A Two-Stage Minimum Cost Consensus Reaching Study for Large Scale Group Decision Making Based on the Opinion Leader–Follower Opinion Evolution

The topic of consensus cost spent in the large scale group consensus decision making (LSGDM) process has drawn more attention as decision-making environments have grown more complicated. Meanwhile, the social network is an important element in LSGDM that can be used to promote group consensus by social relationships among decision makers. Decision makers can be classified into opinion leader and opinion followers, whose opinion evolution show different results. Therefore, taking the social relations of group as an entry point for the LSGDM problem, this paper proposes a minimum cost two-stage consensus decision model based on the opinion leader–follower opinion evolution for the LSGDM problem, and extends it to the distributed linguistic environment. First, the sub-network partitioning method is used to divide the large scale group into several sub-clusters, and then the improved PageRank algorithm is used to calculate the weights of decision makers. Next, the consensus reaching process (CRP) is divided into two stages. In the first stage, an opinion evolution model based on opinion leader–follower is designed on the different opinion evolution processes of opinion leader and opinion follower. On this basis, we propose an intra-sub-cluster minimum cost consensus model based on leader–follower opinion dynamics. The adjustment suggestions are obtained by minimizing the adjustment cost of opinions to reach consensus within the sub-clusters. In the second stage, we use the inter-sub-cluster minimum cost consensus model based on global coordination to lead the sub-clusters to reach the collective consensus with minimum opinion adjustment cost. Finally, a case study on power engineering projects illustrates the feasibility of the model, and comparing with other models reveals its advantages. In general, the two-stage consensus reaching model we proposed can effectively use the leadership role of opinion leaders to facilitate the consensus building process and reduce consensus costs.