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The different preferences of experts in fuzzy group decision-making problems will lead to conflict, which hinders the reaching of consensus. In present conflict management techniques, local conflict among individual experts or the overall level of conflict is often concerned. This paper deals with conflict relations by opinion dynamics to resolve the whole and local conflicts among experts. This paper proposes a conflict resolution method based on opinion dynamics, which mainly includes three parts: (1) trust propagation: taking the consistency index into account in the propagation of trust, aiming at making as objective an assessment as possible of the competence and social status of experts; (2) conflict detection and elimination: reducing conflicts to an acceptable level through multiple rounds of preference adjustment according to the harmony degree; (3) alternatives selection: proposing a scoring function combining extent superiority with number superiority to score and rank the alternatives. Finally, a numerical example is given to illustrate the feasibility of the proposed method. [ABSTRACT FROM AUTHOR]

Decision-making problem is a fundamental activity in human life every day. Regarding group decision-making, individuals have insufficient comprehension of the decision objects owing to the limited experience and knowledge and drawback the evaluation process. Therefore, the evaluation information is missing and the group cannot get the precise information for decision objects resulting in the generation of incomplete information systems. It is meaningful for individuals finding an approach to Leverage and tap into existing information. On the basis, the work presented in this paper focuses on group decision-making problems (GDM) with incomplete information. Under the framework of group decision-making, a GDM approach with an incomplete information system is presented combining the formal concept analysis and rough set theory. Firstly, we propose a concept called formal decision context and discuss the properties of the formal decision context, which could divide the incomplete information system into many cognitive units, and the definitions of cognitive units will be given. Then, the property and the relations of various cognitive units will be discussed. Additionally, the upper and lower approximation space under the formal decision context is founded considering the risk attitudes integrating fuzzy rough set and formal concept context. Considering the order relation of various cognitive units and decision objects, we introduce the dominance relation and the importance degree of each cognitive unit under the framework of formal decision context. Furthermore, a theoretical framework of the multi-criteria decision-making problem is presented and two models for the multi-criteria group decision-making problem are discussed combined with fuzzy rough set and formal decision context from two perspectives, including qualitative analysis and quantitative analysis. Finally, an illustrated example is applied to verify the validity and effectiveness of the proposed models. The contributions of this paper include two aspects. On the one hand, this paper provides a new perspective and paradigm considering MCGDM problems with the incomplete information system from the perspective of group consensus. On the other hand, this paper gives two approaches for group decision-making problems from sorting and set theory by the perspective of multi-granular rough set and group consensus. • A model of formal decision context with incomplete information to describe the cognitive situation. • An approach to MCDM problem combined rough set with formal decision context with incomplete information. • Two approaches to MCGDM problem from qualitative analysis and quantitative analysis. [ABSTRACT FROM AUTHOR]

The current body of research on multi-attribute group decision-making (MAGDM) exhibits some limitations, namely the utilization of the single attribute hierarchy and the assumption of attribute independence. This paper presents a novel approach, referred to as the R-DLMAGDM (R-numbers Dual-Level Multi-Attribute Group Decision-Making) model with interaction factors, which integrates the advantages of R-numbers in risk evaluation. The proposed model aims to address the limitations related to attribute hierarchies and the assumption of attribute independence. The first step in the new model involves establishing the entropy model with R-numbers to determine the expert weights. Subsequently, the R-numbers generalized weighted arithmetic average (RNGWAA) operator and the R-numbers generalized weighted geometric average (RNGWGA) operator are introduced to combine the information provided by the experts. Next, the application of the enhanced correlation coefficient and standard deviation (CCSD) method is utilized to ascertain the relative weights of the dual-level attributes using the inverse order concept. Then, the fuzzy cognitive map (FCM) is employed to evaluate the interrelationships among components in order to derive the final attribute weights. Additionally, the paper discusses the implementation of the R-DLMAGDM model for the assessment of risk in a virtual supply chain in the metaverse. The evaluation process entails the prioritizing of five different alternatives based on four Level 1 criteria and seven Level 2 criteria. The model's flexibility and validity are showcased through the execution of comprehensive sensitivity analysis and three-dimensional comparative analysis. [ABSTRACT FROM AUTHOR]

This paper abstracts the complex heterogeneous multi-attribute group decision-making (CHMAGDM) characterized by two-layer decision-makers (DMs), individual attribute sets, complex relationships among attributes and heterogeneous evaluation information. DMs are composed by internal decision-makers (IDMs) and external decision-makers (EDMs). The evaluation information is represented by linguistic variables (LVs), intervals and real numbers. To handle such CHMAGDM, this paper puts forward an integrated method of prospect theory, DEMATEL (decision-making trial and evaluation laboratory) and QUALIFLEX (qualitative flexible). Firstly, a novel reference point determining approach is proposed based on three special indicators. A linguistic variable inverse prospect value function is designed and introduced to the transformation process from LVs to clouds to reduce the impacts of DMs' psychological behaviors on decision-making. Secondly, a cloud-based DEMATEL approach is proposed to determine the attribute weights, where LVs are employed to judge the relationships among attributes. A new linguistic scale function is initiated and introduced to another transformation process from clouds to LVs. A representative indicator of cloud is designed for facilitating the normalization of direct relation matrix. Moreover, a linear programming model is built to calculate the attribute weights. Thirdly, an extended QUALIFLEX approach is developed to obtain the optimal ranking and EDM weights, where adoption coefficient is provided by IDMs. Another linear programming model is constructed to calculate the optimal collective concordance/discordance index of each permutation. The optimal ranking is generated by the maximum collective concordance/discordance index. Finally, a photovoltaic power station site selection example validates the proposed method. The advantages are demonstrated with sensitivity and comparison analyses. [ABSTRACT FROM AUTHOR]

