Fuzzy control

By the expression "Fuzzy logic" one denotes several topics which are related with the notion of fuzzy subset 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 "fuzzy set theory".

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".

See also

• Fuzzy subalgebra
• Fuzzy associative matrix
• FuzzyCLIPS expert system
• Fuzzy control
• Fuzzy set
• Multi-valued logic
• Neuro-fuzzy
• Paradox of the heap
• Pattern recognition
• Rough set
• Soft-computing

Bibliography

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• Zadeh L.A., Fuzzy algorithms, Information and Control, 5,(1968), 94-102.
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