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The article explores the role of politicians in representative democracies and their impact on decision-making processes. It highlights the potential for bad apples, or unethical and incompetent politicians, to compromise the democratic process. The article suggests that conscientious politicians may need to compromise their moral convictions to resist bad apples and gain necessary support. It also discusses the benefits of public deliberation in empowering politicians to make informed compromises and resist the influence of bad apples. The article emphasizes the complexities and challenges of achieving political competence in representative democracies. [Extracted from the article]

Warehouses represent key links in domestic and international commodity flows. The increasing shortage of workers and increasing costs on the one hand, and the increasing number and stricter demands of users on the other hand lead warehouse managers to realize their operations as efficiently as possible. A proposed model has an objective of enabling companies to monitor warehouse performance in an authoritative, reliable, and simple way and define appropriate corrective measures accordingly. The proposed empirical research consists of three stages, where in the first stage a combination of Principal Component Analysis-Data Envelopment Analysis methods was applied in order to determine efficient warehouses based on 90 decision making units. In the second phase, a completely new method called Interval Fuzzy Rough Pivot Pair-wise Relative Criteria Importance Assessment method used for determining criteria weights was developed and applied, which is one of the most important novelties of this study. In the last phase, the Interval Fuzzy Rough Measurement of Alternatives and Ranking according to the Compromise Solution method was applied to rank the alternatives. Twelve criteria were observed to evaluate 21 alternatives. Based on the results, it was concluded that salary stood out as the most important criterion, while amortization stood out as the least significant criterion. On the other hand, alternatives A9 and A10 stood out as the best-ranked alternatives while A1, A2, and A3 stood out as the least efficient ones. The paper provides clear scientific contributions that are reflected in the reduction of the gap that was observed after reviewing the literature where there is a lack of papers dealing with this task. Also, the combination of methods applied in the paper has not been used so far, so it can be said that this paper represents an excellent basis for further research. The model has practical contributions as it allows decision-makers to make quality decisions regarding the operation of their warehouses in different time periods or observation periods, as well as it represents a decision support tool that can be used for better warehouse management. • New model for warehouse performance evaluation has been proposed. • An integrated PCA-DEA-IFR PIPRECIA-IFR MARCOS Model was developed. • New approach IFR PIPRECIA was developed and presented in literature for first time. • The model enables more accurate and precise decision-making in logistics. [ABSTRACT FROM AUTHOR]

In this paper, we examine an individual consistency control in consensus building for group decision-making that was based on a paper of Li, Rodriguez, Martinez, Dong, and Herrera. we point out their important but questionable results and then present our comments. Our results will help researchers understand the structure of individual consistency control in consensus building under fuzzy environments. [ABSTRACT FROM AUTHOR]

Aggregating various decision information provided by a group of decision makers (DMs) into an integrated one is essential for seeking the optimal solution. This paper aims to propose an effective method for information aggregation in group decision-making (GDM) in an uncertain environment. The approach introduces a family of incentive-induced cluster-based uncertain ordered weighted averaging (II-CUOWA) operators from the perspective of incentive management. Specifically, the II-CUOWA operator is first introduced, involving the definition, the clustering method of judgment information, the calculation method of position weights, and several mathematical properties. Then, the study delves into the exploration of generalized formulas for the II-CUOWA operator, as well as discussing special cases achievable by adjusting internal parameters. Finally, this paper outlines the aggregation process of II-CUOWA operators when addressing GDM problems, accompanied by a practical example illustrating its application and validity in employees' performance assessment. The results show that II-CUOWA operators not only highlight the distributed structure of decision information but also possess the capability to reward or penalize alternatives, thereby guiding their development by considering the manager's incentive preference. The proposed method enriches the methodology of GDM theory from a novel research perspective and provides a solution to practical GDM problems. [ABSTRACT FROM AUTHOR]

As an effective tool to show the fuzziness of qualitative information, the probabilistic hesitant fuzzy set (PHFS) can utilize a group of membership degrees with a clear probability distribution to show the opinions of decision-maker (DM). Given this merit, many probabilistic hesitant fuzzy multi-criteria group decision-making (PHF-MCGDM) methods have been designed. However, most of the existing PHF-MCGDM methods have some limitations, including the difficulty of reflecting DMs' ambiguous and hesitant preferences for criteria weights and the inability to comprehensively show the impacts of DMs' irrational behaviors. To address these limitations, this paper develops a novel PHF-MCGDM method that integrates the defining interrelationships between ranked criteria (DIBR) approach and tri-reference point (TRP) theory. First, the PHF-DIBR approach is constructed to determine criteria weights by fully expressing DMs' ambiguous and hesitant preferences for the importance of criteria. Second, the novel probabilistic hesitant fuzzy correlation coefficient (NPHFCC) is developed for deriving the weights of DMs, which remedies the flaws of the existing correlation coefficients (CC). Moreover, TRP theory is used to describe the psychological behavior effects of DMs and derive the order of alternatives. Finally, the applicability of the proposed method is validated by the case about office flooring material selection, while the sensitivity and comparison analyses are also conducted to further prove its advantages and effectiveness. [ABSTRACT FROM AUTHOR]

The remote sensing satellite observation process involves multiple stakeholders and significant costs, so selecting an appropriate observation scheme and reaching an agreement on the chosen scheme among the evaluators/stakeholders is essential. From this perspective, the observation scheme selection problem can be viewed as a large-scale group decision-making (LSGDM) problem, challenging due to its complex group composition and the high consensus level required. Accordingly, this paper investigates an adaptive bi-directional consensus model that incorporates the evolution of social influence to address the LSGDM problem. Firstly, the dual-attribute affinity propagation algorithm is employed to divide the large-group into manageable subgroups. Secondly, the social influence evolution model is established, where evaluators' social influences are determined by considering their opinion similarity and trust level, and subgroups' social influences are updated by measuring their decision risk. Thirdly, the bi-directional feedback mechanism is designed to adaptively generate adjustment strategies corresponding to different scenarios based on the evolution model. Finally, an observation scheme selection case is analyzed using the proposal to demonstrate its practicality. During the process of remote sensing satellite observation, the selection of an appropriate observation scheme can optimize the utilization of existing satellite resources and ensure the quality of satellite observation services, thereby better meeting the demands of diverse application areas such as environmental monitoring, disaster management, and urban planning. [ABSTRACT FROM AUTHOR]

The additive ratio assessment system (ARAS) method is an effective technique for simplifying complex decision problems by determining the optimal alternative through the relative index (utility degree) to the ideal solution. However, there are still some shortcomings in the existing researches on the extension of this method when it is utilized in different decision environments, such as ignoring the correlation relationship between attributes, the lack of flexibility in the utilization of the decision process, and the relative index to the ideal solution may be scaled up or down with the ratio form. In order to overcome these disadvantages, this paper proposes the novel T-spherical fuzzy (TSF) cross entropy (TSFCE) measure and T-spherical Aczel-Alsina Heronian mean (TSFAAHM) aggregation operators and uses them to improve the ARAS method in the TSF environment. For the TSF multiple attribute group decision-making (MAGDM) problems, a group decision making model based on the improved ARAS is designed. In this model, the experts' weights are obtained by the TSFCE-based similarity measure. The attribute combined weights are calculated by fusing the objective weights obtained by TSFCE-based entropy measure and the subjective weights got by the extended stepwise weight assessment ratio analysis (SWARA) integrated with TSFCE. In the improved ARAS method, the T-spherical Aczel-Alsina Weighted Heronian mean (TSFAAWHM) operator can capture the correlation relationship between the attributes. Compared with the relative index, the TSFCE can reflect the difference between the alternatives and the ideal solution to obtain a more stable solution ranking. Lastly, an illustrative example about the sustainable supplier selection of power battery echelon utilization (PBEU) for a 5G base station is used to demonstrate the proposed method. The effectiveness, practicability and superiority of proposed method are illustrated by parameters influence and methods comparison analysis. [ABSTRACT FROM AUTHOR]