• Study analyzes 1374 papers on sensitivity analysis in Scopus. • RStudio, CiteSpace, and VOSviewer are used. • China has most articles published; India leads in international cooperation. • Top three cited journals: J. Clean. Prod., Expert Syst. Appl., and Comput. Ind. Eng. • Most cited authors are Pamučar D, Kahraman C, and Zavadskas EK. In the present era, the implementation of scientifically grounded Multi-Criteria Decision Making (MCDM) has emerged as a pivotal solution to diverse decision-making challenges across various domains. Although a substantial body of exploratory, conceptual, and experimental studies exists, only 9.457% studies have incorporated sensitivity analyses to assess the robustness of MCDM methods. An exhaustive scientific exploration of sensitivity analysis within the scope of MCDM is thus lacking. This research aims to address this gap through Bibliometric Analysis while examining 1374 articles published between January 2000 and March 2023 from the Scopus database. Using RStudio (Biblioshiny), CiteSpace, and VOSviewer software, the study constructs a visual representation of the most prolific countries, institutions, and authors. Impressively, China takes the lead in article publications, while India excels in international collaboration. "An extended TODIM multi-criteria group decision-making method for green supplier selection in an interval type-2 fuzzy environment," featured in the Journal of Environmental Management, emerges as the most cited paper with a total citation of 455. The study also identifies the top three most cited journals, namely "Journal of Cleaner Production," "Expert Systems With Applications," and "Computers and Industrial Engineering." "North China Electric Power University" is the leading institute with the highest research outputs. "Pamučar D" is the most cited author, with 2594 citations and 39 articles, followed by "Kahraman C" and "Zavadskas EK. This study sheds light on trends in scientific developments and collaborations, providing a model for the application of sensitivity analysis in MCDM research and highlighting global trends. An understanding of the current state of sensitivity analysis research can assist researchers working in the entire domain of MCDM. Additionally, the visualization provides prescriptive data for future work and applications related to sensitivity analysis. [ABSTRACT FROM AUTHOR]

Best-worst method (BWM) is an efficient multi-attribute decision-making (MADM) method. This paper puts forward two decision-making methods with intuitionistic fuzzy (IF) BWM (IF-BWM). Firstly, a new consistency definition of IF-BWM is presented. To comprehensive reflect the consistency level of original IF preference comparisons, an acceptable input-and-output-based consistency ratio (CR) of IF-BWM preference comparisons is defined to measure the consistency level of IF-BWM preference comparisons. A goal linear programming model is built to improve the consistency level of input-based CR from the original IF-BWM preference comparisons. To induce an optimal multiplicative normalized IF weight vector (IFWV), a programming model is set up. Accordingly, a novel individual IF-BWM is proposed. Using the deviation between IF values, an analytic expression of determining experts' weights is formulated. By minimizing the weighted deviation between individual multiplicative normalized IFWVs and group multiplicative normalized IFWV, a programming model is built to determine the optimal group multiplicative normalized IFWV. Subsequently, a novel group IF-BWM is put forward. Two real-life examples are furnished to reveal the validity of proposed individual IF-BWM and group IF-BWM in practice. In view of theoretical aspect, this paper fosters the theory of IF-BWM by firstly proposing an input-based CR, output-based CR, an acceptable input-and-output-based CR and group IF-BWM. The model of improving CR of IF-BWM preference comparisons is initially discussed. This paper has a certain guiding significance for the following research on IF-BWM and provides a novel perspective for an MADM problem with positive and negative preference information. [ABSTRACT FROM AUTHOR]

Interval additive preference relation (IAPR) is an efficient tool for describing the uncertain pairwise comparisons between alternatives in group decision-making (GDM). Existing GDM methods with IAPRs view the preference value as a whole and establish concrete conflict/consensus mechanisms for fusing individual opinions while neglecting the stochastic preference and aggregation modes to meet the different demands of decision. Thus, to reflect the stochastic characteristic in both preference representation and group preference aggregation, this paper presents a novel two-stage stochastic preference analysis on GDM with IAPRs. In first stage, the method involves extracting stochastic additive preference relations (SAPRs) from the IAPRs. A preference relations matrix is then established using a logarithmic least squares model applied to the SAPRs. In second stage, the weighted preference matrix is synthesized by combining the preference relations matrix with the decision makers' weight space. This leads to the computation of positive and negative ideal preference solutions, as well as positive and negative preference distances. Subsequently, the relative preference closeness is calculated based on these distances. Relative ranking results are determined by an algorithm evaluating pairwise comparisons among alternatives, resulting in transitional preference rankings. The second stage involve deriving ranking acceptance indices and ranking confidence degrees through a continuous extraction process, facilitating the establishment of the ultimate best preference rankings. The proposed method's effectiveness and validity are demonstrated by numerical examples and Monte Carlo simulations. • Introduce a two-stage stochastic preference analysis for GDM with IAPRs. • Apply the logarithmic least squares method to the stochastic APRs. • Obtain the ranking acceptability indices and preference confidence degrees with a continuous extraction process. • Demonstrate the effectiveness and validity of the proposed method using Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

