A novel three-way classification and ranking approach based on regret theory and TOPSIS

Abstract

In multi-attribute decision-making (MADM) problems, attribute types typically include benefit attributes and cost attributes. In most existing MADM studies, attribute types are converted to the same type to reduce the effect of diverse attribute types on decision results, inevitably leading to the loss of original information. In view of this, this paper presents a novel three-way decision (TWD) approach based on regret theory (RT) and TOPSIS to handle MADM problems in fuzzy environments without converting attribute types. Firstly, RT is employed to analyze the process of acquiring the relative revenue function for benefit attributes and the relative loss function for cost attributes. Then, we combine RT and TOPSIS method to estimate the conditional probability. Based on two attribute types, we develop the corresponding TWD models. One is to establish a TWD model that maximizes expected revenues based on benefit attributes, and the other is to establish a TWD model that minimizes expected losses based on cost attributes. Subsequently, we introduce the notion of integrated decision domains and investigate the ranking methods for alternatives that belong to the same (or different) integrated decision domains. Finally, we validate the effectiveness and performance of our method through case study and experimental analyses.