In practical decision-making, linguistic term set is a useful tool to describe the uncertainty and fuzziness of data sources. However, in some decisions, when the data source is unreliable or the decision involves future factors, the evaluation given by the linguistic term set will have a certain degree of error. This paper proposes a binary risk linguistic set based on linguistic term set and R-set. The binary risk linguistic set considers the linguistic term set and the risk factors that may lead to errors in language evaluation. In order to facilitate the use of binary risk linguistic set, the risk conversion function and operational laws are introduced. Next, since group decision-making involves multiple experts, considering the social relations between experts, a method to estimate the missing values in the social network matrix is proposed by utilizing the trust intensity propagation operator and the relationship intensity propagation operator. Risk perception can reflect the subjective judgment of experts on the characteristics and severity of a particular risk, and different judgment results can reflect the attitude of experts to risk. Hereby, this study proposes a risk clustering method based on the risk perception of experts. Furthermore, we propose an adaptive weight updating method based on social network matrix. Then, a binary risk linguistic fuzzy behavioral TOPSIS method is proposed to deal with the multi-attribute large-scale group decision-making (MALSGDM) problem. Finally, a case study is used to demonstrate the feasibility of the presented method, and its effectiveness is validated through comparison with other MALSGDM methods. To demonstrate the effectiveness of the proposed method, this study also perform sensitivity and stability assessments of the decision-makers' weight and behavior characteristics. [ABSTRACT FROM AUTHOR]

Cubical fuzzy numbers offer an improved framework for assessing uncertain factors in decision-making. The accumulation of cubical fuzzy opinions is pivotal in every group decision-making process. This research paper focuses on creating innovative cubical fuzzy Bonferroni mean geometric aggregation operators and their weighted adaptations. We build these operators upon the principles of cubical fuzzy Einstein operations. The proposed operators can capture intricate relationships among evaluated cubical fuzzy factors. We formally demonstrate and validate the desirable properties of these introduced operators. In addressing the complexities of multiple criteria group decision-making, we present a Cubical Fuzzy Complex Proportional Assessment (CF-COPRAS) method as a practical solution. Determining the weights of criteria holds significant importance in any decisionmaking methodology. In this paper, we employ the intercriteria correlation (CRITIC) method to establish objective criteria weights. To showcase the effectiveness of our developed method, we apply it to a real-world financial investment risk management scenario within a cubical fuzzy context. Subsequently, we conduct a sensitivity analysis and comparative evaluation to demonstrate the efficacy of our proposed approach. [ABSTRACT FROM AUTHOR]

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Trust network analysis has been widely applied in various fields, such as group recommendation, group decision-making and other related areas. In this paper, we focus on obtaining the complete trust network in which experts express their trust relationships for another with a single linguistic term or distribution assessments of a linguistic term set. We first discuss the conditions of obtaining the complete trust network, and the propagation and aggregation of the trust relationships with a single linguistic term. Since the linguistic term set may be symmetric and uniform, symmetric and non-uniform, or asymmetric and non-uniform, we translate linguistic terms into numerical indexes and define the propagation operator based on the semantics of the linguistic term and the Archimedean t-norm. The propagation result is translated to 2−tuple linguistic model because it may not exist in the initial linguistic term set. Some properties are proposed to verify that the proposed operator is compatible with human thought. Then the 2−tuple distribution assessments on a linguistic term set are defined, and the other aggregation operator is proposed to propagate linguistic distribution assessment trust relationships. The second aggregation operator focuses on both the aggregation of linguistic terms and symbolic proportions of linguistic terms and is a generalization of the first operator. Finally, a numerical example of CouchSurfing comparative analyses further demonstrates that the proposed operators are effective and reasonable, and can consider the different semantics of a linguistic term in practical application. [ABSTRACT FROM AUTHOR]

Intuitionistic fuzzy (IF) sets are valuable tools for describing uncertain information in Multi-Criteria Group Decision Making (MCGDM), where the elements have degrees of membership and non-membership. IF aggregation operator is a popular data processing method that can be used for data dimensionality reduction, feature extraction, data compression, and so on. Some existing MCGDM techniques based on IF aggregation operators have been criticized for reasons that include disregarding the comprehensive correlations of the criteria and ignoring the monotonicity of the decision information. This paper aims to construct some IF aggregation operators based on Yager's triangular norms and Heronian mean to shed light on decision-making issues. At first, some novel IF operations such as Yager sum, Yager product, and Yager scalar multiplication on IFSs are presented. Based on these new operations, the generalized IF Yager Heronian average (GIFYHA) operator and the generalized IF Yager weighted Heronian average (GIFYWHA) operator are proposed and their corresponding properties are also proved in detail. Then, an improved MCGDM algorithm is constructed that relies on suggested operators. Its effectiveness and applicability are verified by applying it to select the best location for a company. In addition, the sensitivity of the parameters in the proposed operator to decision findings is also discussed. Finally, the comparative analysis of the proposed operator with the existing operators shows that the proposed operator is suitable for aggregating IF information with correlations both on "non-empty lattice" and total orders on IF values. [ABSTRACT FROM AUTHOR]

p , q -quasirung orthopair fuzzy set (p , q -QOFS) is an extension of the q -rung orthopair fuzzy set (q -ROFS) theory used to represent uncertainty and vagueness in decision-making processes. The paper aims to utilize robust sine-trigonometric operational laws to investigate the group decision-making process within the p , q -QOFSs framework. The p , q -QOFS possess a distinctive characteristic of handling uncertain information by utilizing a wider space for membership representation compared to q -ROFS. Consequently, the current paper has been categorized into three distinct phases. In the initial phase, novel operational laws will be presented for p , q -QOFSs. The fundamental concept behind these newly proposed operations is to integrate the properties of the sine function, which include being periodic and symmetric about the origin, into the decision-making process for objects. Then, based on these laws, several operators for aggregating information will be obtained, along with their necessary properties and relationships. Lastly, an algorithm will be presented for interpreting the problem of multi attribute group decision-making (MAGDM), utilizing the operators, and demonstrating it with an illustrative example. A comprehensive comparative analysis will be conducted with some of the existing methods to uncover their impacts. [ABSTRACT FROM AUTHOR]

