Optimization Consensus Model Considering Minimum Cost and Maximum Consensus Objectives for Social Network Group Decision-Making

In social network-based group decision-making, achieving consensus often entails costs, leading to an inherent trade-off between cost and consensus. To address this issue, we propose a dual-semantic, multi-objective consensus optimization model that simultaneously minimizes cost and maximizes consensus. The resulting Pareto set offers decision makers (DMs) multiple trade-off solutions between cost and consensus. Specifically, we first develop a 2-tuple trust propagation model that incorporates path knowledge and path length to improve the completeness and accuracy of indirect trust inference. Building on this foundation, we adaptively adjust DM weights by combining trust relationships with dynamic incentive weights. This design balances individual influence and adjustment willingness throughout the consensus-reaching process. Finally, we formulate a multi-objective decision optimization model. This model integrates minimum cost and maximum consensus to generate a modified decision matrix for efficiently aggregating group opinions. A multi-physician collaboration case in a medical diagnostic decision-support system validates the effectiveness of the proposed method.