all. To accomplish a sustainable community, one requires to better recognize the fundamental indicators and selects the most suitable sustainable policies in diverse regions of the community. Considering the huge impact of construction industry on sustainable development, very less research efforts have been made to obtain worldwide sustainable elucidations for this type of industry. As a large sector of construction industry, industrial buildings consume enormous amounts of energy and financial assets, and play a key character in job creation and life quality improvement in the community. In order to assess the sustainable industrial buildings by means of multiple indicators, the present study introduces a hybrid multi-criteria decision-making methodology which integrates the fairly aggregation operator, the MEthod based on the Removal Effects of Criteria (MEREC), the stepwise weight assessment ratio analysis (SWARA) and the additive ratio assessment (ARAS) methods with intuitionistic fuzzy set (IFS). In this respect, firstly new intuitionistic fuzzy weighted fairly aggregation operators are proposed and then employed to aggregate the decision information in the proposed hybrid method. This operator overcomes the limitations of basic intuitionistic fuzzy aggregation operators. To find the criteria weights, an integrated model is presented based on the MEREC for objective weights and the SWARA for subjective weights of indicators under IFS context. To rank the sustainable industrial buildings, an integrated ARAS method is employed from uncertain perspective. Further, a case study concerning sustainable industrial buildings evaluation is presented to illustrate the superiority and practicality of the developed methodology. The advantages of the developed approach are highlighted in terms of stability and reliability by comparison with some of the existing methods. [ABSTRACT FROM AUTHOR]

Pythagorean fuzzy set (PFS), an extended version of intuitionistic fuzzy set (IFS), is verified to be fastest emerging research discipline and is a significant mode to tackle the imprecise and vague information. It provides a broader representation domain than the IFS. Similarity and divergence measures play paramount role in the field of IFSs' doctrine as well as PFSs' doctrine. These measures are integral aspects of utilizing generalized fuzzy sets in real-life problems. In this manuscript, novel similarity and divergence measures for PFSs are developed and compared with extant measures to illustrate their efficiency and reliability. Further, an extended version of multi-objective optimization based on the ratio analysis (MOORA) with the full multiplicative form (MULTIMOORA) approach is introduced by employing developed similarity and divergence measures on PFSs information. To reveal the feasibility and usefulness of the presented approach, a problem of medical equipment supplier selection is discussed from Pythagorean fuzzy perspective. Finally, a comparison with previously developed models is studied to certify the applicability and stability of the introduced MULTIMOORA technique. The outcomes of the work indicate that the present approach is more applicable and efficient than existing techniques under PFSs' context. [ABSTRACT FROM AUTHOR]

Fastest growing population, rapid urbanization, and growth in the disciplines of science and technology cause continually development in the amount and diversity of solid waste. In modern world, evaluation of an appropriate solid waste disposal method (SWDM) can be referred as multi-criteria decision-making (MCDM) problem due to involvement of several conflicting quantitative and qualitative sustainability indicators. The imprecision and ambiguity are usually arisen in SWDM assessment problem, and the q-rung orthopair fuzzy set (q-ROFS) has been recognized as one of the adaptable and valuable ways to tackle the complex uncertain information arisen in realistic problems. In the context of q-ROFSs, entropy is a significant measure for depicting fuzziness and uncertain information of q-ROFS and the discrimination measure is generally used to quantify the distance between two q-ROFSs by evaluating the amount of their discrimination. Thus, the aim of this study is to propose a novel integrated framework based on multi-attribute multi-objective optimization with the ratio analysis (MULTIMOORA) method with q-rung orthopair fuzzy information (q-ROFI). In this approach, an integrated weighting process is presented by combining objective and subjective weights of criteria with q-ROFI. Inspired by the q-rung orthopair fuzzy entropy and discrimination measure, objective weights of criteria are estimated by entropy and discrimination measure-based model. Whereas, the subjective weights are derived based on aggregation operator and the score function under q-ROFS environment. In this respect, novel entropy and discrimination measure are proposed for q-ROFSs. Furthermore, to display the feasibility and usefulness of the introduced approach, a case study related to SWD method selection is presented under q-ROFS perspective. Finally, comparison and sensitivity investigation are presented to confirm the robustness and solidity of the introduced approach. [ABSTRACT FROM AUTHOR]

