## fuzzy computing

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## fuzzy logic

A superset of Boolean logic dealing with the concept of partial truth -- truth values between "completely true" and "completely false". It was introduced by Dr. Lotfi Zadeh of UCB in the 1960's as a means to model the uncertainty of natural language.

Any specific theory may be generalised from a discrete (or "crisp") form to a continuous (fuzzy) form, e.g. "fuzzy calculus", "fuzzy differential equations" etc. Fuzzy logic replaces Boolean truth values with degrees of truth which are very similar to probabilities except that they need not sum to one. Instead of an assertion pred(X), meaning that X definitely has the property associated with predicate "pred", we have a truth function truth(pred(X)) which gives the degree of truth that X has that property. We can combine such values using the standard definitions of fuzzy logic:

truth(not x) = 1.0 - truth(x) truth(x and y) = minimum (truth(x), truth(y)) truth(x or y) = maximum (truth(x), truth(y))(There are other possible definitions for "and" and "or", e.g. using sum and product). If truth values are restricted to 0 and 1 then these functions behave just like their Boolean counterparts. This is known as the "extension principle".

Just as a Boolean predicate asserts that its argument definitely belongs to some subset of all objects, a fuzzy predicate gives the degree of truth with which its argument belongs to a fuzzy subset.

Usenet newsgroup: comp.ai.fuzzy.

E-mail servers: *<fuzzynet@aptronix.com>*,
*<rnalib@its.bldrdoc.gov>*, *<fuzzy-server@til.com>*.

*ftp://ftp.hiof.no/pub/Fuzzy*,
*ftp://ntia.its.bldrdoc.gov/pub/fuzzy*.

*FAQ*.

*James Brule, "Fuzzy systems - a tutorial", 1985*.

*STB Software Catalog*, includes a
few fuzzy tools.

[H.J. Zimmerman, "Fuzzy Sets, Decision Making and Expert Systems", Kluwer, Dordrecht, 1987].

["Fuzzy Logic, State of the Art", Ed. R. Lowen, Marc Roubens, Theory and Decision Library, D: System theory, Knowledge Engineering and Problem Solving 12, Kluwer, Dordrecht, 1993, ISBN 0-7923-2324-6].

Last updated: 1995-02-21

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## fuzzy subset

In fuzzy logic, a fuzzy subset F of a set S is defined by a "membership function" which gives the degree of membership of each element of S belonging to F.

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**fuzzy subset**» fweep » FWIW » fx