Multi-stage type-α constrained minimum-cost consensus for linguistic Z-number large-scale decision-making

Abstract

As an extension of group decision-making in terms of scale and uncertainty, linguistic Z-number large-scale decision-making (LZ-LSDM) is emerging as a prominent research topic in the field of decision science. The unique structure of LZ-LSDM presents new challenges for both clustering analysis and consensus building. Minimum-cost consensus (MCC) based on the optimization principle is widely recognized as an effective tool for managing the consensus-reaching process. However, there is a scarcity of literature that addresses the study of MCC within the context of LZ-LSDM, as well as the application of MCC in the identification and treatment of non-cooperative behaviors. To this end, this study proposes a punishment strategy-driven multi-stage type-α constrained MCC model for LZ-LSDM problems. First, a similarity constraint-based clustering method with linguistic Z-numbers is proposed. Given the clustering results, a type-α constrained MCC (α-CMCC) model with personalized feedback constraints is designed to provide a personalized solution for visualizing opinion adjustment and preventing over-adjustment. Based on the optimal solution obtained by α-CMCC, the identification rule for non-cooperative behaviors is proposed. We conclude three punishment strategies—namely, pure, mixed, and cross—to address non-cooperative behaviors by arranging and combining commonly used punishment approaches. Finally, we illustrate the feasibility and validity of the model through a case study designed to facilitate consensus among an online patient community on knowledge-based recommendations. An exhaustive comparative analysis reveals the advantages and features of the proposed consensus model.