The Probabilistic Hesitant Fuzzy TOPSIS Method Based on the Regret Theory and Its Application in Investment Strategy

Abstract

Abstract The TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) is a popular multi-attribute decision making method. However, the increasing uncertain information with probability and the psychological factor of regret aversion of experts in some situations bring new challenges to the application of classic TOPSIS. This paper expands the application of regret theory to the probabilistic hesitant fuzzy environment and proposes the corresponding concepts of utility function, reject-rejoice function and perceived utility value of the probabilistic hesitant fuzzy element (P-HFE). The maximum deviation model under the probabilistic hesitant fuzzy environment is presented to determine the weights of attributes. Based on which, we propose a new probabilistic hesitant fuzzy TOPSIS (PHFTOPSIS) method based on the regret theory. The detailed implementation process of the PHFTOPSIS method based on the regret theory is also provided. Moreover, we apply the proposed PHFTOPSIS method based on the regret theory to the investment strategy. A comparative analysis with traditional TOPSIS and probabilistic hesitant fuzzy weighted averaging (PHFWA) operator is further conducted to illustrate its advantages.