Multi-attribute group decision making method based on prospect theory under hesitant probabilistic fuzzy environment

Abstract

The hesitant fuzzy element (HFE), as an extension of fuzzy numbers, has received much attention and the occurrence probabilities of each membership in the HFEs are assumed to be equal, i.e., the decision makers (DMs) share the same preference for each membership. Anecdotal observations suggest otherwise. To address this issue, the hesitant probabilistic fuzzy set (HPFS) is proposed, which is more suitable for depicting the DMs’ preferences in decision making. Research reports that psychological behavior matters in the decision-making process. Consequently, this paper proposes a multi-attribute group decision making method under a hesitant probabilistic fuzzy environment that considers the DMs’ psychological state in the decision-making process. A weights determination model is constructed, incorporating objective decision-making information and the subjective preferences of the DMs based on a score function and the minimum relative entropy principle. Finally, an established case example is applied to validate the applicability of the proposed method, and comparative analysis is also completed to verify the validity of the proposed method.