Triple I method of fuzzy reasoning

The theory of the triple I method with total inference rules of fuzzy reasoning is investigated by using Zadehʹs implication operator Rz. The computational formulae for both fuzzy modus ponens (FMP) and fuzzy modus tollens (FMT) are obtained. The reversibility properties for FMP and FMT are analyzed and the reversibility criteria are given. We also investigated the generalized problem of the triple I method and obtained the formulae for the α-triple I FMP and the α-triple I FMT.