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".
["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].