• Two axiomatic notions for information measures are introduced. • Two novel methods for information measures are established. • A convergent group consensus reaching process is developed. • An empirical application is provided to show the advantages. For practical group decision-making (GDM) problems, DMs play varying degrees of importance. Thus, determining the weight of decision makers (DMs) is one of the key issues in GDM. Additionally, it is known that information measures methods have been a growing focus in recent years. Therefore, under the probabilistic linguistic fuzzy information environment, a group consensus reaching approach with the help of information measures is designed. First, two axiomatic notions regarding to entropy and similarity measures for probabilistic linguistic term sets (PLTSs) are introduced. Then, in line accordance with logarithmic function, two novel methods of entropy and similarity measures with PLTSs are established, which is followed by the determination of the weight vector of DMs by using probabilistic linguistic fuzzy entropy. Subsequently, based on probabilistic linguistic fuzzy entropy and similarity measures, we develop a group consensus reaching process (CRP), which is convergent and able to enhance the group consensus level. Moreover, the proposed group CRP can calculate the weight vector with the initial probabilistic linguistic evaluation information of DMs. Finally, for displaying the applicability and merits of the developed group CRP, the numerical example, sensitivity analysis and comparative analysis are provided. It's worth noting that our proposed measure fully utilizes the elements of the original probabilistic linguistic preference relationships (PLPRs), which can reduce the systematic error of the entire decision model, thereby making the results more reflective of the original decision information from DMs. The novelties of this paper are as follows: (1) The proposed novel way can estimate the degree of importance of DMs by the mean fuzzy entropy of PLPRs; (2) We construct two formulas about fuzzy entropy and similarity measures for PLTSs and proof these formulas, which are both reasonable and effective. [ABSTRACT FROM AUTHOR]

Health 4.0 actively focuses on cold supply chains (CSCs) due to digital transformation and technological advancements in refrigeration. With the ill effects of climate change and greenhouse gas emissions, countries globally seek sustainable supply chain management. In this context, integrating sustainability with CSCs becomes crucial. Health sectors actively consider CSC for their activities. In this context, to gain potential suppliers for healthcare management, the present work focuses on grading suppliers from the CSC with sustainability factors. Previous related studies on sustainable cold chain supplier selection (CSSS) (i) have not modeled uncertainty effectively, and (ii) have yet to use any approach under fuzzy Z-numbers information. Therefore, this paper developed an integrated framework, including the Logarithm Methodology of Additive Weights (LMAW) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) methods based on extended fuzzy Z-numbers. The practicality of the framework is exemplified via a case example within the Indian health sector, and results indicate that job creation, value price, and productivity via renewable resources are the most critical factors. Moreover, regarding the findings, the economic dimension is the foremost pillar for effective selection. Sensitivity and comparison analyses are performed to understand the efficacy of the integrated framework as well. The proposed framework could contribute to the relevant literature due to its capacity to cope with complex decision-making problems and find many application areas in engineering. [ABSTRACT FROM AUTHOR]

Aiming at three issues in large-scale group decision-making (LSGDM): risk attitudes, dynamically changing roles, and dynamically adjust evaluation information of decision makers (DMs), this paper constructs an LSGDM model by considering risk attitudes and dynamically changing roles. Firstly, we introduce the concept of risk attitudes and the method of identification and creatively combine it with Decision Making Trial and Evaluation Laboratory to divide DMs into four categories including core DMs, driven DMs, independent DMs, and followers. Considering the dynamically changing roles of DMs, an adjustment method for evaluation information is proposed. Then a double recognition mechanism is developed to determine whether the consensus has been reached. Moreover, we construct a method to determine the weights of DMs. Based on the above research, an LSGDM model based on probabilistic double hierarchy linguistic term set is constructed and applied to a practical problem of the selection of emergency medical distribution schemes. Finally, a sensitivity analysis is performed to examine the impact of different adjustment coefficients on the results, and the validity of our method is further illustrated by comparative analysis. [ABSTRACT FROM AUTHOR]

