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| By the expression '''Fuzzy logic''' one denotes several topics which are related with the notion of [[fuzzy subset|fuzzy subset]] defined in [[1965]] by [[Lotfi Asker Zadeh|Lotfi Zadeh]]. The idea is that we can represent the extension of a vague property by a generalized characteristic function.
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| '''Definition''' Given a nonempty set ''S'', a ''fuzzy subset'' of ''S'' is a map ''s'' from ''S'' into the interval [0,1].
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| The elements in [0,1] are interpreted as truth values and, in accordance, for every ''x'' in ''S'', the value ''s(x)'' is interpreted as the membership degree of ''x'' to ''s''.
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| We have to distinguish two possible interpretations of the expression "fuzzy logic". The first one is given by people interested to applications and to an informal utilization of the notion of [[fuzzy subset]]. In such a case should be better expressions as "fuzzy logic in board sense" or "[[fuzzy set theory]]".
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| Another interpretation is given by people which consider fuzzy logic as a chapter of formal logic, more precisely of multi-valued logic. In such a case one uses the expression "fuzzy logic in narrow sense" or "[[formal fuzzy logic]]".
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| | '''Fuzzy control''' is the main success of fuzzy set theory and it is devoted to useful applications. |
| | The idea is that we can consider IF-THEN rules in which fuzzy quantities are involved. |
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| == See also == | | == See also == |
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| * [[Pattern recognition]] | | * [[Pattern recognition]] |
| * [[Rough set]] | | * [[Rough set]] |
| * [[Soft-computing]] | | * [[Soft-computing]][[Category:Suggestion Bot Tag]] |
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| == Bibliography ==
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| * Cignoli R., D’Ottaviano I. M. L. , Mundici D. , ‘’Algebraic Foundations of Many-Valued Reasoning’’. Kluwer, Dordrecht, 1999.
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| * Cox E., ''The Fuzzy Systems Handbook'' (1994), ISBN 0-12-194270-8
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| * Elkan C.. ''The Paradoxical Success of Fuzzy Logic''. November 1993. Available from [http://www.cse.ucsd.edu/users/elkan/ Elkan's home page].
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| * Gerla G., ''Fuzzy logic: Mathematical Tools for Approximate Reasoning, Kluwer'', 2001.
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| * Hájek P., ''Metamathematics of fuzzy logic''. Kluwer 1998.
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| * Klir G. and Folger T., ''Fuzzy Sets, Uncertainty, and Information'' (1988), ISBN 0-13-345984-5.
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| * Klir G. and Bo Yuan, ''Fuzzy Sets and Fuzzy Logic'' (1995) ISBN 0-13-101171-5
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| * Bart Kosko, ''Fuzzy Thinking: The New Science of Fuzzy Logic'' (1993), Hyperion. ISBN 0-7868-8021-X
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| * Novák V., Perfilieva I, Mockor J., Mathematical Principles of Fuzzy Logic, Kluwer Academic Publishers, Dordrecht, (1999).
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| * Yager R. and Filev D., ''Essentials of Fuzzy Modeling and Control'' (1994), ISBN 0-471-01761-2
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| * Zimmermann H., ''Fuzzy Set Theory and its Applications'' (2001), ISBN 0-7923-7435-5.
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| * Kevin M. Passino and Stephen Yurkovich, ''Fuzzy Control'', Addison Wesley Longman, Menlo Park, CA, 1998.
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| * Wiedermann J. , Characterizing the super-Turing computing power and efficiency of classical fuzzy Turing machines, ''Theor. Comput. Sci.'' 317, (2004), 61-69.
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| * Zadeh L.A., Fuzzy algorithms, ''Information and Control'', 5,(1968), 94-102.
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| * Zadeh L.A., Fuzzy Sets, ‘’Information and Control’’, 8 (1965) 338353.
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