imported>Giangiacomo Gerla |
imported>Meg Taylor |
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| By the expression ''"Fuzzy logic"'' one denotes several topics which are related with the notion of [[fuzzy subset|fuzzy set]] 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 theory of "[[fuzzy subset]]".
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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|fuzzy logic in narrow sense]]".
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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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| * [[Rough set]] | | * [[Rough set]] |
| * [[Soft-computing]] | | * [[Soft-computing]] |
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| [[category:CZ Live]]
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| [[category:Computers Workgroup]]
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| [[category:Mathematics Workgroup]]
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| [[category:Philosophy Workgroup]]
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Latest revision as of 23:34, 14 February 2010
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.
See also
