Three-way multi-criteria group decision-making method in a fuzzy [formula omitted]-covering group approximation space

Abstract

At present, some researchers have studied the decision-making methods in a fuzzy β-covering approximation space, which not only can play the advantages of rough set theory in dealing with inaccurate data, but also inherit the ranking function of traditional decision-making methods. However, these methods merely consider the ranking problem in a single decision-maker environment and most of the decision-making problems in reality are group decision-making problems that need to consider multiple opinions. In light of this, in this paper, we propose the concept of fuzzy β-covering group approximation spaces and establish a three-way multi-criteria group decision-making method, which can solve some ranking and classification problems of objects under a group decision-making environment. Based on a fuzzy β-covering group approximation space, we firstly propose two fuzzy β-fitting neighborhoods with pessimistic and optimistic attitudes to construct a fuzzy binary relation between any two objects. Secondly, we introduce an overall loss function to estimate the risk loss of all objects when they choose different behaviors in different states under a group decision-making environment. Subsequently, based on the conditional probability estimation formula and the overall loss function, we propose a three-way group decision-making idea in a fuzzy β-covering group approximation space, which contains eight different decision-making attitudes to meet the preferences of decision-makers. Furthermore, for the ranking and classification performance of our method, we use numerical analysis, comparative analysis and Spearman analysis to illustrate the feasibility and superiority of the method, and take experimental analysis to test the stability of our method.