Resilience is the sustainable competitive advantage of suppliers in the supply chain, and the ability of resilient suppliers to manage risk and perform better in supply than traditional suppliers in the event of disruption has driven the complexity of the current supply chain. Therefore, studying how to select a resilient supplier is necessary for establishing a supply chain with flexibility in the case of interruption. A hybrid fuzzy Multi-Criteria Group Decision-Making (MCGDM) framework is developed in this paper for Resilient Supplier Selection Problems (RSSPs). First, Probabilistic Uncertain Linguistic Term Sets (PULTSs) are introduced to deal with the subjectivity and uncertainty of experts' assessments. Second, considering that experts may have different views on the relative importance of resilient criteria depending on their different knowledge backgrounds, the Probabilistic Uncertain Linguistic Best–Worst Method (PUL-BWM) is constructed to determine the weights of resilient criteria under different experts. In addition, given that the traditional Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) cannot handle the information metrics with negative values or reflect the correlation of information, the extended TOPSIS method based on a novel Probabilistic Uncertain Linguistic Synthetic Correlation Coefficient (PULSCC) is constructed to select the optimal resilient supplier. The novel PULSCC also overcomes the drawbacks of the existing correlation coefficient between PULTSs by considering the mean, variance, and information completeness of PULTSs. Finally, an example of resilient supplier selection in the automotive industry is performed to validate the applicability and feasibility of the proposed approach. The sensitivity and comparative analyses are conducted to demonstrate the effectiveness and superiority of the proposed framework. [ABSTRACT FROM AUTHOR]

Intelligent computing has distinct cognitive characteristics, especially when dealing with some multi-attribute group decision-making questions, it is regarded as a human behavior based on cognition. Pythagorean fuzzy set (PFS) is not only an extension of intuitionistic fuzzy set (IFS), but also can handle some fuzzy decision-making problems of multi-attribute information on a larger scale, especially some new methods have been rapidly spread and developed in decision-making science. In this paper, some defects in the existing ranking criteria for Pythagorean fuzzy numbers (PFNs) were pointed out through some counterexamples, the main reasons of these flaws are analyzed, so that all IFNs are unified into PFNs space through coordinate transformation. Secondly, a novel improved score formula and ranking method are proposed by the residual sector area (RSA) and hesitancy degree of PFNs in a geometric background, and the rationality of this ranking criterion is further demonstrated through rigorous mathematical methods, and then the fundamental properties of the score function are discussed. Finally, the superiority of the novel score function was interpreted through comparison and analysis with other existing seven score formulas, and the new score formula was applied to multi-attribute group decision-making problems through an example, and the superiority of the novel method was fully displayed. In fact, the proposed method achieves a perfect ranking of all PFNs, especially for the equivalent PFNs, it can be achieved precise comparison or ranking, which overcomes some flaws of other methods, and ending the confusion caused by the independent ranking of IFNs and PFNs. [ABSTRACT FROM AUTHOR]

Multi-attribute group decision-making (MAGDM) is an important research field in modern decision science, and its theories and methods are fully applied. Therefore, research on MAGDM has important practical significance and high practical value. First of all, this paper gives the relevant definitions and calculation rules of 2TLPFSs, as well as the Hamming distance, cumulative prospect theory (CPT), etc, secondly introduces the entropy weight method and the traditional EDAS method, respectively, and then gives the EDAS method for MAGDM with 2TLPFs (2TLPF-EDAS) on the basis of the previous research and the concrete steps of EDAS method for MAGDM based on CPT with 2TLPFs (2TLPF-CPT-EDAS) method combining entropy weight method. In addition, the 2TLPF-CPT-EDAS method is applied to the numerical example of product research and development (R&D) problem, and the result is compared with other three methods. It is found that the 2TLPF-CPT-EDAS method is feasible, and the application field is further expanded. Finally, the full paper is summarized, and based on the problems of the current work, the focus of future work is laid out. [ABSTRACT FROM AUTHOR]

This paper applies the cumulative prospect theory to improve the traditional integer subscript hesitant fuzzy linguistic term set (IS-HFLTS). The proposed variable subscript hesitant fuzzy language set (VS-HFLTS) takes into account the subjectivity and differences of investors' behavior when investing in the securities market, and extends the application of behavioral finance to multi-criteria group decision-making portfolio. To evaluate the financial products, the VS-HFLTS multi-criteria group decision-making portfolio evaluation system is constructed in the research. The hesitant fuzzy linguistic value function and the purchase appetite weight function are proposed to convert the natural linguistic evaluation into a quantitative score for the judgment of future portfolio return in the securities market. Furthermore, a variable subscript hesitant fuzzy linguistic portfolio model is put forward for the risk-averse, risk-neutral, and risk-seeking investment decision-makers. The optimal portfolio strategy is obtained by solving the equivalent non-linear model. Meanwhile, an optimized group decision-making portfolio strategy is established to better achieve the goal of increasing group decision-making investors' returns or reducing risks. Finally, numerical simulations are performed to find effective frontiers for future portfolio selection, which verifies the validity and feasibility of the models and methods proposed in this paper. [ABSTRACT FROM AUTHOR]

The main innovation of this paper is to transform Pythagorean fuzzy numbers (PFNs) into the analytic representation of centroid coordinates and hesitation factors through the transformation, and then the unified ranking method, distance measure and similarity with respect to PFNs are proposed using geometric method. These concepts can not only overcome some defects of existing methods, but also be applied to multi-attribute group decision-making problems. In this paper, the centroid coordinate representation of PFN is first introduced with regard to the hesitation region, when considering the degree of nonzero hesitation, the hesitation factor is proposed by comparing with the smallest element (0,1), and a new ranking method for PFNs is given by calculating the hesitation factor in the Pythagorean fuzzy number environment. Secondly, the distance measure and degree of similarity are put forward through the hesitation factor and centroid coordinates, and the Pythagorean fuzzy priority weighted average (PFPWA) operator is given by improving the priority weight parameter. Besides, the basic properties of PFPWA operator are discussed. Finally, the positive (negative) hesitation factor solutions, bidirectional projections and degrees of closeness for group comprehensive evaluation matrix are obtained, and a new TOPSIS method for dealing with multi-attribute decision-making problems is given under the Pythagorean fuzzy environment. The given example shows that the proposed method not only expands the scope of application and reduces the loss of some fuzzy information, but also eliminates the impact of abnormal data on the aggregation results by considering the priority of experts. [ABSTRACT FROM AUTHOR]

Experts have shifted from precise numerical representations to more complex linguistic representations in response to the growing complexity of occupational health and safety (OHS) risk assessment problems. However, there are more difficulties in accurately assessing risk when dealing with complex linguistic representations. Furthermore, in uncertain situations including complex linguistic representations, the multi-criteria decision-making (MCDM) approaches now in use for OHS risk assessment fail to synchronize the assessment of criteria and alternatives. To address these issues, this paper proposes a novel approach for OHS risk assessment that extends the idea of simultaneous evaluation of criteria and alternatives (SECA) to group decision-making (GDM) with complex linguistic representations. Firstly, flexible linguistic expressions (FLEs) are employed to represent experts' complex linguistic risk assessments. Secondly, to accurately quantify the flexible linguistic assessment information, a numerical scale optimization model is constructed based on maximizing the closeness between individual and collective assessments, with the aim of obtaining the numerical scales of linguistic terms and flexible linguistic term sets. Then, an extended SECA-GDM method considering flexible linguistic scale optimization is proposed to simultaneously determine the risk criteria weights and priority order of occupational hazards. Finally, a case study is conducted to verify the effectiveness of the proposed method. ● FLEs are used to represent complex linguistic risk assessment information. ● A scale optimization model for flexible linguistic assessments is built. ● An extended SECA-GDM method for the OHS risk assessment is developed. ● A case study is presented to illustrate the feasibility of the proposed method. [ABSTRACT FROM AUTHOR]