• A CODAS-based group decision model is designed for the T-spherical fuzzy context. • A T-spherical fuzzy Minkowski distance operator based on Heronian mean is proposed. • A novel ordered weighted Heronian Minkowski distance (TSFOWHMD) operator is advanced. • The TSFOWHMD operator is utilized to improve the CODAS method. • The applicability of the developed methodology is verified through a case study. T-spherical fuzzy sets (TSFSs) are more flexible and efficient tools to deal with ambiguous, uncertain and vague information in complex real-world decision-making problems than various extended intuitionistic fuzzy sets. This paper aims to develop a novel T-spherical fuzzy (TSF) Combinative Distance-Based ASsessment (CODAS) based on the Heronian Minkowski distance aggregation operator, this new method can capture interrelationship between input arguments. Some TSF weighted Heronian Minkowski distance (TSFWHMD) aggregation operators with generalization are developed based on Heronian mean and Minkowski-type distance, their properties are discussed as well as their families are analyzed. Furthermore, the TSF MAGDM methodology based on the improved CODAS is designed, where the Minkowski-type distance is used to define the TSF similarity for computing the expert weights and to construct the maximizing deviation method (MDM) for determining the attribute weights, respectively. The TSF ordered weighted Heronian Hamming distance (TSFOWHHD) and TSF ordered weighted Heronian Euclidean distance (TSFOWHED) operators derived from the TSFOWHMD operator are integrated into the CODAS method, which is an improved method for both measuring the deviation of the negative ideal solution from each alternative and capturing the correlation between attributes. Finally, the feasibility and practicality of developed methodology are illustrated with an example of CAE (Computer Aided Engineering) software selection for lithium-ion power battery (LiPB) design, sensitivity analysis and method comparisons are performed to elucidate the reliability and validity of the developed methodology. [ABSTRACT FROM AUTHOR]

In traditional multi-attribute group decision-making (MAGDM) methods, the aggregation of expert evaluation information, the normalization of attribute scales, and the determination of attribute prior weights can lead to information loss and inconsistent results. In addition, these methods cannot identify and improve the shortcomings of non-optimal alternatives. Considering these, this paper proposes a MAGDM method based on data envelopment analysis (DEA) by setting up a parallel expert evaluation system, thus integrating the initial opinions of all experts to rank the alternatives from a global perspective. First, we construct the multi-expert evaluation process as a parallel system from the global perspective so that the decision-making process is based on the initial expert evaluation information. Then, a new directional distance function model based on endogenous projection directions is proposed to measure the alternatives under each expert subsystem, eliminating data processing and artificial weight assignment. The non-optimal alternatives can be improved to an efficient state by adjusting the attribute levels to target values. Next, we propose a DDF super-efficiency model to perform a full ranking of the alternatives. Finally, a case study is provided to demonstrate the rationality and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In group decision making (GDM), due to complexity of various factors, decision makers (DMs) often provide incomplete preference relations (PRs) in preference matrix. Interval-valued probabilistic uncertain linguistic term set (IVPULTS) is a flexible and accurate tool to depict evaluation information of experts. In this paper, we mainly propose a new concept pertaining to interval-valued probabilistic uncertain linguistic preference relation (IVPULPR) that applies the IVPULTS to preference relations. Firstly, some new basic theoretical concepts of IVPULTS are developed including ordered IVPULTS, normalization method and new expectation function. Secondly, we establish several goal programming models to estimate the unknown elements in incomplete IVPULPR and propose the expected additive consistency of IVPULPR. To improve the consistency level, two optimization models are constructed based on the idea of minimum adjustment. Thirdly, we derive the experts' weights in terms of information uncertainty, where a new method to measure information uncertainty of IVPULTS is proposed. For the sake of improving group consensus, we construct a group consensus index (GCI) and two optimization models depending on the adjustment mechanism of expert weight. Finally, a complete GDM framework with incomplete IVPULPR is devised based on the analysis of IVPULPR consistency and group consensus. Through an experiment analysis by using an UCI dataset, we find that the proposed GDM model can not only precisely express fuzzy preference information of DMs, but also ensure achievement of acceptable consistency and group consensus under the condition of not changing the initial preference as much as possible. [ABSTRACT FROM AUTHOR]

• A multi-attribute group decision method based on the interval-valued intuitionistic fuzzy set is proposed. • A sustainability evaluation of an agricultural water-land-energy-carbon nexus is provided. • Multidimensional indicators are combined through stability, coordinativity and connectivity. • The water, land, energy and carbon subsystems of the agricultural system are quantified based on dual uncertainty. • The model is shown to solve real-world relationship management problems. The interactions between agricultural subsystems, resource scarcity and ecological degradation increase the need for agricultural sustainability assessments in relation to water, land, energy and carbon emissions. In addition, uncertainties caused by natural factors and human activities complicate sustainability assessments. Therefore, this study proposes a regional agricultural sustainability assessment method based on the water-land-energy-carbon (WLEC) nexus system under high uncertainty. This method couples the interval-valued intuitionistic fuzzy set (IVIFS) and multi-attribute group decision making (MAGDM) methods to quantitatively characterise and assess element management and corresponding relationships within the agricultural WLEC nexus system in a multidimensional manner. The paper is able to (1) clarify the role of the coupled agricultural "water-land-energy-carbon" nexus and (2) address the double ambiguity and uncertainty in the indicators and more objectively reflect the interval fluctuations of natural resources and social activities in both positive and negative scenarios. (3) Sustainability management of agricultural resources is carried out according to different regional conditions. The method was applied to Heilongjiang Province in northeast China, and the coupling of agricultural WLEC nexus system in 13 administrative regions of the study area was quantitatively analysed. The degree of agroecological sustainability from a multidimensional perspective is higher in Daxinganling and lower in the provincial capital, Harbin. The recommended range of groundwater use in the study area is [16%,28%] to ensure ecological sustainability when total agricultural output fluctuates between 285,395.18 and 404,495.33 billion yuan. This methodology helps policy makers understand the overall dynamics of agricultural sustainability in an environment of multiple uncertainties and gives suggestions for better assessing management. [ABSTRACT FROM AUTHOR]

