Minimum cost consensus model for CRP-driven preference optimization analysis in large-scale group decision making using Louvain algorithm

Abstract Large-scale group decision-making problems based on social network analysis and minimum cost consensus models (MCCMs) have recently attracted considerable attention. However, few studies have combined them to form a complete decision-making system. Accordingly, we define the satisfaction index to optimize the classical MCCM by considering the effect of the group on individuals. Similarly, we define the consistency index to optimize the consensus reaching process (CRP). Regarding the evolution of the consensus network, the Louvain algorithm is used to divide the entire group into several subgroups to ensure that each subgroup is independent but has strong cohesion. By constructing the MCCM based on the satisfaction index and the optimized consensus-reaching process, the group opinions in each subgroup are ranked to obtain the final ranking of alternatives. Finally, to verify the validity of CRP and the practical value of the proposed model, we conduct consensus network evolution and decision-making analysis in the case of a negotiation between the government and polluting companies to achieve uniform pollution emissions. Sensitivity analysis is performed to demonstrate the stability of the subgroup weights. Furthermore, a comparative analysis using existing models verifies the effectiveness of the proposed model.