Investigations of T-power based implications satisfying some functional equations related to reasoning schemes

Abstract

In fuzzy logic, the fuzzy reasoning rules generalized hypothetical syllogism (GHS), generalized modus tollens (GMT) and generalized reduction to absurdity (GRA) play an indispensable role in selecting appropriate fuzzy implications in specific tasks. In order to enhance the set of fuzzy implications satisfying these three properties to a greater extent, in this work, we investigate in detail under what conditions the T-power based implications will satisfy (GHS), (GMT) and (GRA). Then the necessary and sufficient conditions are given. The results obtained can not only provide a theoretical basis for selecting fuzzy implication satisfying these properties, but also help us further insight the behaviour of this new kind of fuzzy implication.