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Author Gainfs, B. R.
Source CiteSeerX
Content type Text
File Format PDF
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Fuzzy Reasoning ♦ Fuzzy Set ♦ Set Theory ♦ Linguistic Hedge ♦ Mathematical Structure ♦ Base Logic ♦ Numeric Value ♦ Psychological Derivation ♦ Borderline Case ♦ Multivalued Logic ♦ Continuous Degree ♦ Third Case ♦ Set Membership ♦ Logical Antecedent ♦ Lotfi Zadeh ♦ Fuzzy Logic ♦ Lukasiewicz Infinite-valued Logic ♦ Classical Approach
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 ofpreeisifying 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. Thefuzzification of mathematical structures leads naturally to the concepts of fuzzy logics and inference, and consideration of implication suggests Lukasiewicz 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. 1.
Educational Role Student ♦ Teacher
Age Range above 22 year
Educational Use Research
Education Level UG and PG ♦ Career/Technical Study
Learning Resource Type Article
Publisher Date 1976-01-01