Complex Fermatean Fuzzy Soft Sets: Theory, Properties, and Application to Decision Analysis

Abstract

This study introduced the concept of the complex Fermatean fuzzy soft set (CFFSS), which gener- alized the complex Pythagorean fuzzy soft set by incorporating higher flexibility in representing uncertainty and hesitation. Fundamental definitions and properties of CFFSS, such as subset, complement, union, intersection, and more, are established and supported with corresponding examples. Furthermore, a novel multi-attribute decision-making (MADM) algorithm based on the CFFSS framework is developed to handle complex-valued uncertainty in real-world problems. To demonstrate its applicability, the proposed algorithm is applied to a practical case involving the selection of the most suitable inverter among multiple alternatives. The results validate the effectiveness and reliability of the proposed approach in reducing uncertainty and ambiguity during the decision-making process, highlighting its potential usefulness in various applied domains.