Abstract: This paper gives an overview of the theory of fuzzy sets and fuzzy reasoning as proposed and developed by Lotfi Zadeh. In particular it reviews the philosophical and logical antecedents and foundations for this theory and its applications. The problem of borderline cases in set theory and the two classical approaches of precisifying them out, or admitting them as a third case, are discussed, leading to Zadeh's suggestion of continuous degrees of set membership. The extension of basic set operations to such fuzzy sets, and the relationship to other multivalued logics for set theory, are then outlined. The fuzzification of mathematical structures leads naturally to the concepts of fuzzy logics and inference, and consideration of implication suggests Łukasiewicz infinite-valued logic as a base logic for fuzzy reasoning. The paradoxes of the barber, and of sorites, are then analysed to illustrate fuzzy reasoning in action and lead naturally to Zadeh's theory of linguistic hedges and truth. Finally, the logical, modeltheoretic and psychological derivations of numeric values in fuzzy reasoning are discussed, and the rationale behind interest in fuzzy reasoning is summarized.
Publication Year: 1976
Publication Date: 1976-11-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 356
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