Selecting the optimal renewable energy source (RES) is a complex multi-criteria decision-making (MCDM) problem due to the association of diverse conflicting criteria with uncertain information. The utilization of Fermatean fuzzy numbers is successfully treated with the qualitative data and uncertain information that often occur in realistic MCDM problems. In this paper, an extended complex proportional assessment (COPRAS) approach is developed to treat the decision-making problems in a Fermatean fuzzy set (FFS) context. First, to aggregate the Fermatean fuzzy information, a new Fermatean fuzzy Archimedean copula-based Maclaurin symmetric mean operator is introduced with its desirable characteristics. This proposed operator not only considers the interrelationships between multiple numbers of criteria, but also associates more than one marginal distribution, thus avoiding information loss in the process of aggregation. Second, new similarity measures are developed to quantify the degree of similarity between Fermatean fuzzy perspectives more effectively and are further utilized to compute the weights of the criteria. Third, an integrated Fermatean fuzzy-COPRAS approach using the Archimedean copula-based Maclaurin symmetric mean operator and similarity measure has been developed to assess and rank the alternatives under the FFS perspective. Furthermore, a case study of RES selection is presented to validate the feasibility and practicality of the developed model. Comparative and sensitivity analyses are used to check the reliability and strength of the proposed method. [ABSTRACT FROM AUTHOR]

The application of blockchain technology (BT) to sustainable supply chain management (SSCM) has enriched the operations management processes with higher degrees of safety, traceability, transparency, and efficiency. This technology effectively helps prevent fake products and fraud across the supply chains, reducing costs and enhancing efficiency. However, the implementation of BT in supply chain management (SCM) is still in the initial stages since companies generally pay too much attention to the adoption phase while neglecting the managerial/organizational strategies required to succeed in this path; they also overlook the establishment of an effective link to the three main pillars of sustainability (i.e., the environmental, social, and economic aspects). Despite high potentials formerly confirmed for BT, a number of barriers have blocked the rapid adoption of this technology. Accordingly, the current study attempts to propose an innovative model hybridizing the combined compromise solution (CoCoSo) and criteria importance through inter-criteria correlation (CRITIC) methods to identify and evaluate the barriers to the BT adoption in SSCM in the manufacturing sector. In the proposed model, CRITIC is responsible for calculating the criteria weights, and CoCoSo for evaluating the preference order of the organization. To exhibit the practicality of the introduced model, a case study is taken to evaluate the barriers to the adoption of BT in SSCM within PFSs environment. Moreover, we exhibit a sensitivity analysis over parameter values in view of examining the stability of our proposed approach. Finally, we draw attention to a comparison between our developed PF-CRITIC-CoCoSo decision-making framework with an existing PF-WASPAS method to show its superiority and potency. [ABSTRACT FROM AUTHOR]

When there isn’t enough evidence, it can be hard for decision-makers (DMs) to evaluate their evaluations of strategic decision issues in the right way. An expansion of Pythagorean fuzzy sets (PFSs), known as interval-valued PFSs (IVPFSs), can provide sufficient information space for DMs so that they can assess their evaluations using interval numbers. The purpose of this work is to examine the aggregation procedures used by IVPFSs using Aczel-Alsina operations. We first generalize the Aczel-Alsina t-norm and t-conorm to IVPF circumstances and introduce several unique IVPFS operations, such as Aczel-Alsina sum, Aczel-Alsina product, Aczel-Alsina scalar multiplication, and Aczel-Alsina exponentiation, that contribute to the emergence of many special IVPF aggregation operators, including the IVPF Aczel-Alsina weighted average (IVPFAAWA) operator, IVPF Aczel-Alsina order weighted average (IVPFAAOWA) operator, and IVPF Aczel-Alsina hybrid average (IVPFAAHA) operator. Furthermore, we define several features of the operators, illustrate them with a few specific examples, and investigate the relationships between the aforementioned operators. Additionally, we use these operators to develop a system for trying to manage multiple attribute decision-making (MADM) using IVPF data. Ultimately, a mathematical formulation involving the selection of an emerging IT software company is given to represent the decision steps of the recommended methodology. The outcome demonstrates the reasonableness and viability of the new methodology. We explore the effects of the parameter on decision-making results for a variety of values. A comparative study is also presented. [ABSTRACT FROM AUTHOR]