Trapezoidal Atanassov's intuitionistic fuzzy numbers (TrAIFNs) is one of the useful tools to manage the fuzziness and vagueness in expressing decision data and solving decision making problems. In this paper, based on the operation laws defined by strict t-norms and t-conorms, four kinds of power geometric operators, i.e., triangular (co)norms-based (T-based) power geometric operator of TrAIFNs, T-based weighted power geometric operator of TrAIFNs, T-based power ordered weighted geometric operator of TrAIFNs, and T-based power hybrid geometric operator of TrAIFNs, are developed. To minimize loss of information in process, a new ranking method of TrAIFNs are presented based on the newly proposed possibility differences of TrAIFNs; Moreover, utilizing strict t-conorms, a new similarity measurement of TrAIFNs is innovated. Thereby, in combination with all the referred elements, two approaches to multiple attributes group decision making using TrAIFNs are developed. In the end, the feasibility of those methods and the superiority over the existing methods are demonstrated by a numerical example. [ABSTRACT FROM AUTHOR]

Motivated by the concepts of low carbon and environmental protection, electric vehicles have received much attention and become more and more popular all around the world. The expanding demand for electric vehicles has driven the rapid development of the charging pile industry. One of the prominent issues in charging pile industry is to determine their sites, which is a complex decision-making problem. As a matter of factor, the process of charging piles sites selection can be regarded as multi-attribute group decision-making (MAGDM), which is the main topic of this paper. The recently proposed linguistic spherical fuzzy sets (LSFSs) composed of the linguistic membership degree, linguistic abstinence degree and linguistic non-membership degree are powerful tools to express the evaluation information of decision makers (DMs). Based on the concept of LSFSs, we introduce probabilistic multi-valued linguistic spherical fuzzy sets (PMVLSFSs), which can describe DMs' fuzzy evaluation information in a more refined and accurate way. The operation rules of PMVLSFSs are also developed in this article. To effectively aggregate PMVLSFSs, the probabilistic multi-valued linguistic spherical fuzzy power generalized Maclaurin symmetric mean operator and the probabilistic multi-valued linguistic spherical fuzzy power weighted generalized Maclaurin symmetric mean are put forward. Based on the above aggregation operators, a new method for MAGDM problem with PMVLSFSs is established. Further, a practical case of suitable site selection of charging pile is used to verify the practicability of this method. Lastly, comparative anal-ysis with other methods is performed to illustrate the advantages and stability of proposed method. [ABSTRACT FROM AUTHOR]

The seamless integration of computerized methodologies into industrial engineering problem-solving is pivotal for optimizing efficiency. In the specific domain of multi-attribute group decision-making (MAGDM) with probabilistic linguistic term sets (PLTSs), these methodologies offer systematic approaches to consensus building, ensuring effective decision processes in intricate scenarios. Within the realm of PLTSs, the consensus-reaching process (CRP) for MAGDM is gaining prominence. This paper addresses this evolving area by proposing ordinal and cardinal CRPs within the framework of PLTSs, specifically incorporating the regret theory (RT) of three-way decisions (TWD). The paper introduces an initial distance formula under PLTSs, providing a complementary approach to assess similarity relations among decision-makers (DMs). To account for diverse semantics across DMs, personalized individual semantics (PIS) is integrated into the CRP, recognizing variations in DMs' alternatives and attributes. To enhance realism, the paper introduces the concepts of individual alternative sets and individual attribute sets. Additionally, the paper integrates ordinal and cardinal consensus, establishing a dynamic feedback adjustment mechanism grounded in the principles of RT and TWD. The method's reasonableness is validated through a real case study, and a comparative analysis with the existing methods underscores the superiority of the approach presented in this paper. • A new valid distance formula is proposed for probabilistic linguistic term sets. • Constructing a new utility maximization method to derive personalized individual semantics. • The individual attribute and alternative sets are proposed to construct group consensus. • A consensus methodology is designed to incorporate both ordinal and cardinal consensus. • Designing a feedback adjustment mechanism based on regret theory and three-way decision. [ABSTRACT FROM AUTHOR]

Probabilistic linguistic term set (PLTS), which consists of multiple linguistic terms and their probabilities, has been proposed to tackle qualitative information in informs of linguistic expressions. Since experts are inclined to compare alternatives in pairs, the probabilistic linguistic preference relation (PLPR), a matrix whose elements are PLTSs, has attracted wide attention since it was first introduced in 2016. Fruitful research achievements regarding PLPRs have been generated, especially in group decision making (GDM). This paper reviews 88 selected articles published from 2016 to June 4, 2023 regarding PLPRs, and presents a review of researches on theory and applications of PLPRs. First, we conduct a bibliometric study of these selected articles in terms of publication and citation trends, most productive countries/regions, categories of publications and keyword co-occurrence relationships. Next, the theory of PLPRs including definition, missing element deduction, consistency checking, prioritization, and decision-making analysis methods are recalled. We also review real-world applications of these publications and find that PLPRs have been mainly applied in four areas, including healthcare management, project evaluation, environment and energy management, and emergency management. In the end, we propose future research directions related to the probabilistic linguistic decision-making theory and provide insights for researchers and practitioners who have an interest in complex linguistic decision making. [ABSTRACT FROM AUTHOR]

Precision agriculture refers to the use of advanced technologies and data analytics to optimize farming practices, maximize crop yields, and reduce resource wastage. In precision agriculture monitoring, unmanned aerial vehicles (UAVs) have emerged as a valuable tool for large-scale implementation. The selection of suitable UAVs is a critical aspect of precision agriculture and is deliberated as significant multi-attribute group decision-making (MAGDM) problem. In decision issues, the evaluation of experts about any available options plays an important role. In this context, interval-valued q-rung orthopair fuzzy set (IVq-ROFS) is a useful tool allowing experts to provide their evaluations in a wider space and better deal with incomplete information. This paper aims to develop a new approach to determining expert weights using distance and similarity measures for interval-valued q-rung orthopair fuzzy numbers (IVq-ROFNs). To achieve this, an average group assessment based on individual assessments is constructed. The experts' weights were then established by computing similarity measures between the individual evaluations and the average group assessment. Moreover, the technique for order of preference by similarity to the ideal solution (TOPSIS) method is extended to address the MAGDM problem under IVq-ROF information. An example involving UAV selection for precision agriculture is provided to demonstrate the validity of the suggested method, and the impact of parameters on decision results is discussed. Finally, a comparative analysis with existing approaches demonstrates the superiority and advantages of the proposed technique. [ABSTRACT FROM AUTHOR]

In new industrial product development, human-involvement conceptual design evaluation (CDE) is an information-intensive and multi-criteria group decision-making (MCGDM) process. To capture and formalize the uncertain information from decision-makers (DMs), several derivations of fuzzy number such as triangular intuitionistic fuzzy number (TIFN), Z-number, and interval number have been employed in CDE, which only cover limited information. The main contributions of this paper are as follows: firstly, a new kind of fuzzy number by taking advantage of TIFN, Z-number and interval number, i.e., interval intuitionistic fuzzy-Z-number (IIFZN), is presented to utilize DM's preference value (PV) for alternative, as well as his important rating (IR) and familiarity degree (FD) judgements for evaluation criterion. IIFZN is composed of not only the membership and non-membership of PV or IR, but also the affiliated confidence coefficient transformed from FD. Then, in terms of the IIFZN-based decision-making matrix, this study proposes new ideal solution definition rules and distance measurement metric in technique for order preference by similarity to ideal solution (TOPSIS) to form a new TOPSIS-IIFZN method. The proposed method will enable DM easily find the alternative which is most preferable for important and familiar criteria and least preferred for less important and unfamiliar criteria as the best one. It is more rational than traditional PV-only CDE method, which will help company to save manufacturing resources. Besides theoretical research, one practical example and three more complex comparative experiments have been carried out to validate the performance of TOPSIS-IIFZN. By comparing with other MCGDM methods using different types of fuzzy numbers, it proves that TOPSIS-IIFZN can obtain more reasonable evaluation results. Meanwhile, besides PV, the RI and FD factors also play great influences in CDE. [ABSTRACT FROM AUTHOR]