Given that the majority of existing approaches for multi-criteria group decision making (MCGDM) rely solely on the preferences of decision makers (DMs) and fail to consider the various relationships between alternatives, this paper attempts to model the relevant relational structures using graphs and introduce the concept of graph neural networks (GNNs) in the context of group decision-making. By leveraging the powerful expressive capabilities of GNNs, the aim is to mine additional information pertinent to the decision-making process and screen out alternatives for the final decision. To begin, we provide a mapping of MCGDM to the graph domain and construct a corresponding relation graph among alternatives. Additionally, to deal with uncertain or vague information, we transform the group decision-making problem into a Pythagorean fuzzy environment and define a novel measure of entropy specifically designed for Pythagorean fuzzy sets (PFSs) in the entropy weight model to determine the weights of criteria. Simultaneously, we propose a new distance measure for PFSs, which is then applied to the extended Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) method to rank alternatives. Furthermore, we develop a GNNs-based Pythagorean fuzzy MCGDM approach that incorporates the aforementioned techniques for group decision-making. Finally, to validate the effectiveness and superiority of this approach, we employ it to address a supplier selection issue. Compared with baseline group decision-making approaches, our approach can indeed capture the relationships among alternatives in complex group decision-making scenarios and outperforms the best-performing baseline by nearly 2.8% in terms of ranking accuracy. • A mapping from multi-criteria group decision making to the graph domain is provided. • A normalized entropy measure is defined in Pythagorean fuzzy sets. • A modified Pythagorean fuzzy distance measure is proposed. • A Pythagorean fuzzy group decision-making approach based on graph neural networks is developed. [ABSTRACT FROM AUTHOR]

As an effective approach in ranking decision making units (DMUs), cross-efficiency evaluation is only extended to two basic network systems: series and parallel, which is not applicable to the common complex network system in reality. By using the directional distance function (DDF), this paper extends the cross-efficiency evaluation to a complex system called the parallel two-stage system, which consists of several independent parallel processes and each of them is a sub-system with a general two-stage series structure. The proposed method is able to decompose the cross-efficiency measure of the system into the weighted average of those of processes, stages and overall stages, respectively, and as a result, successfully achieves the layer-by-layer decomposition of cross-efficiency measures under complex nested networks. An empirical study on 40 open-ended equity funds in China from 2018 to 2020 verifies that the newly proposed method not only has a stronger performance discrimination power than self-evaluation, but also can identify the relationships among efficiencies of the system, processes and stages, and meanwhile it can reflect the effects of processes and stages on the system. More importantly, our method has a better practical value for actual fund investment selection. [ABSTRACT FROM AUTHOR]

• A self-organized mechanism based consensus framework is presented. • Non-cooperative behaviors are detected and managed at the element level of MAEMs. • A novel distance-based ordinal consensus measurement is proposed. • Simulation analysis is presented to show the effectiveness of our proposals. In consensus-based multi-attribute group decision making (MAGDM) problems, decision makers (DMs) may exhibit non-cooperative behaviors since they usually have different individual interests (sometimes conflicting) or limited knowledge, which strongly affects the efficiency of consensus and the quality of decision outcomes. Additionally, the existing MAGDM studies mainly focus on the cardinal consensus, and the ordinal consensus is ignored. Thus, this paper proposes a self-organized mechanism based framework to manage non-cooperative behaviors and ordinal consensus in MAGDM. First, a dual-membership function based on the basic idea of synergy theory is designed to detect non-cooperative behaviors at the element level of the multiple attribute evaluation matrix (MAEM), and then the weights of elements with non-cooperative behaviors are penalized automatically. In this way, the negative effects of non-cooperative behaviors can be eliminated. Next, a novel preference ranking-based ordinal consensus approach is proposed, which calculates an ordinal consensus based on the preference rankings of alternatives between individuals and the group. If the pre-defined consensus level is not reached, the feedback adjustment is used to help DMs modify their MAEMs to improve the consensus level; otherwise, the selection process is utilized to choose the optimal alternative(s). Finally, detailed simulation experiments and comparative analysis are designed to show the properties and effectiveness of the proposed framework, and an illustrative angel investment case is presented to demonstrate the calculation process and usability. [ABSTRACT FROM AUTHOR]

