Fuzzy abduction is the procedure for deriving a fuzzy set of hypotheses which explains a given fuzzy set of events using a set of implications with a truth value. The derived fuzzy set of hypotheses is called a fuzzy explanation. This paper starts with reexamination of modus ponens and modus tolens in a multi-valued logic. Then, it introduces the concepts of fuzzy explanation and fuzzy abduction based on the examination, and discusses the necessary and sufficient conditions of existence for

more »

... y explanations. We then propose a procedure by which to obtain approximate fuzzy explanations which may be necessary when the conditions are not satisfied.