Cooperative game theory based consistency and consensus reaching process for group decision making with fuzzy preference relations

Fuzzy preference relations (FPRs) are potent in denoting the pairwise comparison of objects. Besides the consistency analysis, the consensus is critical to making decision results reasonably in group decision making (GDM). Different from current research that either adopts feedback interactive method or optimal model-based total minimum adjustment method, this paper introduces new consensus adjustment mechanisms in the perspective of cooperative games, which determine decision makers (DMs) consistency and consensus adjustments by considering all consistency and consensus adjustment coalitions (CCACs). Compared with previous methods, the main merit of the new method is the reasonable and fair allocation of consistency and consensus adjustment. To achieve this goal, this paper first regards DMs as players in cooperative games and considers each DM coalition's consistency and consensus adjustment as its payoff. Then, two crucial single-valued payoff indices are offered to allocate the consistency and consensus adjustments to DMs. The axioms of these payoff indices identify rationality and efficiency. Further, a new method is performed that follows the ordinal consistency, acceptable additive consistency, and consensus. Finally, a case study is offered to show the concrete application of the new method, and a comparison is carried out.