Multi-attribute group decision-making (MAGDM) is an analytical decision-making framework which gathers the views of multiple experts, and they often assess alternatives by degree adverbs in realistic scenarios. In order to treat expert opinions well, q-rung orthopair fuzzy sets (q-ROF) emerged as a data disposal tool, however, how to aggregate the information rationally remains a challenge. In this paper, q-ROF evidential reasoning methodology (q-ROF ERM) is proposed to guarantee the functionality in the case of conflicting, extreme information evaluations from experts and attributes. Second, the q-ROF attribute reduction (AR) framework is invented for attribute importance measurement. The flexibility and elegance of the model are boosted by the variation of the λ parameter and its lead to the elimination of redundant attributes. In addition to this, the q-ROF output three-way decision (TWD) framework is created to give the classification and ranking of alternatives. The relative output function derived from fuzzy distance measure and the adjustable utility pursuit coefficient τ afford both objectivity and subjectivity to the program selection, allowing the evaluation outcomes to be relevant to human cognition. Finally, the comparative experiments and sensitivity analyses of the two cases illustrate the scientificity and reliability of the presented framework in the MAGDM scenario. • A q-ROF contradictory information fusion method is proposed. • A similarity attribute reduction with λ method is established for q-ROF weights. • Q-ROF output three-way decision considers the utility pursuit τ is designed. • A q-ROF classification and ranking that fits human psychology is conducted. [ABSTRACT FROM AUTHOR]

Large-scale group decision-making (LSGDM) is a complex process involving numerous decision-makers (DMs). However, considering such a large number of DMs increases the complexity of the process. it seems necessary to pay much more attention to aspects such as a proper dimensionality reduction for scalability, consensus processes with automatic feedback, and effective management of non-cooperative DMs. To address such aspects, this paper presents a novel framework for LSGDM, based on Extended Comparative Linguistic Expressions With Symbolic Translation (ELICIT). We first extend the K-means clustering algorithm by incorporating individual assessments and trust relationships to classify DMs into subgroups, enhancing decision-making efficiency. We then develop a feedback mechanism based on two optimization consensus models for ELICIT information, that automatically provides optimal recommendations. An essential aspect of our proposal is the management of non-cooperative behaviors by utilizing the normal distribution to detect and penalize misbehaviors. Furthermore, we introduce a Data Envelopment Analysis (DEA) cross-efficiency method based on ELICIT values to rank all alternatives once an acceptable group consensus degree is reached. The framework's effectiveness is demonstrated through a practical application case study, accompanied by a parametric analysis. Comparisons with existing LSGDM methods highlight the superiority of our proposal in terms of efficiency. • A K-Means clustering algorithm based on ELICIT information and trust relationships is generalized. • A novel feedback mechanism based on two optimization models is built. • A novel approach for identifying and managing non-cooperative behavior is constructed. • An extended DEA cross-efficiency model for ranking alternatives is employed. • A novel large-scale group decision-making framework is developed. [ABSTRACT FROM AUTHOR]

In high-end equipment project selection, which involves high technical complexity, significant capital investment, and cross-industry applications, it is essential to involve experts from diverse fields in the decision-making process. To address the challenge of large-scale group decision-making, this paper proposes a three-way large-scale group decision-making model for triple-path consensus reaching process based on a rewards-and-punishments mechanism. The model consists of three stages. Firstly, the group consensus degree is calculated based on the initial input. If the specified threshold is not met, the consensus adjustment iteration stage is entered and decision makers are divided into three regions based on the Pareto principle. Secondly, separate calculations are conducted for the moving benefits and costs of decision makers in different regions, with the total benefits and costs used as targets for the NSGA-II algorithm. The Pareto solution set is obtained, and the solution with the least number of moving objects is selected as the three-way decision-making movement strategy. This process is repeated until the consensus threshold is reached or one of the regions is empty. Finally, based on the final adjustment results, scores are calculated for each project and a ranking is established as a selection suggestion. To demonstrate the feasibility and effectiveness of the model, ten high-end equipment projects are taken as examples, and the sensitivity of the model is tested by adjusting the number of decision makers. In conclusion, the proposed three-way large-scale group decision-making model based on a rewards-and-punishments mechanism for triple-path consensus reaching process is an effective and feasible approach for high-end equipment project selection. [ABSTRACT FROM AUTHOR]

In large-scale group decision-making (LSGDM) events, conflicts among decision makers (DMs) usually occur, causing serious damage to the decision-making process. Accurate conflict detection and timely management in LSGDM can improve the efficiency of the consensus reaching process (CRP) and reduce the overall conflict degree. This paper presents a conflict management-based consensus reaching process (CM-CRP) to achieve centralized and efficient management of DMs. In CM-CRP, to further manage the conflict relationships among DMs, a new clustering algorithm is considered where DMs with conflicting opinions are clustered into a subgroup. To improve the accuracy of the management and precisely the portray behaviors of DMs, for a multi-attributes LSGDM event, the confidence of DMs at the attribute level is captured. Further, the dynamic opinion weight operator is proposed in CM-CRP combining the confidence level and conflict degree of DMs, which enables a more accurate measurement of DMs' receptivity to others' opinions. Comparative experiments prove that the proposed CM-CRP outperforms the existing CRP, and several simulations investigate the effect of different factors on the CM-CRP. • The model proposed can manage conflict among decision-makers intensively. • The clustering algorithm promotes information fusion and knowledge exchange. • New confidence levels improve decision efficiency and quality. • Dynamic opinion weights describe the decision-makers' receptivity to opinions. [ABSTRACT FROM AUTHOR]