The role of cloud services in the data-intensive industry is indispensable. Cision recently reported that the cloud market would grow to 55 billion USD, with an active contribution of the cloud to healthcare around 2025. Inspired by the report, cloud vendors expand their market and the quality of services to seek growth globally. The rapid growth of the cloud sector in the healthcare industry imposes a challenge: making a rational choice of a cloud vendor (CV) out of a diverse set of vendors. Typically, the healthcare industry 4.0 sees the issue as a large-scale group decision-making problem. Previous studies on a CV selection face certain challenges, such as (i) a lack of the ability to handle multiple users' views, as well as experts'/users' complex linguistic views; (ii) the confidence level associated with a view is not considered; (iii) the transformation of multiple users' views into holistic data is lacking; and (iv) the systematic prioritization of CVs with minimum human intervention is a crucial task. Motivated by these challenges and circumventing them, a new big data-driven decision model is put forward in this paper. Initially, the data in the form of complex expressions are collected from multiple cloud users and are further transformed into a holistic decision matrix by adopting probabilistic linguistic information (PLI). PLI represents complex linguistic expressions along with the associated confidence levels. Later, a holistic decision matrix is formed with the missing values imputed by proposing an imputation algorithm. Furthermore, the criteria weights are determined by using a newly proposed mathematical model and partial information. Finally, the evaluation based on the distance from average solution (EDAS) approach is extended to PLI for the rational ranking of CVs. A real-time example of a CV selection for a healthcare center in India is exemplified so as to demonstrate the usefulness of the model, and the comparison reveals the merits and limitations of the model. [ABSTRACT FROM AUTHOR]

The assessment of sustainable supplier is very significant for supply chain management (SCM). The procedure of sustainable supplier selection (SSS) is a complex process for decision experts (DEs) due to the association of diverse qualitative and quantitative attributes. As the uncertainty is usually ensued in the SSS and hesitant fuzzy set (HFS), an extension of fuzzy set (FS) has been demonstrated as one of the effective ways to treat the uncertain information in realistic problems. The objective of this paper is to propose an integrated hesitant fuzzy–data envelopment analysis (DEA)–full consistency method (FOCUM)–multi attribute border approximation area comparison (MABAC) method called HF-DEA-FUCOM-MABAC framework to assess the multi-attribute decision-making (MADM) problems on HFSs settings. In this line, first, the efficient alternatives are chosen using the DEA method. Second, The FUCOM is used to compute the subjective weight of attributes. Third, The HF-MABAC method is presented to prioritize the alternatives in an MADM problem. In the following, a case study of SSS problem for an Auto-making company is taken to show the practicality and utility of the presented approach. Next, we present a sensitivity investigation with different attribute weights set to observe the steadiness of the presented approach. Finally, we draw attention toward a comparison between presented approach with the extant HF-FOCUM-TOPSIS model to show its advantage and potency as well. [ABSTRACT FROM AUTHOR]

