A regret theory-based three-way decision model under comparative linguistic expressions
Zhanhao Liu, Huangjian Yi, Yushan Yao, Jiajia Wang · Applied Soft Computing · 2025
In real world, experts often prefer to utilize linguistic expressions over numerical data when evaluating alternatives. However, due to the complexity of actual decision-making, single linguistic terms are insufficient for experts to express their judgments accurately. Thus, it is necessary to employ a richer form of linguistic expression, known as comparative linguistic expressions (CLEs). Furthermore, existing multi-attribute decision-making (MADM) models under CLE suffer from the following limitations: (1) they fail to provide decision-making references for alternatives; (2) they do not incorporate the psychological factors of experts. In order to address the aforementioned challenges, this paper proposes a novel regret theory (RT)-based three-way decision (TWD) model under CLE. First, the attribute weights are calculated by an improved optimization model. This model combines index variability with comprehensive entropy, enabling a more objective conclusion to be drawn regarding the relative importance of attributes. Second, an enhanced neighborhood relationship is introduced, which is shown to fulfill the properties of Symmetry, Reflexivity, and Non-transitivity. Building on this foundation, this study integrates RT with the neighborhood relationship to construct a wide TWD framework. This framework incorporates decision-making references for the alternatives and accounts for the influence of experts’ psychological factors. Subsequently, the ranking of alternatives is determined using the technique for order preference by similarity to ideal solution (TOPSIS) method. Finally, the feasibility of the proposed method is demonstrated through a real-case study. Comparative experiments and parameter sensitivity analysis are designed to demonstrate the superiority and effectiveness of the model.