logic which as opposed to classical logic takes variable factors such as time and probability into account
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:
news: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)
A form of artificial intelligence based on fuzzy-set theory, recognizes that statements are not necessarily only true or false, but also can be very unlikely or more or less certain. Fuzzy logic allows computers to emulate the human reasoning process, which makes decisions based on vague or incomplete data, by assigning values of degree to all the elements of a set. The use of fuzzy logic in products reduces time-to-market, lowers development costs, and improves product performance.
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