Fermatean fuzzy set, a generalization of the fuzzy set, is a significant way to tackle the complex uncertain information that arises in decision-analysis procedure and thus can be employed on a wider range of applications. Due to the inadequacy in accessible data, it is hard for decision experts to exactly define the belongingness grade (BG) and non-belongingness grade (NG) by crisp values. In such a situation, interval BG and interval NG are good selections. Thus, the aim of the study is to develop the doctrine of interval-valued Fermatean fuzzy sets (IVFFSs) and their fundamental operations. Next, the score and accuracy functions are proposed for interval-valued Fermatean fuzzy numbers (IVFFNs). Two aggregation operators (AOs) are developed for aggregating the IVFFSs information and discussed some axioms. Further, a weighted aggregated sum product assessment method for IVFFSs using developed AOs is introduced to handle the uncertain multi-criteria decision analysis problems. A case study of e-waste recycling partner selection is also considered to elucidate the feasibility and efficacy of the introduced framework. Finally, sensitivity and comparative analyses are given to elucidate the reliability and robustness of the obtained results. [ABSTRACT FROM AUTHOR]

The world has been challenged since late 2019 by COVID-19. Higher education institutions have faced various challenges in adapting online education to control the pandemic spread of COVID-19. The present study aims to conduct a survey study through the interview and scrutinizing the literature to find the key challenges. Subsequently, an integrated MCDM framework, including Stepwise Weight Assessment Ratio Analysis (SWARA) and Multiple Objective Optimization based on Ratio Analysis plus Full Multiplicative Form (MULTIMOORA), is developed. The SWARA procedure is applied to the analysis and assesses the challenges to adapt the online education during the COVID-19 outbreak, and the MULTIMOORA approach is utilized to rank the higher education institutions on hesitant fuzzy sets. Further, an illustrative case study is considered to express the proposed idea's feasibility and efficacy in real-world decision-making. Finally, the obtained result is compared with other existing approaches, confirming the proposed framework's strength and steadiness. The identified challenges were systemic, pedagogical, and psychological challenges, while the analysis results found that the pedagogical challenges, including the lack of experience and student engagement, were the main essential challenges to adapting online education in higher education institutions during the COVID-19 outbreak. [ABSTRACT FROM AUTHOR]

In today's world, the demand for sustainable third-party reverse logistics providers (S3PRLPs) becomes an increasingly considerable issue for industries seeking improved customer service, cost reduction and sustainability perspectives. However, the assessment and selection of right S3PRLP is a complex uncertain decision-making problem due to involvement of numerous conflicting attributes, imprecise human mind and lack of information. Recently, Fermatean fuzzy set (FFS) has been recognized as one of the suitable tools to tackle the uncertain and inaccurate information. In this paper, we introduce a hybrid methodology based on CRITIC and EDAS methods with Fermatean fuzzy sets (FFSs) to solve the S3PRLP selection problem in which the attributes and decision makers' weights are completely unknown. In this framework, CRITIC approach is applied to calculate the attribute weight and EDAS method is used to evaluate the priority order of S3PRLP options. To do this, a new improved generalized score function (IGSF) is developed with its elegant properties. Also, a formula is discussed to calculate the decision makers' weights based on the developed IGSF. Next, developed framework is applied to assess a case study of S3PRLP selection problem with Fermatean fuzzy information, which elucidates the usefulness and practicality of the proposed method. Finally, comparative study is implemented to show the strength of introduced framework with extant approaches. The outcomes of the work confirm that the introduced approach is more feasible and well-consistent with the other extant approaches. [ABSTRACT FROM AUTHOR]

Green supplier selection (GSS) is a crucial issue in green supply chain management. CAPS indicate that industries spend yearly USD 25 million per procurement, which is a huge amount that necessitates a systematic GSS to avoid financial catastrophes. Literatures on GSS reveal that researchers have not addressed the issue of missing preferences, consistency of decision matrices, and repairing inconsistencies. Moreover, handling of complex linguistic expressions is another open challenge in GSS. Motivated by these research gaps, a two-stage decision framework was proposed. From the analysis of different linguistic models, it is clear that a double-hierarchy linguistic model is flexible for handling complex expressions. In the preprocessing stage, preferences were imputed using the case-based method. Later, consistency of matrices was determined using the Cronbach's coefficient, and inconsistent matrices were repaired using the iterative method. In the next stage, new mathematical models were formulated to calculate weights of experts and criteria. Preferences were sensibly aggregated by using the Maclaurin symmetric mean operator, which captures the criteria interrelationship. Green suppliers were prioritized by using the TODIM method. Finally, the practicality, strengths, and weaknesses of the proposed framework were realized by demonstrating a case study of GSS and comparison with other methods. Results infer that the proposed framework (i) is consistent with the existing models, and the values are 0.60, 0.86, and 0.75, respectively; (ii) is robust with 100% rank-order stability even after adequate weight alterations; and (iii) finally can better discriminate suppliers with a broad deviation range of 0.34–0.35. [ABSTRACT FROM AUTHOR]