Fuzzy sets, which have a crucial role in the decision making theory, model uncertainty by means of membership and non-membership functions. q-rung orthopair fuzzy sets, which are the natural extension of fuzzy, intuitionistic fuzzy and Pythagorean fuzzy sets, are quite successful in modeling data thanks to their larger domains. However, in a q-rung orthopair fuzzy set the membership and non-membership degrees of an element to a set are given just by a pair of certain numbers from the closed interval [0, 1] that causes a strict modelling. Various types of interval valued fuzzy sets, multi fuzzy sets or circular fuzzy sets change these strict modelling with a sensitive one. In this paper, we introduce a new fuzzy set notion via continuous functions that take values on a closed interval to provide a more sensitive tool in decision making theory. In this new fuzzy set notion, the membership and non-membership degrees of an element to a fuzzy set are represented by continuous functions instead of numbers. Actually, we study not only with points, but also with functions by taking into account the sufficiently large and continuous neighborhoods of the points. Thus more sensitive and realistic models are made by relieving the precision of the fuzzy data or linguistic argument. The data carried to function space environment is processed with the function theoretic tools via aggregation functions, distance measures or score functions. This fact distinguishes the new fuzzy set notion from the other continuous extensions in the literature such as interval valued or circular structures. Moreover, we provide an extended Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) in this new fuzzy environment and apply it to a multi criteria group decision making problem from the literature. Finally, we provide a comparison analysis and a complexity analysis. We also visualise the time complexity of the proposed extended TOPSIS for different numbers of decision makers. [ABSTRACT FROM AUTHOR]

Linguistic intuitionistic variables (LIVs), allowing decision makers to employ linguistic variables to express their qualitative positive and negative judgments, are powerful for denoting qualitative information. Considering the advantages of LIVs, this paper develops a new group decision-making (GDM) method with linguistic intuitionistic fuzzy preference relations (LIFPRs) and researches its utilization to choose the best green cold chain logistics partner. To achieve this goal, a definition for multiplicatively consistent LIFPRs is first offered. Then, an algorithm to determine missing linguistic variables is provided, and optimization for adjusting inconsistent judgments is built. In addition, a similarity measure-based consensus index is offered, which is adopted to improve the consensus level. After that, an algorithm for GDM with LIFPRs is provided. Finally, a case study for green cold chain logistics partner selection is performed to testify the application of the new method, and a comparative discussion is conducted to highlight the feasibility. [ABSTRACT FROM AUTHOR]

The linguistic 𝑞-rung orthopair fuzzy (L𝑞-ROF) set is an important implement in the research area in modelling vague decision information by incorporating the advantages of 𝑞- rung orthopair fuzzy sets and linguistic variables. This paper aims to investigate the multicriteria decision group decision making (MCGDM) with L𝑞-ROF information. To do this, utilizing Hamacher 𝑡-norm and 𝑡-conorm, some L𝑞-ROF prioritized aggregation operators viz., L𝑞- ROF Hamacher prioritized weighted averaging, and L𝑞-ROF Hamacher prioritized weighted geometric operators are developed in this paper. The defined operators can effectively deal with different priority levels of attributes involved in the decision making processes. In addition, Hamacher parameters incorporated with the proposed operators make the information fusion process more flexible. Some prominent characteristics of the developed operators are also wellproven. Then based on the proposed aggregation operators, an MCGDM model with L𝑞-ROF context is framed. A numerical example is illustrated in accordance with the developed model to verify its rationality and applicability. The impacts of Hamacher and rung parameters on the achieved decision results are also analyzed in detail. Afterwards, a comparative study with other representative methods is presented in order to reflect the validity and superiority of the proposed approach. [ABSTRACT FROM AUTHOR]

The objective of this article is to answer the question: On what basis, or under what conditions can moral responsibility be attributed to a collective? The author assumes that the moral world is not only populated by individuals, but it also includes groups. The goal of the paper is to show that raising the question of collective responsibility in its moral dimension depends on the ontological recognition of the collective as a new entity with its own intentions, which is different from the entities of individuals who make it up. The author first presents some solutions based on the methodological individualism, which derive the existence of collective moral responsibility from the internal rules of group decision-making and from collectively shared goals. The author sees the problem of the examined views in the fact that the combination of the methodological individualism with a certain collectivist vision does not guarantee the recognition of collective entities in their real existence. Based on the holistically oriented research of V. Descombes, the study subsequently focuses on defining the ontological status of the collective. Using his arguments, the paper concludes that applying the idea of moral responsibility at the collective level presupposes recognition of the collective as a supra-individual entity sui generis and as a subject of collective intentionality. [ABSTRACT FROM AUTHOR]

In learning groups, individuals have a few similarities in terms of the regularity of learning time, requirement for learning resources, and requirement for tutoring and accompanying. Analyzing the differences and connections of the learning behavior of different groups is helpful for generating more effective, targeted, and comprehensive learning decisions, however, existing studies are not extensive or deep enough in analyzing the learning behavior of different type learning groups. For this reason, this paper attempts to explore a learning decision-making model based on the influence of group learning behavior. At first, this paper made use of the advantages of Q-learning to improve the conventional behavior tree model, constructed a new model and used it to research the group learning behavior; then, this paper combined decision-making idea with the game model, and adopted a complex network structure to explore the evolution law of group learning decision-making based on multiple games. At last, this paper used experimental results to prove the effectiveness of the constructed model. [ABSTRACT FROM AUTHOR]

In consideration of the different importance degrees that may be assigned to all possible linguistic terms, this paper investigates a novel three-way group decision-making method based on the probabilistic linguistic term set (PLTS) information systems. We first construct PLTS information systems based on multiple attributes. Considering the reliabilities of the experts, we determine the weights of the experts by the similarities of the information provided by the expert with regard to other experts. Subsequently, using the evidential reasoning (ER) method, we aggregate the information provided by all experts and obtain the conditional probability of each object. The introduction of the ER rules and the weights of experts successfully solve the problem of conflict between the evaluation information. Then an approach is presented to calculate loss functions and thresholds, which reduces the subjectivity of the decision-making process. Next, the decision result of each object is deduced based on the minimum-loss principle. Finally, a case study about the selection of mask foundries during the COVID-19 is used to demonstrate the effectiveness of our proposed method. And the superiority of our proposed method are proved by comparative analysis. [ABSTRACT FROM AUTHOR]

