Some Remarks on the Generalized Scheme of Reduction to Absurdity and Generalized Hypothetical Syllogism in Fuzzy Logic

Abstract

In this paper we investigate two generalizations, in fuzzy logic, of classical scheme of reduction to absurdity. We compare them with two possible generalizations of classical hypothetical syllogism (in fuzzy logic) and we show that generalized hypothetical syllogism is more general. We present new results concerning solutions of an inequality and an equation connected directly with generalization of scheme of reduction to absurdity in fuzzy logic.