Pythagorean fuzzy full implication multiple I method and corresponding applications

Abstract

The overwhelming majority of existing decision-making methods combined with the Pythagorean fuzzy set (PFS) are based on aggregation operators, and their logical foundation is imperfect. Therefore, we attempt to establish two decision-making methods based on the Pythagorean fuzzy multiple I method. This paper is devoted to the discussion of the full implication multiple I method based on the PFS. We first propose the concepts of Pythagorean t-norm, Pythagorean t-conorm, residual Pythagorean fuzzy implication operator (RPFIO), Pythagorean fuzzy biresiduum, and the degree of similarity between PFSs based on the Pythagorean fuzzy biresiduum. In addition, the full implication multiple I method for Pythagorean fuzzy modus ponens (PFMP) is established, and the reversibility and continuity properties of the full implication multiple I method of PFMP are analyzed. Finally, a practical problem is discussed to demonstrate the effectiveness of the Pythagorean fuzzy full implication multiple I method in a decision-making problem. The advantages of the new method over existing methods are also explained. Overall, the proposed methods are based on logical reasoning, so they can more accurately and completely express decision information.