The paper aims to present a new method to solve the multi-attribute group decision-making (MAGDM) problem under the probabilistic hesitant fuzzy environment. For this, we present the novel concept of gained and lost dominance score (GLDS) method based on cumulative prospect theory (CPT). The major advantage of the proposed GLDS method is that it concentrates on the loss aversion of the decision-makers (DMs), while we integrated the CPT to evaluate the risk aversion considering the DM's rational behavior. Meanwhile, the weights among criterions are evaluated by using the process of analytic hierarchy process (AHP) method. The stated MAGDM algorithm has been implemented in a numerical example of sustainable supplier selection (SSS) for medical device manufacturing enterprises. SSS is an active development with the global advocacy of green economy and green supply chain and considered it as the typical MAGDM issue. The results have been compared with several of the existing approaches to validate its supremacy. [ABSTRACT FROM AUTHOR]

Live-streaming e-commerce is the future development direction of the retail industry. When retailers choose a live-streaming e-commerce platform, they face the test of various risks of the platform, such as insecure control of capital flow, insufficient support of public domain traffic, etc. Therefore, it is necessary to evaluate the risks of the platform to help retailers identify the platform with the lowest risk. Considering the complexity of the risks of live-streaming e-commerce platforms and the ambiguity of the decision-makers thinking, the current method for multi-criteria group decision-making (MCGDM) method in a fuzzy environment rarely discusses the decision-makers weight for the criterion. This paper proposes interval-valued intuitionistic fuzzy multi-criteria group decision-making based on the decision-makers' professionalism to evaluate the platform's risks. This method determines the decision-maker's weight for the criterion based on the professionalism of the decision-maker and uses the technique for order preference by similarity to an ideal solution (TOPSIS) method to rank the alternative platforms. Finally, a risk assessment of the agricultural product live-streaming e-commerce platforms is used as a case study to demonstrate the feasibility and effectiveness of the proposed method. This research will not only provide practical guidance for retailers to choose the live-streaming e-commerce platform with the lowest comprehensive risk but also provide ideas for the research of live-streaming e-commerce from the perspective of risk assessment. [ABSTRACT FROM AUTHOR]

This paper studies the cost consensus model by considering the uncertain initial opinions and uncertain unit adjustment cost in group decision making. In the past consensus model based on optimization, the initial opinion and unit adjustment cost are usually assumed to be a crisp number for each expert. However, the speed of knowledge updating is often faster than people's cognitive speed, it is difficult and impractical to ask experts to provide a clear initial opinion and determine the unit adjustment cost of each expert. In this paper, a new consensus approach is proposed to solve the above problems. First, a new distance measure is given based on interval-valued initial opinion, which retains the expert's initial judgment and is consistent with most practical decision problems. Second, a linear analytical formula is given to reduce the computational cost of the piecewise function. Third, given the advantages of robust optimization in uncertain optimization, three robust cost consensus models are established to deal with the uncertain cost problem in consensus reaching progress. Finally, the proposed method is applied to P2P loan consensus, and sensitivity analysis and comparative analysis are presented. [ABSTRACT FROM AUTHOR]

The aggregation of fuzzy information is a key process of MCDM methods used to deal with uncertainties. A class of aggregation methods for fuzzy information is fuzzy distance aggregation operators in which distance values are argument variables. This class of aggregation operators permits us to consider an ideal alternative in the aggregation process. But these operators fall in dealing with situations among which distance values cannot be aggregated directly. Therefore, we proposed some distance induced fuzzy operators in which distance values are order-inducing variables so that we can also consider an ideal alternative but take other parameters, also including distance values, as argument variables in an aggregation process. We analyzed the concepts, properties, and generalized forms of proposed distance induced fuzzy operators in this paper. Moreover, aiming at multi-criteria group decision-making (MCGDM), three frameworks of MCGDM methods with the proposed distance induced fuzzy operators are constructed for three different MCGDM situations, respectively. At the end of this paper, an example is used to explain the detailed processes of using the proposed frameworks to make a decision. [ABSTRACT FROM AUTHOR]

One of the most challenging issues in group recommendation is how to consider the dispersion in members' preferences to reach a joint recommendation satisfying all the group. The group recommendation is generated by aggregating either the users' preferences or the individual recommendations. In this paper, we focus on the recommendations aggregation strategy which consists in generating a recommendation list for each group member, then combining these individual lists to produce a single group recommendation list. Many aggregation functions (such as average, least misery, Borda, etc.) were used to resolve the ranking aggregation problem. However, they cannot support the partial information presented over the top-k recommendation lists which may not contain the same set of alternatives. To this end, we propose a group recommendation method based on a novel aggregation function that considers the partial rankings and computes each item's relevance to the target group based on both the users' preferences and the items' positions. We conduct a deep experiment to study the impact of some parameters (such as the individual recommendation algorithms, the aggregation functions, and the group size) on the group recommendations quality. We have shown that the accuracy of the group recommendations does not depend on the algorithm used to generate individual recommendations. However, it is strongly affected by the method used to aggregate data and the group size. Experimental results show a considerable improvement in the group recommendation performance using the proposed solution. [ABSTRACT FROM AUTHOR]

Intuitionistic fuzzy preference relations (IFPRs) can not only deal with the uncertainty and vagueness of decision makers' judgments but also describe the information from the aspects of preferred and non-preferred, respectively. Thus, it has proved to be an efficient tool for solving group decision-making (GDM) problems. However, considering the expression of linguistic information of the current extended IFPRs is limited by a single linguistic term, it is still imperfect to deal with GDM problems. Hence, this paper first proposes a novel extended IFPRs as linguistic dual hesitant fuzzy preference relations (LDHFPRs) by utilizing a set of ordered linguistic terms to describe the preferred and non-preferred evaluation information, which recognize the uncertainty and hesitance of each decision maker and conform to real-life decision-making situations better. Subsequently, we construct the conditions of additive consistency and develop a maximum consistency linear programming model to cope with the problem of inconsistent LDHFPRs. Furthermore, a novel consensus reaching process which pays more attention to the minority but important individual opinions is established. Finally, a real-world application is utilized to demonstrate the effectiveness of the proposed method, and a comparison with the existing related works is presented to show the advantages and innovation of the proposed GDM method. [ABSTRACT FROM AUTHOR]

Consensus reaching process mainly includes consensus measurement and consensus improvement. Ignoring the bounded rational behavior of group members will affect the credibility of decision results. This paper proposes a consensus model that considers bounded rational behaviors of group members under uncertain environment. Firstly, we propose a similarity measure of probabilistic linguistic term sets (PLTSs) based on the Jensen-Shannon divergence, which can measure the difference between different probability distributions corresponding to PLTSs that are used to represent uncertain information. Then, the DEMATEL method is used to determine the weights of criteria according to the relationship between criteria, and a weight penalty mechanism is introduced to improve the consensus level of a group. Next, we combine the TODIM and VIKOR methods to elicit the ranking of alternatives. Finally, a numerical example is given to verify the feasibility and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Intuitionistic fuzzy graphs are extensions of fuzzy graphs that preserve the dualism characteristics of fuzzy graphs and have a stronger capacity to describe ambiguity in actual decision-making issues than fuzzy graphs. In this research paper, the Laplacian energy and correlation coefficient of intuitionistic fuzzy graphs are computed for finding group decision-making problems that are supported by intuitionistic fuzzy preference relations. We propose a novel method for calculating establishments’ comparative position loads by manipulating the undecided corroboration of IFPR and the correlation coefficient of one personality IFPR to the other items. As a result, we comprehend a large number of establishments in the detailed IFPR and devise a correlation coefficient process to investigate the significance of alternatives and the best of the alternatives. Finally, we present a collaborative decision-making technique in a money-investing scheme, and that idea may be devised in disparate beneficial investing schemes. [ABSTRACT FROM AUTHOR]

