Consistency and Consensus Analysis for Group Decision Making With Fuzzy Preference Relations Based on Cooperative Game Theory

Abstract

Consistency and consensus study for group decision making (GDM) with fuzzy preference relations (FPRs) are necessary, which have a decisive impact on the quality of decision results. Consistency can prevent self-contradictory judgments, and consensus limits the deviation among individual judgments within the preset threshold. Because acceptably multiplicative consistency still cannot avoid self-contradictory judgments, this paper considers the ordinal consistency and acceptably multiplicative consistency simultaneously. In view of these aspects, we introduce a new optimal model-based method for GDM with FPRs. As minimum total adjustment and minimum individual adjustment may be inconsistent, we introduce the Solidarity consistency and consensus adjustment mechanism (So-CCAM) to allocate the minimum total adjustment, which fully considers the cooperation and solidarity among decision makers. When the So-CCAM does not exhibit stability, we present the nucleolus consistency and consensus adjustment mechanism (Nu-CCAM), which is the best element in the core according to lexicographical order. After that, an algorithm is offered. To demonstrate the application and efficiency of the new method, an illustrative example is offered, and a comparison is carried out. It offers the first optimization models-based method for GDM with FPRs in view of ordinal consistency, acceptably multiplicative consistency, and consensus analysis. Further, it provides two rational consistency and consensus adjustment mechanisms by cooperative game theory.