Consensus group decision making based on coalitional Nash-bargaining game

Consensus analysis is required to ensure the quality of decision results. It means that some DMs' opinions must be adjusted to reach a consensus. As a result, it harms DMs' benefits because their opinions are not fully considered. Additionally, the consensus-reaching needs cooperation between DMs. Therefore, the consensus improvement can be seen as a cooperative game among DMs. Considering the benefit conflicts of DMs, this paper studies the adjustments of DMs in view of the Nash-bargaining game, which can ensure the global Pareto optimality and maximum fairness of the consensus adjustment scheme. Considering the inconsistency between the Pareto and individual optimal solutions, we first study the Nash-bargaining consensus adjustment solutions between individual DMs. For the situation where DMs form coalitions to reduce their adjustments, two cases for the coalitional Nash-bargaining consensus adjustment solutions of DMs are further studied. Meanwhile, interactive algorithms for the formation of DM coalitions are provided. The main characteristics of the Nash-bargaining consensus adjustment solution are the consideration of personal interest, the rationality of DMs, and the fairness of the allocation scheme. Moreover, this paper takes the choice of the cooperative partner of elderly care institutions as an example to show the concrete application of built models.