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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]

In this article, we propose the concept of flexible linguistic preference relations (FLPRs), in which the flexible linguistic expressions, a more flexible way to form linguistic expressions, are employed. Further, we present a method to rank alternatives based on preference information in FLPRs by exploring the linguistic distribution (LD) and priority-based approximation (PA) of FLPRs. In the LD-based approximation, we first present a two-stage optimization process to approximate FLPRs to distribution linguistic preference relations (DLPRs) following the principles of minimum preference loss and maximum consistency. Then in the PA process, we derive priority vectors from the DLPRs with some desired properties. Finally, a comparative analysis of the priority vectors derived from different kinds of linguistic preference relations is presented to illustrate our proposal. [ABSTRACT FROM AUTHOR]

In this article, we deal with an improved fusion method for multigranular linguistic distribution assessments, a flexible and practical expression, in a multiple criteria group decision-making problem, which permits an accurate transformation between two linguistic labels without the loss of information. The importance degree of decision makers is allocated on the basis of individual consistency elicited from evaluation assessments represented by linguistic distributions, which is described with the aid of the proposed dominance degree of linguistic distribution. To intuitively reflect the group consensus level, a new measure, Jaccard consensus of linguistic distribution, is introduced. Based on this, a consensus-based multicriteria group preference analysis model with multigranular linguistic distribution information is established within a unified framework, which is developed by means of additive multiattribute value utility theory. Furthermore, a corresponding algorithm is matched to obtain a representative value function for decision analysis and an illustrative example is developed to illustrate the effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]

Various linguistic expressions have been presented to model the flexibility of linguistic preference expressions and to support the consensus reaching in linguistic group decision-making (GDM). In this paper, we propose the concept of flexible linguistic expressions (FLEs) as a general linguistic preference expression format to improve the flexibility of the construction of complex linguistic expressions and the elicitation of linguistic preferences and, then, we develop a new linguistic GDM model with FLEs, referred to as FLE-based GDM (FLEGDM). In the FLEGDM, an FLE aggregation process with accurate constraints is developed to improve the quality (i.e., accuracy) of the collective result as well as guarantee the principle of minimum preference-loss through a mixed 0–1 linear programming model. Meanwhile, the consensus rules with minimum preference-loss are designed to support the consensus reaching process (CRS) in the FLEGDM. Finally, we present the detailed comparative analysis involving different linguistic GDM models to show the advantages of the FLEGDM. [ABSTRACT FROM AUTHOR]