Pythagorean Fuzzy Full Implication Triple I Method and Its Application in Medical Diagnosis

This paper is devoted to the research of full implication triple I method under Pythagorean fuzzy environment. We first propose the concepts of Pythagorean t-norm, Pythagorean t-conorm, residual Pythagorean fuzzy implication operator (RPFIO) and Pythagorean fuzzy biresiduum. The full implication triple I method for Pythagorean fuzzy modus ponens (PFMP) and Pythagorean fuzzy modus tollens (PFMT) are also established. In addition, the properties of full implication triple I method of PFMP and PFMT models including the robustness, continuity and reversibility are analyzed. Finally, a practical problem is discussed to demonstrate the effectiveness of the Pythagorean fuzzy full implication multiple I method in medical diagnosis. The advantages of the new method are also explained. Overall, compared with the existing methods, the proposed methods are based on logical reasoning rather than using aggregation operators, so they can more accurately and completely express decision information.