Consensus Reaching Model for 2-Rank Group Decision Making with Personalized Individual Semantics

Traditional group decision-making problems focus on obtaining a complete ranking of all alternatives from best to worst. However, in many real-life scenarios, there are instances where it is necessary to assign only two rank levels to alternatives, creating a ranking where one subset of alternatives is prioritized above another subset. These scenarios are referred to as 2-rank group decision-making problems. Linguistic preference relations serve as an effective tool for expressing decision-makers preferences, as they allow comparisons between two alternatives at a time using linguistic terms. Nonetheless, in 2-rank group decision-making problems with linguistic preference relations, it is common for the same linguistic term to hold different meanings for different decision-makers, a phenomenon known as personalized individual semantics (PISs). Addressing how to model PISs in 2-rank group decision-making problems presents a significant challenge. In this paper, we develop a consensus-reaching model for 2-rank linguistic group decision-making problems, incorporating PISs and consistency control for decision-makers. Specifically, we first employ consistency-driven models to evaluate and improve the consistency of each decision-makers linguistic preference relations. Based on this foundation, we determine the 2-rank preference vectors for both individuals and the group. Subsequently, we propose a 2-rank consensus measurement method and design a 2-rank consensus-reaching process to help decision-makers enhance their consensus level. This involves the development of a PIS-based consensus level maximization model and a PIS-based minimum adjustment model. Furthermore, we introduce an algorithm to implement the consensus-reaching framework. Ultimately, numerical experiments and simulation results are provided to demonstrate the effectiveness of the proposed method.