A new classification and ranking decision method based on three-way decision theory and TOPSIS models

Abstract

The theoretical researches of three-way decision have become saturated. Hence, more and more researchers have focused on the applications and expansions of three-way decision. Combining three-way decision ideas with multi-criteria decision-making is a feasible research direction. In light of this, this paper proposes a novel TOPSIS method based on three-way decision models. First of all, for two types of fuzzy concepts with opposite characteristics, we establish the corresponding three-way decision models. Then, based on the decision regions calculated by these two types of fuzzy concepts, we analyze and study two ranking regulations for objects belonging to the same (different) decision regions, respectively. On the basis of these two regulations, we define the concept of a united decision region and further explore two ranking rules for objects belonging to the same (different) united decision regions, respectively. Subsequently, the positive ideal distance fuzzy set and the negative ideal distance fuzzy set obtained by the core idea of the TOPSIS method are respectively seen as “Cost fuzzy concept” and “Benefit fuzzy concept”. Using the established decision rules based on the united decision regions, the classification and ranking of all objects are obtained. Finally, for the TOPSIS method based on three-way decision models, we test the feasibility and validity of the method from the perspectives of qualitative and quantitative analyses.