Three-stage ranking mechanism: A decision-making fusion of regret psychology and criterion-oriented three-way decision

Abstract

Exploring the application of the three-way decision model in multi-criteria ranking problems from the perspective of criterion-oriented fuzzy concept has emerged as a promising research direction in the current three-way multi-criteria decision-making system. This direction aims to fully meet the decision-maker’s fundamental need and achieve a comprehensive ranking of all objects. However, since the difference between the criterion-oriented fuzzy concept and the criterion evaluation value of a object may be negative, the existing criterion-oriented three-way decision model, due to its inability to effectively handle negative value, poses a risk of deviation in overall ranking results. To address this issue, this paper introduces regret theory to transform this difference into a regret-rejoice value for decision-maker, thereby constructing a novel criterion-oriented three-way decision model and further proposing a three-stage ranking mechanism. Firstly, all objects are preliminarily classified qualitatively based on the relative magnitude relationship between the criterion-oriented fuzzy concept and the criterion evaluation value of a object, resulting in the division of four object subsets. Secondly, the constructed criterion-oriented three-way decision model, combined with weight aggregation method, is employed to determine the internal ranking relationships within these four subsets. Notably, in this three-way decision model, a calculation method for relative loss functions with precision control and a calculation method for conditional probability based on fuzzy clustering results are proposed. Finally, the ranking among subsets is determined by considering the semantic relationships between them, and the overall ranking of all objects is obtained by integrating the internal ranking results of subsets. Through numerical analysis, comparative analysis, and experimental verification, the effectiveness and superiority of the proposed three-stage ranking mechanism are fully demonstrated.