Fuzzy cross-efficiency evaluation based on prospect theory and regret theory

Cross-efficiency in data envelopment analysis is widely used in production as an evaluation method that includes input and output indicators and allows for self-evaluation and mutual evaluation of decision making units (DMUs). However, as the application scenarios continue to expand, the traditional methods gradually fail to meet the needs. Many researchers have proposed improved methods and made great progress in weight determination, but the existing studies still have shortcomings in considering the psychological behavior of decision makers (DMs) and there is still relatively little research on cross-efficiency in fuzzy environments. In this paper, we proposed a method to apply CRITIC to determine weights and introduce both prospect theory and regret theory into the evaluation method of cross-efficiency to obtain the prospect cross-efficiency matrix and regret cross-efficiency matrix respectively, and then applied the Pythagorean hesitant fuzzy operator to aggregate them to achieve the ranking of DMUs through the fraction function. This largely takes into account the subjective preference and regret avoidance psychology of DMs. The applicability of this paper's method is also verified through an example of shopping for a new energy vehicle. Finally, the effectiveness of this paper's method is verified by comparing three traditional methods with this paper's method, which provides an effective method for considering risk preferences in the decision-making process.