Fuzzy control: Difference between revisions
imported>Giangiacomo Gerla No edit summary |
imported>Giangiacomo Gerla No edit summary |
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By the expression ''"Fuzzy logic"'' one denotes several topics which are related with the notion of [[fuzzy subset|fuzzy | 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. | ||
'''Definition''' Given a nonempty set ''S'', a ''fuzzy subset'' of ''S'' is a map ''s'' from ''S'' into the interval [0,1]. | '''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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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 | 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]]". | ||
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]]". | 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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* [[Soft-computing]] | * [[Soft-computing]] | ||
[[category:CZ Live]] | [[category:CZ Live]] | ||
Revision as of 02:16, 18 September 2007
By the expression "Fuzzy logic" one denotes several topics which are related with the notion of fuzzy set defined in 1965 by Lotfi Zadeh. The idea is that we can represent the extension of a vague property by a generalized characteristic function.
Definition Given a nonempty set S, a fuzzy subset of S is a map s from S into the interval [0,1].
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.
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".
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 "fuzzy logic in narrow sense".