One of the most powerful tools to operate imprecision is bipolar complex fuzzy sets (BCFSs), which is an enlargement of bipolar fuzzy sets (BFSs) as well as complex fuzzy sets (CFSs). This paper deals with an integrated MULTIMOORA (multi-objective optimization on the basis of ratio analysis plus full multiplicative form) framework as a generalization of fuzzy MULTIMOORA procedure to assess the multi-criteria decision-making (MCDM) problems with BCFSs. We develop BCF-Archimedean power weighted (ordered weighted) arithmetic and geometric aggregation operators (AOs) and discuss their properties from this point of view. The proposed Archimedean power-weighted AOs can eliminate the influence of extreme evaluating criteria values from some biased experts with different preference attitudes under the BCF setting. Afterward, we put forward an integrated MULTIMOORA algorithm based on the proposed AOs, where criteria weights are estimated using the CRITIC (criteria importance through inter-criteria correlation) method, which is a well-known objective weighting method based on aggregated score values of options, intensity contrast of every criteria and conflict among attributes. In the proposed methodology, criteria values are aggregated based on the MULTIMOORA method that involves three sub-methods: the 'ratio system', the 'reference point' and the 'full multiplicative form' and thus takes less computational time, minimum mathematical evaluations and bears good stability. In the following, third-party reverse logistics providers' (3PRLP) selection problem is brought into consideration to manifest the sufficiency of the developed methodology. At the end of this study, we draw attention to a comparison between the proposed decision-making approach with the corresponding BCF-CRITIC-TOPSIS and BCF-CRITIC-WASPAS methods. [ABSTRACT FROM AUTHOR]

Medical services inevitably generate healthcare waste (HCW) that may become hazardous to healthcare staffs, patients, the population, and the atmosphere. In most of the developing countries, HCW disposal management has become one of the fastest-growing challenges for urban municipalities and healthcare providers. Determining the location for HCW disposal centers is a relatively complex process due to the involvement of various alternatives, criteria, and strict government guidelines about the disposal of HCW. The objective of the paper is to introduce the WASPAS (weighted aggregated sum product assessment) method with Fermatean fuzzy sets (FFSs) for the HCW disposal location selection problem. This method combines the score function, entropy measure, and classical WASPAS approach within FFSs context. Next, a combined procedure using entropy and score function is proposed to estimate the criteria weights. To do this, a novel score function with its desirable properties and some entropy measures are introduced under the FFSs context. Further, an illustrative case study of the HCW disposal location selection problem on FFSs is established, which evidences the practicality and efficacy of the developed approach. Comparative discussion and sensitivity analysis are made to monitor the permanence of the introduced framework. The final results approve that the proposed methodology can effectively handle the ambiguity and inaccuracy in the decision-making procedure of HCW disposal location selection. [ABSTRACT FROM AUTHOR]

