fuzzy logic

fuzzy logic, a multivalued (as opposed to binary) logic 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, 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, 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.

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).

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fuzzy logic

fuzzy logic (fuzzy theory) A branch of logic designed specifically for representing knowledge and human reasoning in such a way that it is amenable to processing by computer. Thus fuzzy logic is applicable to expert systems, knowledge engineering, and artificial intelligence.

The more traditional propositional and predicate logics do not allow for degrees of imprecision, indicated by words or phrases such as fairly, very, quite possibly. Instead of truth values such as true and false it is possible to introduce a multivalued logic consisting of, for example, the values true, not true, very true, not very true, more or less true, not very false, very false, not false, and false. Alternatively an interval such as [0,1] can be introduced and the degree of truth can be represented by some real number in this range. Predicates are then functions that map not into {true, false} but into these more general domains.

Fuzzy logic is concerned with the study of sets and predicates of this kind. There emerge such concepts as fuzzy sets, fuzzy relationships, and fuzzy quantifiers.