# fuzzy logic

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## fuzzy logic,

a multivalued (as opposed to binary) logic**logic,**

the systematic study of valid inference. A distinction is drawn between logical validity and truth. Validity merely refers to formal properties of the process of inference.

**.....**Click the link for more information. developed to deal with imprecise or vague data. Classical logic holds that everything can be expressed in binary terms: 0 or 1, black or white, yes or no; in terms of Boolean algebra

**Boolean algebra**

, an abstract mathematical system primarily used in computer science and in expressing the relationships between sets (groups of objects or concepts). The notational system was developed by the English mathematician George Boole c.

**.....**Click the link for more information. , everything is in one set or another but not in both. Fuzzy logic allows for partial membership in a set, values between 0 and 1, shades of gray, and maybe—it introduces the concept of the "fuzzy set." When the approximate reasoning of fuzzy logic is used with an expert system

**expert system,**

a computer system or program that uses artificial intelligence techniques to solve problems that ordinarily require a knowledgeable human. The method used to construct such systems, knowledge engineering, extracts a set of rules and data from an expert or experts

**.....**Click the link for more information. , logical inferences can be drawn from imprecise relationships. Fuzzy logic theory was developed by Lofti A. Zadeh at the Univ. of California in the mid 1960s. However, it was not applied commercially until 1987 when the Matsushita Industrial Electric Co. used it in a shower head that controlled water temperature. Fuzzy logic is now used to optimize automatically the wash cycle of a washing machine by sensing the load size, fabric mix, and quantity of detergent and has applications in the control of passenger elevators, household appliances, cameras, automobile subsystems, and smart weapons

**smart weapon,**

missile or steerable bomb equipped with a laser, television, or satellite guidance system. Smart weapons, which use guidance systems that rely on external assistance, are distinguished from brilliant weapons, which are totally self-guided.

**.....**Click the link for more information. .

### Bibliography

See L. A. Zadeh, *Fuzzy Logic for the Management of Uncertainty* (1992); D. McNeill and P. Freiberger, *Fuzzy Logic* (1993); B. Kosko, *Fuzzy Thinking: The New Science of Fuzzy Logic* (1993); R. R. Yager and D. P. Filey, *Essentials of Fuzzy Modeling and Control* (1995).

## fuzzy logic

[¦fəz·ē ′läj·ik] (mathematics)

The logic of approximate reasoning, bearing the same relation to approximate reasoning that two-valued logic does to precise reasoning.

## 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: news:comp.ai.fuzzy.

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

[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].

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].

## fuzzy logic

A mathematical technique for dealing with imprecise data and problems that have many solutions rather than one. Although it is implemented in digital computers which ultimately make only yes-no decisions, fuzzy logic works with ranges of values, solving problems in a way that more resembles human logic.Fuzzy logic is used for solving problems with expert systems and real-time systems that must react to an imperfect environment of highly variable, volatile or unpredictable conditions. It "smoothes the edges" so to speak, circumventing abrupt changes in operation that could result from relying on traditional either-or and all-or-nothing logic.

**A Matter of Degree**

The concept was conceived in 1964 by Lotfi Zadeh, former chairman of the electrical engineering and computer science department at the University of California at Berkeley, while he was contemplating how to program software for handwriting recognition. Zadeh expanded on traditional set theory by making membership in a set a matter of degree rather than a yes-no situation. See set theory.