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The purpose of this paper is to develop a multi-attribute group decision-making (MAGDM) method under the q-rung orthopair trapezoidal fuzzy environment, which calculates the interaction between the criteria depending on the proposed q-rung orthopair trapezoidal fuzzy aggregation Choquet integral (q-ROTrFACI) and employ TODIM (an acronym in Portuguese of Interactive and Multi-criteria Decision Making) to consider the risk psychology of decision-makers, to determine the optimal ranking of alternatives.

In MAGDM, q-rung orthopair trapezoidal fuzzy numbers (q-ROTrFNs) are efficient to indicate the quantitative vagueness of decision-makers. The q-ROTrFACI operator is defined and some properties are proved. Then, a novel similarity measure is developed by fusing the area and coordinates of the q-rung orthopair trapezoidal fuzzy function. Based on the above, a Choquet integral-based TODIM (CI-TODIM) method to consider the risk psychology of decision-makers is proposed and two cases are provided to prove superiority of the method.

The paper investigates q-ROTrFACI operator to productively solve problems with interdependent criteria. Then, an approach is proposed to determine the center point of q--ROTrFNs and a q-rung orthopair trapezoidal fuzzy similarity is constructed. Furthermore, CI-TODIM method is devised based on the proposed q-ROTrFACI operator and similarity in q-rung orthopair trapezoidal fuzzy context. The illustration example of business models' solutions and hypertension health management are given to demonstrate the effectiveness and superiority of proposed method.

The paper develops a novel CI-TODIM method that effectively solves the MAGDM problems under the premise of fully considering the priority of criteria and the risk preference of decision-makers, which provides guiding advantages for practical decision-making and enriches the application of decision-making theory.

Reverse logistics (RL) is a type of supply chain management that moves goods from the end customer to the original manufacturer for reuse, remanufacturing and disposal purposes. Owing to growing environmental legislations and the development of new technologies in marketing, RL has attracted more significance among experts and academicians. Outsourcing RL practices to third-party reverse logistics provider (3PRLP) has been identified as one of the most important management strategies due to complexity of RL operations and the lack of available resource. Current sustainability trends have made 3PRLP assessment and selection process more complex. In order to select the 3PRLP, the existence of several aspects of sustainability motivates the experts to establish a new multi-criteria decision analysis (MCDA) approach.

With the growing complexity and high uncertainty of decision environments, the preference values of 3PRLPs are not always expressed with real numbers. As the generalized version of fuzzy set, intuitionistic fuzzy set and Fermatean fuzzy set, the theory of q-rung orthopair fuzzy set (q-ROFS) is used to permit decision experts (DEs) to their assessments in a larger space and to better cope with uncertain information. Given that the combined compromise solution (CoCoSo) is an innovative MCDA approach with higher degree of stability and reliability than several existing methods.

To exhibit the potentiality and applicability of the presented framework, a case study of S3PRLPs assessment is taken from q-rung orthopair fuzzy perspective. The assessment process consists of three sustainability aspects namely economic, environment and social dimensions related with a total of 14 criteria. Further, sensitivity and comparative analyses are made to display the solidity and strength of the presented approach. The results of this study approve that the presented methodology is more stable and efficient in comparison with other methods.

Thus, the objective of the study is to develop a hybrid decision-making methodology by combining CoCoSo method and discrimination measure with q-ROFS for selecting an appropriate sustainable 3PRLP (S3PRLP) candidate under uncertain environment. In the proposed method, a novel procedure is proposed to obtain the weights of DEs within q-ROFS context. To calculate the criteria weights, a new formula is presented based on discrimination measure, which provides more realistic weights. In this respect, a new discrimination measure is proposed for q-ROFSs.

The purpose of this paper is to develop the linguistic q-rung orthopair fuzzy set (LqROFS) information VIKOR method based on the bi-direction Choquet integral (BDCI), taking into account the correlation between information. The method can enrich the existing studies related to LqROFS information and better solve the problem of MAGDM problem.