In recent years, the important role of sustainable development is highlighted in the literature; therefore, a company to make a sustainable business success needs to be well focused on social, environmental, economic, and technological characteristics of the business to address risks and capture value properly. The process of Sustainability Enterprise Risk Management (SERM) is typically implemented to integrate all social, economic, environmental, and technological aspects in a systematic way to properly manage emerging risks and other non-quantifiable risks for company survival. Therefore, in this study, an attempt has been carried out to develop a comprehensive framework to implement the ERM framework under the sustainability platform by considering 29 sub-criteria based on four main aspects, including social, environmental, technological, and economic. In addition, a new fuzzy decision-making approach using the VIKOR (VlseKriterijumska Optimizacija Kompromisno Resenje) approach under q-rung orthopair fuzzy set (q-ROFSs) called VIKOR-q-ROFSs approach is introduced to identify, rank, and evaluate the main criteria of SERM in the universal appeal for all industries such as Chinese manufacturing Small And Mid-Size Enterprises (SMEs) based on expert opinions and literature review. To determine the weights of SERM criteria by the decision experts, this study has introduced q-ROFNs. Moreover, to facilitate the q-ROFNs, a novel q-rung orthopair fuzzy weighted averaging operator (q-ROFWAO) is proposed. Furthermore, VIKOR is applied to rank and evaluate the manufacturing SMEs as the alternatives for this study. The results of this paper showed that technological suitability was the important risk factor followed by technological advance, occupational safety and health, product and services responsibility, (benefit) anti-corruption labor practices, and technological practicability. In addition, the findings of the analysis show that the proposed method was efficient and effective in evaluating risk assessment of SERM in the SMEs. [ABSTRACT FROM AUTHOR]

Group decision-making (GDM) is a complex process. The diversity, discrimination, and inevitable uncertainty due to human intervention characterize such problems that add to this complexity. To circumvent this challenge, there is an urge for an appropriate knowledge representation and decision-making approaches. The present paper is concerned with a prescriptive approach to GDM that can aid a group of decision-makers (DMs) to arrive at a decision. To this end, the recent concept of probabilistic linguistic term set is utilized. The discrimination among the alternatives, as in the real world, are mimicked using an integrated framework that adopts CRITIC and variance methods for attribute weight calculation, Gini index for calculating the weights of DMs, Maclaurin symmetric mean for aggregating preferences, and weighted distance-based approximation for prioritization of alternatives. A real-world problem on electric bike selection illustrates the usefulness of the proposed work. Finally, comparative analysis with extant methods demonstrates the technical results, and it is inferred that the proposed work is (i) highly consistent (from Spearman correlation) and (ii) produces broad rank values (from standard deviation) that could be efficiently discriminated for rational decision-making and backup management during critical situations. [ABSTRACT FROM AUTHOR]

Over two decades, telecommunication market has been continuing a huge growth in urban, semi-urban and rural regions of India. Investigating and choosing the desirable cellular mobile telephone service providers (TSPs) based on operative constraint can facilitate to obtain the ideal of TSPs selection. Here, the evaluation commonly encompasses different TSP options under various operational factors; thus, the assessment of TSPs can be considered as a rigorous multi-criteria decision-making (MCDM) issue. This paper initiates a structure for the exploration of the TSPs in the Madhya Pradesh region, India. To do this, a framework associated with grey relational analysis (GRA) on intuitionistic fuzzy sets (IFSs) is planned to obtain the performance of various telecom participants. The developed approach is based on the conception of the best and worst solutions. To find the attribute weights, a divergence measure is developed and employed by relative comparisons. Additionally, to show the proficiency and practicality, a selection problem of TSPs options of Madhya Pradesh circle, India is presented within the IFSs context. By employing the developed model, an expert can enlarge tactics to enhance the performance by standard operational factors. Comparison and sensitivity analysis are considered to validate the developed approach in the prioritization of the TSPs options. [ABSTRACT FROM AUTHOR]

