Regret-theory-based three-way decision making in hesitant fuzzy environments: A multi-attribute approach and its applications

Decision-making is intricately linked to the psychological behavior of decision-makers, particularly their susceptibility to risk uncertainty and the consequent emergence of regret psychology. The hesitant fuzzy information system is an effective mechanism for encapsulating the substantial uncertainty inherent in real-world data. While existing three-way multi-attribute decision-making (TWD-MADM) methods have made significant progress in handling uncertainty, they often overlook the psychological factors of decision-makers, such as regret aversion. This paper introduces a three-way decision-making method (TWD-MADM-RT-HFS), grounded in regret theory, for multi-attribute decision-making in a hesitant fuzzy environment. Unlike traditional TWD-MADM approaches, our method explicitly incorporates regret theory to model decision-makers’ psychological behavior, providing a more realistic framework for decision-making under uncertainty. The methodology involves computing a relative outcome matrix using the PROMETHEE-II method to assess the gains and losses of objectives. A novel regret-based perceived utility function is proposed to quantify decision-makers’ aversion to regret, followed by calculating satisfaction-based weight functions for different events across various states. The integration of these weight functions with the perceived utility function yields a new expected utility function, pivotal for ranking and classifying alternatives. To validate the effectiveness of the proposed methodology, the Algerian Forest Fires Dataset was selected for application testing and successfully classified into three categories: fire, possible fire and no fire. The results were then ranked in detail based on the probability of their occurrence. It is anticipated that this classification will help to predict fire risk more accurately in the future, so that timely measures can be taken to prevent and control fire hazards. The method’s feasibility, effectiveness, and superiority are validated through a comparative analysis with existing methods in real-case scenarios. The stability of the model is further confirmed by conducting sensitivity analyses under different parameter settings.