Consensus Reaching Process for Traditional Group Decision Making in View of the Optimal Adjustment Mechanism.

Consensus reaching process (CRP) is a key topic in the area of group decision making (GDM). When the consensus level is not high enough, it becomes necessary to adjust the original opinions of decision makers (DMs). To offer the adjustment reference for DMs, we build the programming models to determine the minimum modification to be carried out from the individual and global perspectives. Meanwhile, all DMs are divided into two subgroups: DMs with acceptable and unacceptable consensus levels. If some DMs with unacceptable consensus level do not accept the relevant modifications, the Nash bargaining game-based programming model is built for the fairness and efficiency of modifications. When some DMs refuse to make any modifications or tend to modify the opinions in their way, with respect to different group consensus situations, we make the minimum hybrid penalty mechanism by the Nash bargaining game-based programming models. For each case, we determine the corresponding optimal modification mechanism in view of the fixed individual total modification and the maximum consensus level. Furthermore, we study the arrangements of weights of DMs according to their cardinal and ordinal consensus contributions. Based on these results, we present a new algorithm and illustrate its application by a numerical example. Moreover, we carry out the sensitivity and comparison analysis. We summarize the conclusions and future research directions in the end. The main originality of the new method includes: the fairness and efficiency of modifications, and the determination of the hybrid penalty mechanism.