In the context of the increasingly competitive post-epidemic social marketing era, the sustainable development of supply chain finance is also facing the impact of more complex risk factors. However, the issue concerning how to scientifically and reasonably select the appropriate applicant company for financing cooperation on the basis of risk evaluation remains unresolved. For the smooth operation of banks' sustainable supply chain finance (SSCF) business, this paper aims to develop a novel multi-attribute group decision-making (MAGDM) method considering the robustness and comprehensiveness among risk attributes and decision-makers (DMs). First, based on the idea that quantitative assessment values and qualitative linguistic sets can more accurately express uncertain risk information and importance degree of indicators, a novel concept is proposed that combines the probabilistic linguistic term set (PLTS) with the plithogenic set to evaluate the risk attributes of each alternative. Additionally, risk decision matrices evaluated by DMs are integrated and transformed through the operation of PLTS scoring function aggregation operators and the plithogenic contradiction degree. For deriving the integrated weight information of attributes, the objective attribute weights are determined on the basis of the subjective weights by adjusting coefficients. Then, the ranking order of alternatives is generated by applying the VIKOR method and constructing a MAGDM model with plithogenic PLTSs. Finally, the solving of a practical example concerning the selection of financing objects for SSCF oriented by risk evaluation verifies the effectiveness of the proposed model, where five risk indicators are developed, and the superiority of our studies is demonstrated by comparing with the existing TOPSIS and ELECTRE methods. [ABSTRACT FROM AUTHOR]

In this paper, we propose a hybrid concept of q-rung orthopair fuzzy soft set and hypersoft set (HSS), called q-rung orthopair fuzzy hypersoft set (q-ROFHSS), which is used to express insufficient and undefined information in decision-making problems. Then we define some basic operations for q-ROFHS number (q-ROFHSN). Furthermore, correlation coefficients (CC) have been applied widely in many research domains and practical fields. In this work, we present correlation coefficients, weighted correlation coefficients, and some properties are also discussed, and then correlation coefficient-based TOPSIS (prioritization technique for order preference by similarity to ideal solution) method is developed under the q-rung orthopair fuzzy hypersoft settings. Using the established TOPSIS method, a decision-making procedure is proposed under q-rung orthopair fuzzy hypersoft environment to solve the uncertain and ambiguous information. In the end, a practical example is investigated and a comparison analysis is executed with other existing methods to illustrate the feasibility, practicality and superiority of our proposed method. [ABSTRACT FROM AUTHOR]

Fuzzy sets have undergone several expansions and generalisations in the literature, including Atanasov's intuitionistic fuzzy sets, type 2 fuzzy sets, and fuzzy multisets, to name a few. They can be regarded as fuzzy multisets from a formal standpoint; nevertheless, their interpretation differs from the two other approaches to fuzzy multisets that are currently available. Hesitating fuzzy sets (HFS) are very useful if consultants have hesitation in dealing with group decision-making problems between several possible memberships. However, these possible memberships can be not only crisp values in [0,1], but also interval values during a practical evaluation process. Hesitant bipolar valued fuzzy set (HBVFS) is a generalization of HFS. This paper aims to introduce a general framework of multi-attribute group decision-making using social network. We propose two types of decision-making processes: Type-1 decision-making process and Type-2 decision-making process. In the Type-1 decision-making process, the experts' original opinion is proces for the final ranking of alternatives. In Type-2 decision making processs, there are two major aspects we consider. First, consistency tests and checking of consensus models are given for detecting that the judgments are logically rational. Otherwise, the framework demands (partial) decision-makers to review their assessments. Second, the coherence and consensus of several HBVFSs are established for final ranking of alternatives. The proposed framework is clarified by an example of software packages selection of a university. [ABSTRACT FROM AUTHOR]

The metaverse, constructed through digital technology, serves as a virtual realm intertwining with reality. Within this context, the challenge of evaluating data from diverse sources arises, and the application of large-scale group decision-making (LSGDM) methods emerges as a viable solution. Handling incomplete information and reducing dimensionality for large-scale decision-makers (DMs) is crucial in addressing complex decision-making problems. Moreover, addressing missing data is a fundamental and pivotal concern in tackling real-world decision challenges, given the ubiquitous presence of information gaps that cannot be straightforwardly integrated into decision models. Besides, the intricacies of LSGDM amplify this challenge by introducing a wealth of DMs, thereby augmenting the complexity and diversity of decision-related information. This paper proposes an approach to supplement missing data by double-dimensions. This paper explores various facets of similarity relationships within the data to enhance data completeness. Additionally, this paper categorizes DMs into clusters based on their relevance and establishes a two-stage consensus-reaching process (CRP) that takes into account both group sizes and individual consensus contributions. These CRPs play a crucial role in enhancing the overall consistency and consensus within the decision group. Subsequently, this paper applies a robust decision-making method rooted in MULTIMOORA (Multi-Objective Optimization by Ratio Analysis plus the complete MULTIplicative form) to rank decision objects. Finally, this paper employs this proposed methodology in a practical case study that involves evaluating the operational status of a metaverse's urban construction metro system. Following these considerations, a comprehensive stability analysis of relevant parameters is conducted to guarantee the robustness and reliability of the decision-making process. • A similarity-based double-dimensional patching method for absent values is proposed. • A clustering-based dimensionality reduction for decision-makers is developed. • A two-stage consensus-reaching process based on weight adjustments is constructed. • A robust decision-making method based on MULTIMOORA and TODIM is explored. [ABSTRACT FROM AUTHOR]

The maximum expert consensus model (MECM) is a commonly used consensus model in group decision making (GDM). In traditional MECM, the consensus constraints are not fully considered and the adjustment cost of decision maker (DM) is certain. Moreover, directing the DM's opinion in a visual path is seldom considered in the consensus reaching process (CRP) of MECM. Inspired by these issues, this paper first proposed two MECMs with different types of consensus constraints. Then, this paper incorporated an adjustment path into MECM by using feedback coefficients that can prevent opinions from being overadjusted. Furthermore, the robust MECM (RMECM) is developed to address the uncertainty of unit adjustment cost under three uncertainty sets. Finally, the feasibility of the proposed models is verified by applying them to the allocation of special funds in the Chinese film industry, which is a large-scale group decision making (LSGDM) problem. The sensitivity analysis and comparative analysis are also conducted to show the efficiency of the proposed models. • Two MECMs with different constraints are proposed. • An explicit adjustment path is incorporated into the traditional MECM. • RMECMs are proposed to address the uncertainty in CRP under three uncertain scenarios. • The proposed models are applied to a specific LSGDM problem. [ABSTRACT FROM AUTHOR]

Density Peak Clustering (DPC) was proposed in the journal Science in 2014 and has been widely applied in many fields due to its simplicity and effectiveness. However, there are few studies on the effectiveness of DPC algorithm and its variants on non-clean data sets. Inspired by the idea that DPC algorithm combines density and distance when determining clustering center, this paper creatively designs a two-stage density clustering method with fuzzy connectivity (TS-DCM). It could be used to distinguish different cluster partitions and further identify noise points and sample points. In addition, this paper also introduces a new clustering index: fuzzy connectivity, which could not only adjust the selection of DPC cutoff distance, but also provide a reference for adaptive adjustment of TS-DCM parameter selection, greatly improving the operating efficiency of the clustering algorithm. At the same time, a self-adaptive two-stage density clustering method (STS-DCM) is proposed to adjust the selection of parameters according to the feedback of clustering results. Finally, compared with other traditional and popular clustering algorithms, it is verified that the proposed algorithm has significant advantages in speed and accuracy. Moreover, for non-clean data sets, the algorithm is robust and effective. • Propose fuzzy connectivity as an important index for density clustering; • A two-stage density clustering algorithm(TS-DCM) is proposed; • A novel STS-DCM algorithm to determine the parameter selection. [ABSTRACT FROM AUTHOR]

