An adaptive optimization consensus mechanism for group decision making using the Shapley allocation scheme

Adaptive consensus mechanism adopts differentiating consensus improvement strategies according to different consensus levels, which is reasonable and efficient for reaching consensus in group decision making. However, previous adaptive consensus methods adopt the feedback iteration mechanism, which has drawbacks such as time-consuming, over-consensus adjustment, and failure of consensus-reaching. Therefore, this paper studies the adaptive consensus mechanism by optimization models to avoid the above issues of the feedback iteration mechanism. In our approach, corresponding optimization models are constructed to identify non-consensus judgments, non-consensus alternatives, and non-consensus decision makers, respectively. Meanwhile, the related total minimum consensus adjustments are ascertained. Since the uniqueness of the consensus adjustment scheme cannot be ensured according to the built models, we regard it as a cost allocation problem in cooperative games, and define three types of consensus adjustment cooperative games. After that, the Shapley function, a well-known single payoff index, is adopted to allocate total consensus adjustments in different cases. Additionally, we employ the optimization model to determine the modified values of non-consensus judgments by minimizing the number of adjustment judgments. Finally, numerical study and comparison are made.