Since applying Choquet integral (CI) depict information interaction is a common operation in MAGDM. However, the traditional CI has some limitations. The unidirectional alignment may affect the MAGDM results. Therefore, a LqROFS-VIKOR method based on BDCI is proposed, where BDCI is used to aggregate the decision matrix. Furthermore, it is not reasonable to apply exact numbers to express the similarity between two qualitative data. Then a new method of defining similarity using linguistics is proposed. The similarity is used to calculate attribute weights.

The validity and potential application of MAGMD method with linguistic q-rung orthopair fuzzy information based on BDCI are demonstrated in a numerical examples study.

According to the study of available literature, the current research on LqROFS is incomplete. The existing studies of both similarity and aggregate operators have certain shortcomings. The definition of similarity proposed in this paper is more in line with reality. And compared with the existing methods, the BDCI-based aggregate operator can describe the interaction between information more reasonably. Based on this VIKOR method based on BDCI under the LqROFS environment can better select the alternative.

The “Internet of Things (IoT)” is a platform for involving smart devices via the Internet at a worldwide scale. It supports the “supply chain (SC)” and “information and communication technology (ICT)” infrastructure to be well integrated into an organization and externally with customers and suppliers. The “sustainable supply chain (SSC)” is currently unavoidable if a company seeks to satisfy the aggressive change in its customers' requirements. Numerous studies have confirmed that manufacturing firms have to accelerate the shift of their focus toward sustainability and the implementation of novel technologies, such as IoT, to accomplish their organizational goals most effectively. Although the literature consists of many theoretical approaches to IoT and numerous studies that have extremely concentrated upon the IoT technology and its potential applications, it lacks research with a focus on the challenges that arise when applying IoT to the “sustainable supply chain management (SSCM)”.

The present study proposes an integrated framework using the “Criteria Importance Through Intercriteria Correlation (CRITIC)” and “VlseKriterijumska optimizcija I kaompromisno resenje in Serbian (VIKOR)” models and employs to evaluate the IoT challenges to implement the SSCM. For estimating the criteria weights, the CRITIC tool is utilized. The organization's prioritization is obtained by the VIKOR procedure, which delivers simple mathematical procedures with precise and consistent outcomes.

To exhibit the practicality of the introduced model, a case study is taken to evaluate the IoT challenges to implement the SSCM within the “q-Rung Orthopair Fuzzy Sets (q-ROFSs)” environment. Moreover, the authors exhibit a sensitivity investigation over given parameter values, examining the stability of developed approach. Finally, the authors draw attention to a comparison between developed q-ROF-CRITIC-VIKOR decision-making approach with an existing q-ROF-TOPSIS method to show its superiority and potency.

The outcome of the study lies in observing the top benefits of individual businesses, and their entire SSCs can be found by implementing IoT. This paper investigates the most important challenges that individual firms and entire SSCs might while applying IoT. It provides a deep insight regarding the effects of IoT upon SSCM and the issues every firm need to contemplate when it is to apply IoT solutions.

The poor leadership style is a key obstacle to the effective implementation of Industry 4.0 technologies. To successfully apply the Industry 4.0 technologies, which can enhance the sustainability of firms, senior management needs to be inspiring and transformational. On the other hand, numerous factors can hinder the Industry 4.0 transition and “Circular Supply Chain (CSC)” transformation. Therefore, the main purpose of this study is to evaluate the related barriers of CSCs in the era of Industry 4.0 transition.

The current study developed an innovative decision-making approach with the help of the “Combined Compromise Solution (CoCoSo)” method and “Criteria Importance Through Intercriteria Correlation (CRITIC)” method on the “q-Rung Orthopair Fuzzy Sets (q-ROFSs).” CRITIC in this combined method was used to predict the importance or weighting degrees of the CSCs barriers in the age of Industry 4.0 transition.

The results of this study found that the absence of knowledge about the Industry 4.0 technologies and circular approaches was the first barrier followed by the problems associated with data security in relationship management in circular flows, the deficiency of knowledge regarding the data management among stakeholders and the lack of awareness about the potential benefits of autonomous systems in labor-oriented “End-of-Life (EOL)” activities for CSCs in the era of Industry 4.0 transition.

