NOTE ON THE ARITHMETIC RULE BY ZADEH FOR FUZZY CONDITIONAL INFERENCE

Abstract

This paper shows that Zadeh's arithmetic rule for fuzzy conditional propositions “If x is A then y is B” and “If x is A then y is B else y is C” can infer quite reasonable consequences in a fuzzy conditional inference if new compositions of “max-[Odot] composition” and “max- composition” are used in the compositional rule of inference, though, as was pointed out before, this arithmetic rule cannot get suitable consequences in the compositional rule of inference which uses max-min composition. Moreover, it is shown that the arithmetic rule satisfies a syllogism under these two compositions.