A utility-based three-way group decision consensus model with overlapping subgroups

This paper introduces a relative utility function-based consensus method for three-way group decision (TWGD) in a social network scenario where overlapping subgroups and non-overlapping subgroups co-exist. Firstly, we construct a three-way decision (TWD) model rooted in utility theory, which proposes a novel objective calculation method for the relative utility functions based on evaluation values. The relative utility matrices of decision makers (DMs) are derived on this basis. Secondly, a utility and trust-driven overlapping clustering algorithm is designed to maximize the overall trust level and the difference between subgroup clustering centers, aiming to divide the group into several manageable subgroups. In addition, we identify contrarian DMs, triggering a delegation-exit mechanism, and determine the weights of subgroups and DMs. Thirdly, a three-way group consensus decision model is formulated to provide targeted adjustment strategies for different types of DMs. To improve group consensus, we address the influence of key DMs on the opinions of overlapping subgroups with a minimum adjustment consensus model. Finally, we demonstrate the feasibility and scientificity of the proposed method through the illustrative example, sensitivity analysis, and comparative analysis.