Linguistic Hedges and Reasonable Fuzzy Inferences

Abstract

In many cases of human reasoning, the reasoning ways based on vague statements and loose concepts is often considerable. Furthermore, some vague concepts are often represented by transformations of another vague concepts. In order to make such a fuzzy inference and a transformation with fuzzy concepts, some fuzzy conditional inference rules and various linguistic hedges are proposed by Zadeh, Mamdani and Mizumoto. The relationship between the linguistic hedges and some fuzzy inference rules are reported by Mizumoto. However, the only intuitive discussion about the reasonableness for such fuzzy inference has been made. This paper introduces the concept of inference reasonableness with respect to “fuzzy modus ponens” and “fuzzy modus tollens”. Then, the necessary and sufficient conditions for the reasonable fuzzy inference by the max-min composition of the fuzzy sets and the fuzzy relations is derived. Furthermore, the property of linguistic hedge which induce quite reasonable inference results for several fuzzy conditional inference rules is investigated.