Fuzzy abduction based on Lukasiewicz infinite-valued logic and its approximate solutions

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 fuzzy explanations. The authors then propose a procedure by which to obtain approximate fuzzy explanations which may be necessary when the conditions are not satisfied.<<ETX>>