Software quality evaluation (SQE) is a multi-dimensional decision-making problem. The increasingly complex socioeconomic environment has made group decision making (GDM) more important. Determination of the relative contribution (weight) of individual decision makers is an important part of the GDM process. Calculation of the similarity between decision matrices, potentially using a comprehensive projection measure, is also critical. This paper presents: (1) a new entropy-based approach to determine the weight of decision makers; (2) a novel normalized projection approach to measuring the similarity between two decision matrices; and (3) new group regret and satisfaction reference matrices that are modeled in a GDM setting. A comprehensive GDM method is proposed and adopted for SQE. An experimental analysis is conducted to investigate the practicability, feasibility, and validity of the proposed GDM method. The experimental results confirm the proposed GDM method as practicable, producing stable rankings of alternatives, with the same ranking of alternatives being produced in almost all of the dynamic experimental cases. [Display omitted] • A new entropy-based approach is introduced that measures expert contribution. • A new normalized projection measure is proposed. • A new regret reference matrix is introduced for group decision-making. • A new satisfaction reference matrix is introduced for group decision-making. • A novel group decision-making method is applied to software quality evaluation. [ABSTRACT FROM AUTHOR]

Heterogeneous multi-attribute group decision making (HMAGDM) is a kind of complex decision making problem, which exists widely in reality. The purpose of this paper is to extend data envelopment analysis (DEA) for solving the HMAGDM problems whose attribute values include real numbers, intervals, intuitionistic fuzzy numbers, triangular fuzzy numbers, trapezoidal fuzzy numbers and linguistic variables. For this purpose, a method to HMAGDM based on a fuzzy DEA cross-efficiency model is proposed. In the proposed method, heterogeneous information is uniformly transformed into intervals, which are expressed as variables with unknown parameters. On this basis, a fuzzy DEA cross-efficiency model is established to calculate the individual cross-efficiency intervals of decision making units (DMUs). The model takes into consideration all possible attribute values of each DMU in the intervals, and obtains stable evaluation results through peer evaluation mode and iteration. Then, a maximizing group consensus model is established to calculate the weights of decision makers (DMs). Given the weights of DMs, the individual cross-efficiency intervals can be aggregated into the collective cross-efficiency interval, and DMU can be ranked based on this. An example of supplier selection is presented to illustrate the practicability and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The paper aims to present one of the extensions of the single-valued neutrosophic set, by utilizing the features of the exponential and logarithmic (EL) parameters. The present idea is to integrate the features of the EL operations into the standard neutrosophic set to enhance their diversity. The proposed set is named an exponential-logarithm single-valued neutrosophic set. The major feature of the proposed set is to include one attitude character parameter which can help the decision-maker to give their decision as per their needs. In the defined set, the uncertainties which are present during the analysis are handled with the help of the advancement of the neutrosophic set. Later on, we stated some basic operations to aggregate the information by defining the several weighted operators. The characteristics of these proposed operators are also illustrated in detail. In addition to it, we state the new exponential entropy measure and investigate the impact of the membership degrees of the proposed set. Finally, we construct a multi-attribute group decision-making algorithm to address the decision-making problems based on the stated concept. The attribute weights are derived by using exponential entropy measures. Several case studies are illustrated and the performance of the algorithm is compared with several existing studies. The sensitivity analysis and advantages of the proposed algorithm are also stated. • Presented a new exponential-logarithm-based SVNS to handle the uncertainties. • Define new entropy measure for weight extraction. • Proposed MAGDM algorithm based on proposed operations. • Several case studies are taken to illustrate the method. [ABSTRACT FROM AUTHOR]

Intuitionistic fuzzy (IF) theory has become main approach to representing imprecision and vagueness. The IF divergence measure (IFDivM) based on Jensen–Shannon divergence is perhaps the most widely used measure to compare the similarity of multiple intuitionistic fuzzy sets (IFSs). In the present paper, this IFDivM is examined and applied to multiple examples. It is found that some extant IFDivMs hardly satisfy the axiomatic definition, and in a few cases even unable to show divergence of trivial IFSs. To address these inconsistencies, a new IFDivM based on Jensen–Shannon divergence is proposed, free from these problems. The effectiveness of the proposed IFDivM is tested on several critical cases, and precise analysis of its properties is performed. It is proved that the proposed IFDivM satisfies the axiomatic definition of IFDivMs. To illustrate the practical significance of the IFDivM, a novel intuitionistic fuzzy (IF) TODIM method, based on the proposed IFDivM, is developed, termed as GIF-TODIM method. Unlike the existing IF-TODIM methods, GIF-TODIM does not suffer from the revere ordering inconsistencies. The proposed GIF-TODIM method and the proposed IFDivM are applied to a real-world case study on supplier selection. A detailed comparative analysis is performed taking the TOPSIS method and other IFDivMs as baselines. The role of attitude on the final choice is analyzed in great detail. It is found that the proposed GIF-TODIM method is indeed useful, effective, and superior to the counterpart methods, when it comes to real-world situations. Concomitantly, in the present work, it is also revealed that the TOPSIS method based on the 2-D Hamming distance is a special form of the proposed GIF-TODIM method, when decision-makers have the same attitude towards losses and gains. Thus, an interesting relationship between TOPSIS and TODIM is identified under the intuitionistic fuzzy environment, which is bound to propel significant research in the area of decision making under uncertain conditions. As a whole, the article offers comprehensive analyses of IFDivMs and the TODIM method under the intuitionistic fuzzy environment. • Construct a new IF divergence measure (IFDivM) based on Jensen–Shannon divergence. • Develop a GIF-TODIM method based on the new IFDivM. • Apply the proposed GIF-TODIM method to a supplier selection problem. • Provide parameter analysis and comparative analysis with TOPSIS and other IFDivMs. • Show that TOPSIS based on 2-D Hamming distance is a special form of our GIF-TODIM. [ABSTRACT FROM AUTHOR]

