Several methods for fuzzy conditional inferences

L.A. Zadeh and E.H. Mamdani have proposed methods for a fuzzy reasoning in which the antecedent involves a fuzzy conditional proposition "If x is A then y is B", with A and B being fuzzy concepts. This paper points out that the consequences inferred by their methods do not always fit our intuitions, and suggests several new methods which fit our intuitions under several criteria such as modus ponens and modus tollens.