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In large-scale group decision making (LSGDM), appropriate clustering analysis is important to consensus reaching since it can reduce the interactive complexity among individuals. According to the traditional clustering method, a conflict may arise between the consensus reaching levels and total adjustment costs within clusters when individuals have different unit adjustment cost, which reflects their willingness to make concessions. Since this conflict may aggravate the consensus complexity, we propose a new $K$ -means clustering method that considers both preferences and the preference adjustment cost. The preference adjustment cost is attached to preferences with a parameter that can be determined by balancing this conflict. Because of such conflict, the proposed clustering algorithm can improve the similarity of intracluster individuals on the preference adjustment cost by offsetting some acceptable consensus reaching levels within clusters. According to the proposed clustering algorithm, individuals who have both similar preferences and adjustment willingness are classified into the same clusters. In this way, the moderator can provide similar compensation strategies for intracluster individuals, which will decrease the adjustment complexity. A practical case study of team construction examines the application of the proposed algorithm, and the related comparative analysis shows that it is convenient for managers to persuade individuals to reach a consensus under the improved clustering results. [ABSTRACT FROM AUTHOR]

In most existing linguistic distribution multiple criteria group decision-making (MCGDM) models, the sample size of group linguistic distribution assessment (LDA) is often neglected, and the decision makers are viewed to be independent. The probabilistic distribution is closely related to the sample size, and there exist more or fewer interference effects among different individual opinions. Thus, this article develops a quantum framework for modeling interference effects in the linguistic distribution MCGDM process. First, considering the sample size information, we redefine the LDAs and provide a new computational model for them. Second, to integrate a series of LDAs, the linguistic distribution weighted averaging (LDWA) operator is presented. Mathematic proofs reveal that the new LDWA operator can not only ensure the information integrality but also can avoid the conjunctive and disjunctive operations. Third, to explore the interference effects among individual opinions, a quantum framework is constructed. In this process, individual opinions are viewed as various wave functions occurring synchronously. They interfere with each and influence the aggregation result. Finally, an illustrative example of Internet finance soft power evaluation is provided to verify the effectiveness. Sensitivity and comparative analyses are also implemented to assess the stability and validity of our method. [ABSTRACT FROM AUTHOR]

Ranking of fuzzy numbers (FNs) is a key stage within fuzzy multicriteria decision analysis (FMCDA). However, the influence of FNs dependence on their ranking, including ranking alternatives within FMCDA, has not been studied yet. In this article, for studying such an influence, the widely used defuzzification-based fuzzy ranking methods, centroid index, and integral of means, along with their modifications, which are pairwise comparison defuzzification ranking methods, are explored. The authors argue that classical defuzzification ranking methods are intended to deal with independent FNs, whereas their modifications may be used for ranking of dependent FNs. It is provided a proof in which, pairwise comparison Yuan’s and defuzzification integral of means ranking methods, are equivalent when ordering independent and can differ when ordering dependent FNs; at the same time, Yuan’s and modified integral of means ranking methods are equivalent when ordering both independent and dependent FNs. Intransitivity of the two modified ranking methods when ordering dependent FNs as well as intransitivity of alternatives in FMCDA for fuzzy multiattribute value theory (FMAVT) as an example is proved. The distinctions in ranking of dependent FNs by all ranking methods under consideration are explored through ordering alternatives within FMAVT. For this, a real-life case study is considered, and the distinctions in ordering alternatives by classical and modified ranking methods are demonstrated. Statistical analysis of distinctions in ordering alternatives by FMAVT with different ranking methods is implemented with the use of Monte–Carlo simulation. The significance of distinctions for the choice and ranking multicriteria problems, as well as for justification of utilizing ranking methods under consideration in FMCDA, is discussed. [ABSTRACT FROM AUTHOR]

