Pythagorean fuzzy full implication multiple I method and corresponding applications

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.

Fuzzy Reasoning Method Based on Distance Measure and Its Reductive Property

This paper shows a basic and original fuzzy reasoning method that can draw a novel study direction of the approximate inference in fuzzy systems with uncertainty. Firstly we propose a criterion function for checking of the reductive property about fuzzy modus ponens (FMP) and fuzzy modus tollens (FMT). Secondly unlike fuzzy reasoning methods based on the similarity measure, we propose a principle of new fuzzy reasoning method based on distance measure and then present two theorems for FMP and FMT. Thirdly through the several computational experiments, we show that proposed method is simple and effective, and in accordance with human thinking. Finally we pointed out conclusion that proposed method does satisfy the convergence of the fuzzy control and has not information loss.