Fermatean Fuzzy TOPSIS Method Based on Prospect Theory

Intuitionistic fuzzy sets, Pythagorean fuzzy sets and generalized orthogonal fuzzy sets are widely used in some multi-attribute decision-making problems. A generalized orthogonal fuzzy set is a Fermatean fuzzy set when the cubic sum of the degrees of affiliation and non-affiliation does not exceed 1. The Simple Fermatean fuzzy TOPSIS method addresses that decision makers are completely rational while making decisions, and applies the revised closeness to the measurement to rank the alternatives. Prospect theory considers the irrational behavior of the decision maker in the actual decision-making process, the decision maker facing the loss is risk-preferring (introducing the coefficient \( \uptheta \) ), and is risk averse when facing the gain. In this paper, prospect theory and Fermatean fuzzy sets are combined to explore the multi-attribute decision-making problem, and the Fermatean fuzzy TOPSIS method based on prospect theory is proposed, Calculating the comprehensive gain/loss ratio to rank the alternatives. The results show that the optimal choice is S3 and the discriminant mean of the absolute value of \( \Phi^{+}{\rm (S)}/\,\Phi^{-}{\rm (S)} \) obtained by pooling expert fuzzy evaluations using the Fermatean fuzzy TOPSIS method based on prospect theory is higher than the discriminant mean of the relative proximity obtained by using the Fermatean fuzzy TOPSIS method, which can be interpreted as a better synthesis of the expert fuzzy evaluations. In the future, the Fermatean fuzzy TOPSIS method based on prospect theory has a wide range of application value in several fields, which can be used to solve complex decision-making problems and improve the accuracy and effectiveness of decision-making.