A Minimum Adjustment Cost Consensus Framework Considering Harmony Degrees and Trust Propagation for Social Network Group Decision Making

In consensus-based social network group decision-making (SN-GDM) problems, the low degree of harmony caused by opinion discrepancies and weak trust relationships may lead to high consensus costs and conflict among experts. To address these problems, we design a minimum adjustment cost consensus framework considering harmony degrees in SN-GDM with incomplete 2-tuple linguistic trust. First, considering the decay of trust through its propagation process, a discount-factor-based 2-tuple linguistic trust propagation operator is proposed to estimate the unknown trust relationships among experts. Then, the harmony degrees are measured based on opinion discrepancies and 2-tuple linguistic trust values, and experts’ weights could be obtained. To improve the consensus levels of the inconsistent experts, a minimum adjustment cost consensus model considering harmony degrees is explored to generate interval recommendations. The existence of optimal solutions and the convergence of the proposed consensus model are also proved. Finally, the validity of the proposed consensus framework is verified by the case of base station selection. With the higher overall harmony degree and individual consensus level, we extend the classical minimum cost consensus model and incorporate the harmony degrees among experts into the consensus reaching process.