A Fuzzy Soft Set Based Triple I Method

Soft set theory can analyze complex concepts from different sides.The results are all approximate portrays of complex concepts.After synthesizing these approximations,we can get a relatively accurate description of complex concepts.As a new mathematical tool to deal with the problem of uncertainty,the soft set theory has drawn wide attention from the academic circles.This paper focuses on triple I inference method based on fuzzy soft sets.Main contributions of the current work are listed as follows:1 The reversibility and the continuity of fuzzy soft set based triple I reasoning method are investigated.For fuzzy implication operators that are induced by left continuous t norms,the conditions of reversibility of triple I reasoning method for FSMP are provided.Besides,for Lukasiewicz fuzzy implication operator,G?del fuzzy implication operator and R₀fuzzy implication operator,the continuity of triple I reasoning method for FSMP is proved.2 An intuitionistic fuzzy soft set based triple I reasoning method are investigated.Triple I reasoning method for both intuitionistic fuzzy soft modus ponens（IFSMP）and intuitionistic fuzzy soft modus tollens（IFSMT）with respect to left-continuous intuitionistic t-norms and its residual intuitionistic implication are presented and computational formulas of inference conclusion are given.Besides,the reversibility property of Triple I methods of IFSMP and IFSMT are analyzed.3 An interval-valued fuzzy soft set based triple I reasoning method are investigated.Triple I reasoning method for both interval-valued fuzzy soft modus ponens（IVFSMP）and interval-valued fuzzy soft modus tollens（IVFSMT）with respect to left-continuous interval-valued t-norms and its residual interval-valued implication are presented and computational formulas of inference conclusion are given.Besides,the reversibility property of Triple I methods of IVFSMP and IVFSMT are analyzed.