A limitation may be that despite the generalizability of the proposed framework, the results may differ when it is implemented in different sectors. By emphasizing the obstacles to sustainable operations of supply chains (SCs) in the context of circular economy (CE) and Industry 4.0, researchers working in the same domain may be encouraged to find ways to remove such obstacles in different settings. As suggested in this study, the priority of various barriers helps researchers suggest effective strategies for the sustainable development of companies within the current dynamic business atmosphere.

The findings of this paper can aid industry practitioners in fixing their attention on the digitization or automation of their systems in the context of sustainability or resource circularity. Note that within the current context of CE, one of the crucial issues is how to conserve the existing resources; the answer to this question can save the environment.

The current paper proposed a new multi-criteria decision-making method using q-ROFSs to analyze, rank and evaluate the CSC barriers in the age of Industry 4.0 transition. To this end, a new decision-making approach with the help of CRITIC and CoCoSo methods on q-ROFSs called q-ROF-CRITIC-CoCoSo was introduced to evaluate the CSCs barriers in the era of Industry 4.0 transition.

The authors develop some prioritized operators named Pythagorean fuzzy prioritized averaging operator with priority degrees and Pythagorean fuzzy prioritized geometric operator with priority degrees. The properties of the existing method are routinely compared to those of other current approaches, emphasizing the superiority of the presented work over currently used methods. Furthermore, the impact of priority degrees on the aggregate outcome is thoroughly examined. Further, based on these operators, a decision-making approach is presented under the Pythagorean fuzzy set environment. An illustrative example related to the selection of the best alternative is considered to demonstrate the efficiency of the proposed approach.

In real-world situations, Pythagorean fuzzy numbers are exceptionally useful for representing ambiguous data. The authors look at multi-criteria decision-making issues in which the parameters have a prioritization relationship. The idea of a priority degree is introduced. The aggregation operators are formed by awarding non-negative real numbers known as priority degrees among strict priority levels. Consequently, the authors develop some prioritized operators named Pythagorean fuzzy prioritized averaging operator with priority degrees and Pythagorean fuzzy prioritized geometric operator with priority degrees.

The authors develop some prioritized operators named Pythagorean fuzzy prioritized averaging operator with priority degrees and Pythagorean fuzzy prioritized geometric operator with priority degrees. The properties of the existing method are routinely compared to those of other current approaches, emphasizing the superiority of the presented work over currently used methods. Furthermore, the impact of priority degrees on the aggregate outcome is thoroughly examined. Further, based on these operators, a decision-making approach is presented under the Pythagorean fuzzy set environment. An illustrative example related to the selection of the best alternative is considered to demonstrate the efficiency of the proposed approach.

The aggregation operators are formed by awarding non-negative real numbers known as priority degrees among strict priority levels. Consequently, the authors develop some prioritized operators named Pythagorean fuzzy prioritized averaging operator with priority degrees and Pythagorean fuzzy prioritized geometric operator with priority degrees. The properties of the existing method are routinely compared to those of other current approaches, emphasizing the superiority of the presented work over currently used methods. Furthermore, the impact of priority degrees on the aggregate outcome is thoroughly examined.

Single-valued neutrosophic sets (SVNSs) are efficient models to address the complexity issues potentially with three components, namely indeterminacy, truthness and falsity. Taking advantage of SVNSs, this paper introduces some new aggregation operators (AOs) for information fusion of single-valued neutrosophic numbers (SVNNs) to meet multi-criteria group decision-making (MCGDM) challenges.

Einstein operators are well-known AOs for smooth approximation, and prioritized operators are suitable to take advantage of prioritized relationships among multiple criteria. Motivated by the features of these operators, new hybrid aggregation operators are proposed named as “single-valued neutrosophic Einstein prioritized weighted average (SVNEPWA) operator” and “single-valued neutrosophic Einstein prioritized weighted geometric (SVNEPWG) operators.” These hybrid aggregation operators are more efficient and reliable for information aggregation.