Three-way multi-attribute decision-making (3MADM) integrated with double hierarchy hesitant fuzzy linguistic term set (DHHFLTS) can not only effectively express the uncertainty of language, but also help reduce the risk of wrong decision-making. However, the existing compared methods for DHHFLTSs dismiss the variances in psychological reference points, resulting in mismatches in form and connotation for some linguistic terms. Furthermore, it is difficult or even impossible to obtain an accurate degree of difference using the existing DHHFLTS distance method for these linguistic terms. This directly affects the accuracy of obtaining conditional probabilities results in the three-way decision model. Therefore, this paper introduces the concept of the superior gradus for double hierarchy linguistic term set (DHLTS) and double hierarchy hesitant fuzzy linguistic element (DHHFLE), respectively. Then, some novel compared methods are defined that allow the identification of differences between linguistic variables. Subsequently, based on the superior gradus, a novel distance measurement is designed with a risk parameters. Through the adjustment of risk parameters, this method can respectively obtain optimistic and pessimistic results. Also, the relative loss functions designed for DHHFLTSs aim at getting more objective decision-making results. Finally, the paper proposes a novel 3MADM method under the double hierarchy hesitant fuzzy linguistic information system (DHHFLIS) and applies it to service assessment. To verify the effectiveness and rationality, the medical diagnosis data set is used, and the results are compared with other classic MAMD methods. • 3MADM with DHHFLTS reduces the risk of wrong decision-making. • Superior gradus is introduced to identify DHHFLTS's variances. • Novel distance measurement is designed with a risk parameters. • Relative loss functions for DHHFLTS enhance objective results. • Novel 3MADM method is applied in service assessment and compared with classic MAMD. [ABSTRACT FROM AUTHOR]

This paper proposes a novel plan-do-check-act (PDCA) based group decision making model to evaluate the GSCM performance of manufacturing organizations. This research employs an integrated fuzzy multi-criteria decision-making (MCDM) approach in which the fuzzy-analytical hierarchy process (FAHP) method determines criteria weights and the fuzzy-technique for order preference by similarity to the ideal solution (FTOPSIS) method ranks the organizations. Five qualitative criteria are selected from the extant literature, which encompass both environmental, operational, and economic aspects of sustainability. Data is collected by developing a questionnaire, establishing a decision-makers' committee, and carrying out a survey. To illustrate the industrial application of the proposed model, this study considers a real-world case study in the Indian manufacturing sector, in which three organizations (Organization A, Organization B, and Organization C) are selected from three distinct industrial segments, namely the leather industry, the pharmaceutical industry, and the steel industry, respectively. The result reveals that the environmental impact of harmful substances released from production is the most influential parameter. The result also reveals that Organization C is the benchmark organization and its strategies can guide other organizations for GSCM performance improvement. Moreover, the proposed model is capable of handling vagueness and ambiguity in decisions. [ABSTRACT FROM AUTHOR]

Spherical fuzzy sets (SFSs) provide more free space for decision makers (DMs) to express preference information from four aspects: approval, objection, abstention and refusal. The partitioned Maclaurin symmetric mean (PMSM) operator is an effective information fusion tool, which can fully capture the interrelationships among any multiple attributes in the same block whereas attributes in different block are unrelated. Therefore, in this paper, we first extend PMSM operator to spherical fuzzy environment and develop spherical fuzzy PMSM (SFPMSM) operator as well as spherical fuzzy weighted PMSM (SFWPMSM) operator. Meanwhile, we discuss some properties and special cases of these two operators. To diminish the impact of extreme evaluation values on decision-making results, then we integrate power average (PA) operator and PMSM operator to further develop spherical fuzzy power PMSM (SFPPMSM) operator and spherical fuzzy weighted power PMSM (SFWPPMSM) operator and also investigate their desirable properties. Subsequently, a new multiple attribute group decision making (MAGDM) method is established based on SFWPPMSM operator under spherical fuzzy environment. Finally, two numerical examples are used to illustrate the proposed method, and comparative analysis with the existing methods to further testy the validity and superiority of the proposed method. [ABSTRACT FROM AUTHOR]

In Multi-Criteria Group Decision-Making (MCGDM), linguistic evaluation is widely used due to its flexibility. In particular, Personalized Individual Semantics (PIS), namely decision-makers hold heterogeneous understandings of the same word, has been extensively studied to elicit numeric meaning to the linguistic scale. However, few studies consider the need to tailor linguistics to the different indicators used, as well as the semantic difference in the same level linguistic that experts use when situations change. The traditional PIS models overlook the psychological aspect of the decision makers. To solve these problems, this paper proposes a method that considers semantic differences arising from the decision-makers and the indicators and incorporates the experts' psychological behavior. We apply this method to assess the alternatives for a smart refrigerator product service system. The results suggest that a large semantic difference, when evaluating the linguistic indicators, can influence the final outcome. We validate the flexibility and the effectiveness of the method by comparing against the base case of no semantic difference, using the Euclidean and Manhattan distance measures. • We proposed a method to obtain more accurate numeric meanings of the linguistic terms. • The method can tailor linguistics to the different indicators. • The method considers semantic differences arising from the decision-makers and the indicators. • The method incorporates the psychological behavior of the decision-makers. • The method uses more information, including alternative-preference matrix, criteria-preference matrix and decision matrix. [ABSTRACT FROM AUTHOR]

The increasing complexity of social activities requires an expanding number of people to be involved in decision-making, so that the large-scale multi-attribute group decision-making problems have gained widespread attention. After overviewing the researches of large-scale multi-attribute group decision-making methods, we have found that: The existing methods only consider consensus based on evaluation information of alternatives, while ignoring the consensus on importance of attributes. Thus, in order to tackle the issues and describe the hesitancy of decision makers in the decision-making process, this paper proposes a novel dual consensus method in large-scale multi-attribute group decision making under hesitant fuzzy linguistic environment. In the consensus reaching process, the method considers not only the consensus on the evaluation information of alternatives, but also the consensus on the importance of attributes, where both consensus reaching processes are implemented by the particle swarm optimization algorithm. The subjective weights of attributes are derived from the consensus reaching process of preference matrices, and the objective weights of attributes are obtained from the consensus reaching process of decision matrices, so as to acquire the comprehensive weights. After that, the overall ranking of alternatives can be obtained by TODIM. Finally, the proposed method is applied to a case study of medical imaging equipment purchasing decision-making, and the comprehensive analysis is provided to clarify advantages of the proposed method. • Propose a novel dual consensus method which considers alternatives and attributes. • The decision-making process is realized by particle swarm optimization algorithm. • Attribute weights contain both subjective and objective information. • Apply the proposed method to medical imaging equipment purchasing decision-making. • Clarify the advantages of the proposed method through comprehensive analyses. [ABSTRACT FROM AUTHOR]