Interval-valued intuitionistic fuzzy sets (IVIFSs) are proven to be the fastest growing research area and are more flexible way to handle the uncertainty. Information measures play vital role in the study of uncertain information; therefore, number of new interval-valued intuitionistic fuzzy divergence and entropy measures have been proposed in the literature and applied for different purposes. Recently, multi-criteria decision-making (MCDM) methods with IVIFSs have broadly studied by researchers and practitioners in various fields. In this paper, firstly surveys of IVIF-divergence and entropy measures are conducted and then demonstrated some counter-intuitive cases. Then, novel divergence and entropy measures are originated for IVIFSs to avoid the shortcomings of previous measures. Later on, systematic reviews of Portuguese for Interactive Multi-criteria Decision Making (TODIM) method are presented with recent fuzzy developments. Based on classical TODIM method, a new approach for MCDM is introduced under IVIF environment which considers the bounded rationality of decision makers. In the present method, the proposed entropy measure is utilized to compute the weight vector of the criteria, and the proposed divergence measure is applied in the calculation of dominance degrees. To illustrate the effectiveness of the present approach, a decision-making problem of vehicle insurance companies is presented where the evaluation values of the alternatives are given in terms of IVIF numbers. Comparison with some existing methods shows the applicability and consistency of the present method. [ABSTRACT FROM AUTHOR]

Recently, the organizations have concentrated on sustainability development and introduced several strategies for sustainability due to government policies, society concern, environmental impacts and needs of economy. Uncertainty commonly occurred in the sustainability development. Pythagorean fuzzy sets (PFSs), an extension of IFSs, have been demonstrated as an extremely valuable tool to tackle the uncertainty and ambiguity arisen in many practical situations. Thus, the proposed study focuses under Pythagorean fuzzy environment. In the present study, an approach is developed on the basis of Pythagorean fuzzy sets and Technique for Order Preference by means of Similarity to Ideal Solution method for the purpose of solving sustainable recycling partner selection problems with completely unknown decision experts and criteria weights. To calculate criteria weights, new similarity measure based on trigonometric function for PFSs is developed. Aiming at showing the way our approach can be effectively used to evaluate the realistic multi-criteria decision making problems, we carry out a case study of sustainable recycling partner selection problem. In addition, the results obtained from the proposed method are compared to those of some presently existing methods to validate the proposed method. The analytical results confirm the proficiency and reasonableness of the proposed method. [ABSTRACT FROM AUTHOR]

Due to innovative and practical technology, the selection of a right physician is an important issue for patients. However, uncertainty and vagueness frequently arise during the process of selecting physicians. Intuitionistic fuzzy type-2 sets (IFT2Ss) (recently named as Pythagorean fuzzy sets) provide an important tool to handle the uncertainty arises in real-life decision-making problems. This paper presents an extended weighted aggregated sum product assessment (WASPAS) method based on novel information measures (entropy and divergence measures) and operators under IFT2Ss context. In the proposed WASPAS method, entropy and divergence measure-based formula is developed to find the criteria weights. For this, several intuitionistic fuzzy entropy and divergence measures are developed for IFT2Ss. To increase the stability of the proposed methodology, the criteria's weights are calculated in the form of objective and subjective weights. Further, to reveal the applicability and effectiveness of proposed method, an uncertain multi-criteria decision-making problem of physician selection is executed with intuitionistic fuzzy information of second type. Finally, the validity of the proposed method is implemented by comparison with existing methods and sensitivity analysis and also proves that the proposed method is valid and feasible in the physician selection processes with information given in intuitionistic fuzzy type-2 numbers (IFT2Ns). [ABSTRACT FROM AUTHOR]

Uncertainty is the most usual problem in decision making, for which intuitionistic fuzzy set (IFS) considered as appropriate means allowing numerous feasible degree of an element to a set. In this paper, we mention first dilemma of the existing divergence measures for IFSs. Next, we propose new divergence and entropy measures for IFSs and compare with the existing measures. To facilitate the interactive or interdependent features among elements in a set, new Shapley-weighted divergence measures for IFSs are developed via the eminent Shapley function, which can be perceived as generalization of the allied weighted divergence measures. Furthermore, we develop Shapley-weighted divergence measures based VIKOR method, which is stimulated by conventional VIKOR method. The proposed method is more adaptable and sinuous for correlative decision-making problems, which is used to determine the ranking order of alternatives and find the optimal one(s), so that it is surmounted the difficulty of the decision makers. To demonstrate the validity of the proposed method, numerical examples related to pattern recognition and multi-criteria decision making are presented, which displays the advantages and feasibility. [ABSTRACT FROM AUTHOR]