The management of uncertainty in decision-making problems remains a very challenging and timely research issue despite many proposals. An interesting topic in this area in recent years has been Granular Computing. In this paper, we present a coherent framework for various models of information granules, using hierarchies of information for dealing with knowledge acquired and processed at different levels of abstraction. Granular Computing, a paradigm for handling higher types of uncertainty in decision analysis, is considered a new conceptual and algorithmic asset of decision-making studies and, in particular, data-driven decision-making. Most relevant studies have focused on categories of information granules, namely intervals, fuzzy sets, rough sets, and shadowed sets. To better understand this promising area, this study provides a comprehensive overview of Granular Computing for decision-making through literature analysis, enhancing a variety of extensions, applications, and challenges. • We propose a comprehensive review for granular computing in decision making. • We provide a bibliometric review for granular computing in decision making. • We review main applications in granular computing in decision making. • We provide some future directions for granular computing in decision making. [ABSTRACT FROM AUTHOR]

The Failure mode and effect analysis (FMEA) is an effective risk evaluation approach which has been widely used to assist in risk controlling in various workplaces. However, in practice, the conventional FMEA approach suffers from the drawbacks associated with the risk evaluation and priorization methods. In this paper, a novel risk priorization method for FMEA based on the extended MULTIMOORA (Multi-Objective Optimization by Ratio Analysis plus the Full Multiplicative Form) method is proposed. First, the interval type-2 fuzzy sets are applied to deal with the uncertainty of risk evaluation in FMEA. Second, the distance-based method is used to calculate the importance weight of each risk factor. Then, an extended MULTIMOORA method is presented to rank risk priority of each failure mode, in which the distance measure for interval type-2 fuzzy number is incorporated. Finally, a practical case in steel company is selected to illustrate the application and feasibility of the proposed approach. A comparative analysis is conducted to demonstrate the effectiveness of the developed risk priorization method. [ABSTRACT FROM AUTHOR]

Pythagorean fuzzy sets, originally proposed by Yager (IFSA world congress and NAFIPS annual meeting (IFSA/NAFIPS), pp 57-61, 2013), which are convenient to describe vagueness and impression in real-world problems, can be regarded as a novel extension of intuitionistic fuzzy sets. Generalized Maclaurin symmetric mean comes as an extension of classical Maclaurin symmetric mean. Their prominent feature is that they can both capture overall interrelationships and also focus on individual importance among the arguments. However, the generalized Maclaurin symmetric mean can only be considered for aggregating numeric information. In this paper, we investigate the generalized Maclaurin symmetric mean and further extend to Pythagorean fuzzy environment. We develop the Pythagorean fuzzy generalized Maclaurin symmetric mean (PFGMSM), the Pythagorean fuzzy weighted generalized Maclaurin symmetric mean (PFWGMSM), and discuss a variety of their desirable properties. To better understand the proposed parameterization operators, we provide an innovative way to extend the classical superiority and inferiority ranking (SIR) group decision model to Pythagorean fuzzy environment. Then, an approach formed with the aid of PFWGMSM and SIR to multiple attribute group decision-making with Pythagorean fuzzy information is developed. Finally, an illustrative example concerning supply chain financial risk decision-making is provided to verify the proposed method and demonstrate its effectiveness. [ABSTRACT FROM AUTHOR]

Type-2 fuzzy sets (T2FSs) have the advantage of representing higher-order uncertainty, they have demonstrated superior performance in several applications. In order to fully measure the uncertainty for T2FSs. In this study, several distribution characteristics of uncertainties within T2FSs are analyzed through type-1 fuzzy sets (T1FSs), and the axiomatic framework of fuzzy entropy and overall entropy of T2FSs is established as well. First, a new representation method for T2FSs is given. On this basis, the axiomatic definitions of fuzzy entropy for T1FSs and T2FSs are constructed by analyzing the distribution characteristics of fuzziness, and the construction theorems and basic properties of fuzzy entropy are studied. Further, the overall entropy of T2FSs is given, on this basis, a novel type-2 fuzzy entropy-based decision-making method is proposed, and applied to the selection of cold medicine through online reviews on AliHealth.cn. Finally, the feasibility and effectiveness of the developed definitions and methods are demonstrated by three comparative analyses. • A new mathematical expression of T2FSs is defined. • The axiomatic framework of fuzzy entropy of T2FSs is constructed. • The overall entropy of type-2 fuzzy information is defined. • A novel decision-making method based on overall entropy is developed. • A real application through online review is proposed. [ABSTRACT FROM AUTHOR]