Interaction behavior-driven consensus model in an asymmetric costs context for group decision making in dynamic social networks

Interaction behaviors continually shape trust relationships and opinions in social network group decision-making (SNGDM). However, existing SNGDM methods typically rely on static environment assumptions, overlooking interaction behaviors as a driving force for consensus building. To fill this gap, this study proposes an interaction behavior-driven consensus model integrating dynamic social networks and asymmetric costs, both of which arise from interaction behaviors. Firstly, to characterize the outcomes of interpersonal interactions, opinion inclinations are introduced and estimated by an improved Friedkin–Johnsen model, serving as direct contributors to trust relationship updating and adjustment willingness differing. Secondly, trust relationship updating is formulated as a closed-form optimization model, and individual weights are determined by a convex optimization model concerning power and credibility. Thirdly, to incorporate heterogeneous adjustment willingness, a minimum cost consensus model (MCCM) with asymmetric costs is designed. Consistency constraints are involved in the proposed MCCM to ensure acceptable feedback. The proposed MCCM is transformed into a two-stage optimization model for tractable solutions. Furthermore, to improve consensus efficiency, a two-stage consensus reaching process is developed, in which interpersonal interactions and moderator feedback are implemented to facilitate consensus building through weight reallocation and opinion adjustment. Finally, the proposed method is validated through an illustrative example, with sensitivity and comparison analyses confirming its robustness and practical value.