Interval-valued intuitionistic fuzzy sets (IVIFSs) are very flexible tool to cope with the uncertainty arises in multi-criteria decision making (MCDM) problems. In recent times, MCDM problems with interval-valued intuitionistic fuzzy information have achieved more attention from researchers in different areas and consequently, several MCDM methods have been extended for IVIFSs. In this paper, a novel approach based on WASPAS method is developed under IVIFSs. The developed method is based on the operators of IVIFSs, some amendments in the classical WASPAS method and a new process for calculation of criteria and decision experts’ weights. In process for calculating weights, new procedures is propoesd to compute the decision experts’ weights and criteria weights based on interval-valued intuitionistic fuzzy information measures (entropy, divergence and similarity measures) to achieve more realistic weights. Innovative information measures are developed based on the exponential function for IVIFSs to determine the weights of the criteria and decision experts. Since the uncertainty is an unavoidable feature of MCDM problems, the developed method can be a constructive tool for decision-making in an uncertain environment. Further, an uncertain decision making problem of reservoir flood control management policy is implemented with interval-valued intuitionistic fuzzy information, which reveals the effectiveness and reliability of the proposed IVIF-WASPAS method. To validate the result, comparative analysis with existing methods and sensitivity analysis are presented under interval-valued intuitionistic fuzzy environment. [ABSTRACT FROM AUTHOR]

This paper presents a novel decision-making approach, known as TODIM, in interval-valued intuitionistic fuzzy (IVIF) environment, which determines an optimal alternative by considering psychological behaviours of decision makers under risk. In recent years, TODIM technique has been developed by several authors in various discipline, but they are not able to deal with interdependent characteristics among the criteria. In the present manuscript, the TODIM technique is discussed on the basis of Shapley values under IVIFSs for some situations where elements in a set are correlated. To determine the Shapley values, an entropy measure for IVIFSs is proposed and compared with existing entropy measures. A similarity measure for IVIFSs is introduced to measure the dominance degree of each alternative over others. Mathematical illustration is demonstrated to show the competency of the proposed similarity measure. To deal with interdependent or interactive problem, we have developed Shapley-weighted similarity measure for IVIFSs based on proposed similarity measure and Shapley function. Application of proposed Shapley-weighted similarity measure is presented in pattern recognition problem and then compared with existing measures. Finally, an example of plant location selection is taken to demonstrate the validity and benefit of the proposed technique. [ABSTRACT FROM AUTHOR]

The need and strategy of eco-economy encourage enterprises to reach sustainability by employing sustainable supply chain management. Contrary to the numerous literatures focusing on green design and sustainability practices, this paper presents sustainable recycling partner (SRP) assessment with economic, environmental and social pillars. To propose an integrated framework for SRP selection in small-and-medium enterprises (SMEs), interval-valued intuitionistic fuzzy set (IVIFS)-based model is applied to deal with the vague, uncertain and qualitative information. Inspired by these topics, we propose IVIF-improved Dombi weighted averaging and IVIF-improved Dombi weighted geometric operators to aggregate the decision-making expert’s preferences and discuss some sophisticated characteristics of developed aggregation operators. Further, we establish an integrated weighting model by combining the IVIF-symmetric point of criterion (IVIF-SPC) and IVIF-rank sum (IVIF-RS) tools. Then, the classical multi-objective optimization on the basis of ratio analysis plus full multiplicative form (MULTIMOORA) model has been extended using the proposed divergence measure and improved Dombi operators for treating multi-criteria decision analysis problems on IVIFS setting. To explore the effectiveness and practicability of the proposed model, a case study of SRP selection in SMEs is conducted. The results of the developed model, “Namo e-waste management limited (NEWML),” should be considered as the first SRP in SMEs in India. Further, the sensitivity investigation and comparative discussion are presented to check the stability and robustness of the presented technique. [ABSTRACT FROM AUTHOR]