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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

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: news:comp.ai.fuzzy.

E-mail servers: fuzzynet@aptronix.com,

rnalib@its.bldrdoc.gov, fuzzy-server@til.com.

FAQ.

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].