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The Dual Triple I Methods of FMT and IFMT

The Triple I method for the model of intuitionistic fuzzy modus tollens (IFMT) satisfies the local reductivity instead of the reductivity. In order to improve the quality of the Triple I method for lack of reductivity, the paper is intended to present a new approximate reasoning method for IFMT problem. First, the concept of intuitionistic fuzzy difference operator is proposed and its properties on the lattice structure of intuitionistic fuzzy sets are studied.Then, the dual Triple I method for FMT based on residual fuzzy difference operator is presented and the dual Triple I method is generated for IFMT. Moreover, a decomposition method of IFMT is provided. Furthermore, the reductivity of methods is investigated. Finally, α-dual Triple I method of IFMT is proposed.