In view of the lack of research on two-sided matching group decision-making and the rare application of Fermatean fuzzy numbers in two-sided matching decision-making, a multi-attribute personnel-position matching group decision-making methodology is proposed. First, the group decision-making problem for multi-attribute personnel-position matching is described. To address this problem, a new algorithm is designed to determine the attribute weights. The group comprehensive Fermatean fuzzy evaluation matrix can be obtained by aggregating the attribute weights, the Fermatean fuzzy evaluation matrices given by the decision-makers and the weights of decision-makers. Moreover, another novel algorithm is designed to calculate the weight of the group consistency attribute. The synthetic Fermatean fuzzy evaluation matrix is obtained by aggregating the group consistency attribute weights and the Fermatean fuzzy evaluation matrices given by the candidates. Moreover, based on the group comprehensive Fermatean fuzzy evaluation matrix and the synthetic Fermatean fuzzy evaluation matrix, a multi-objective two-sided matching model is established to maximize the satisfaction of two-sided agents. The optimal two-sided matching scheme is obtained by the model solution. Finally, the feasibility, effectiveness and innovation of the proposed methodology are verified by an example analysis of personnel-position matching. The main contributions of this paper are listed as follows: (1) Group decision-making of two-sided matching based on Fermatean fuzzy information is explored. (2) A Fermatean fuzzy induced ordered weighted average (FFIOWA) operator that aggregates Fermatean fuzzy numbers is introduced. (3) Two new algorithms for calculating the unknown attribute weights are designed. (4) A satisfaction calculation method considering the accuracy coefficient is proposed. (5) The model for Fermatean fuzzy multi-attribute personnel-position matching group decision-making is developed. [ABSTRACT FROM AUTHOR]

During the multi-attribute group decision-making (MAGDM) processing, the individuals often hold different opinions about the alternatives. It is necessary to aggregate the different individual opinions into a unified group opinion. In the real world, experts sometimes use linguistic expressions to evaluate attributes in uncertain environments. To address the problem of reducing the information loss of expert opinion aggregation in MAGDM, this paper proposes a MAGDM approach based on linguistic concept lattices in the context of uncertain linguistic expression. A linguistic concept lattice for multi-expert linguistic formal context is first constructed based on linguistic truth-valued lattice implication algebra, which can express both comparable and incomparable linguistic information in the decision-making process. Different expert opinions are aggregated via the extent of fuzzy linguistic concepts, which can reduce information loss in the aggregation process. Second, meet-irreducible elements in the linguistic concept lattice are introduced to reduce the computational complexity of obtaining all fuzzy linguistic concepts in the decision-making process. the distance between the intents of different fuzzy linguistic concepts is considered to enhance the rationality of linguistic decision results. In addition, the expert's decision-making process for each alternative is visualized via linguistic concept lattices. Finally, the case study and comparative analysis illustrate the validity and rationality of the proposed approach in MAGDM with linguistic information. • The fuzzy linguistic concepts are used to aggregate expert opinions. • The comparable and incomparable linguistic information is handled in MAGDM. • Visualize the decision-making process of experts by constructing concept lattices. • A novel linguistic concept lattice-based MAGDM approach is proposed. [ABSTRACT FROM AUTHOR]

In group decision-making, the expressed opinion of a social individual may be inconsistent with or even opposite to his/her own private opinion or inner thought. Expressed and private opinions (EPOs) models were then developed to study decision-making mechanisms with private opinions. However, most of the existing EPOs models assumed that the individual private opinion is often fixed, or updated by his/her own private opinion and neighbors' expressed opinions, ignoring the behavior characteristics of social individuals. In this paper, a novel EPOs model is built under a more realistic scenario where the individual private opinions are updated by reasoning the neighbors' private opinions from their behaviors while the expressed opinions are subject to social pressure. Meanwhile, we investigate the group opinion formation under the proposed EPOs model over a Leader–Influencer–Follower hierarchical network. The evolution process under the proposed EPOs model shows that, on the one hand, when the social pressure is monotonically increasing, group expressed opinions often reach consensus, and the consensus reaching time is closely related to the pressure increase rate. On the other hand, group private opinions and behaviors of the individuals show polarization. The simulation results reveal the sociological phenomena of "the golden mean" and "inconsistent words and deeds", respectively. • Private opinions are considered in collective decision-making. • Reasoning private opinions from behaviors. • Agents are suffering from social pressure. • Opinions update using expressed and pseudo-private opinions. • Opinion formation over hierarchical social networks. [ABSTRACT FROM AUTHOR]