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].
(1995-02-21)
Nearby terms:
futz « fuzzball « fuzzy computing « fuzzy logic
» fuzzy subset » fweep » FWIW
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