A robust approach for MCGDM problems is developed to take advantage of newly developed hybrid operators. The effectiveness of the proposed MCGDM method is demonstrated by numerical examples. Moreover, a comparative analysis and authenticity analysis of the suggested MCGDM approach with existing approaches are offered to examine the practicality, validity and superiority of the proposed operators.

The study reveals that by choosing a suitable AO as per the choice of the expert, it will provide a wide range of compromise solutions for the decision-maker.

The purpose of this article is to conduct a main path analysis of 627 articles on the theme of Pythagorean fuzzy sets (PFSs) in the Web of Science (WoS) from 2013 to 2020, to provide a conclusive and comprehensive analysis for researchers in this field, and to provide a study on preliminary understanding of PFSs.

The research topic of Pythagorean fuzzy fields, through keyword extraction and describing the changes in characteristic themes over the past eight years, are firstly examined. Main path analysis, including local and global main paths and key route paths, is then used to reveal the most influential relationships between papers and to explore the trajectory and structure of knowledge transmission.

The application of Pythagorean fuzzy theory to the field of decision-making has been popular, and combinations of the traditional Pythagorean fuzzy decision-making method with other fuzzy sets have attracted widespread attention in recent years. In addition, over the past eight years, research interest has shifted to different types of PFSs, such as interval-valued PFSs.

This paper implicates to investigate the growth in certain trends in the literature and to explore the main paths of knowledge dissemination in the domain of PFSs in recent years.

This paper aims to identify the topics in which researchers are currently interested, to help scholars to keep abreast of the latest research on PFSs.

The purpose of this article is to present the idea of a T-spherical hesitant fuzzy set associated with probability and to develop an extended multi-attributive border approximation area comparison (MABAC) method under probabilistic T-spherical hesitant fuzzy (Pt-SHF) settings.

The authors define some basic operational laws for Pt-SHF sets (Pt-SHFSs) and a comparison method of two probabilistic T-spherical hesitant fuzzy numbers (Pt-SHFNs) is proposed. Moreover, some Pt-SHF aggregation operators and the multi-attributive border approximation area comparison (MABAC) method are established under Pt-SHF scenario to solve group decision making problems.

The developed Pt-SHF MABAC method for multi-attribute group decision making (MAGDM) can overcome the drawbacks of conventional MABAC method and limitations for decision makers, which they face while providing their assessment concerning any object.

Clearly, this paper is devoted to MABAC method, MAGDM and probabilistic T-spherical hesitant fuzzy set theory.

The approach established can be used in a variety of scenarios, including decision making, engineering, and economics. An explanatory example is illustrated which shows the superiority and effectiveness of our proposed technique.

If a T-spherical fuzzy MAGDM problem under the probabilistic scenario needs to be evaluated, the involvement of probabilities in fuzzy system will be lost because of no information. This work fills a gap in literature by establishing the notion of probabilistic t-spherical hesitant fuzzy set to deal with the ambiguity, uncertainty in decision making problems.

The aim of this study as to find out an approach for emergency program selection.

The authors have generated six aggregation operators (AOs), namely picture fuzzy Yager weighted average (PFYWA), picture fuzzy Yager ordered weighted average, picture fuzzy Yager hybrid weighted average, picture fuzzy Yager weighted geometric (PFYWG), picture fuzzy Yager ordered weighted geometric and picture fuzzy Yager hybrid weighted geometric aggregations operators.

First of all, the authors defined the score and accuracy function for picture fuzzy set (FS), and some fundamental operational laws for picture FS using the Yager aggregation operation. After that, using the developed operational laws, developed some AOs, namely PFYWA, picture fuzzy Yager ordered weighted average, picture fuzzy Yager hybrid weighted average, PFYWG, picture fuzzy Yager ordered weighted geometric and picture fuzzy Yager hybrid weighted geometric aggregations operators, have been proposed along with their desirable properties. A decision-making (DM) approach based on these operators has also been presented. An illustrative example has been given for demonstrating the approach. Finally, discussed the comparison of the proposed method with the other existing methods and write the conclusion of the article.

To find the best alternative for emergency program selection.