Fuzzy logic

This article is about the Boolean logic extension. For the album by Super Furry Animals, see Fuzzy Logic (album).

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Super Furry Animals - Fuzzy Logic (album)

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Fuzzy logic is an extension of Boolean logic dealing with the concept of partial truth. Whereas classical logic holds that everything can be expressed in binary terms (0 or 1, black or white, yes or no), fuzzy logic replaces boolean truth values with degrees of truth.

Related Topics:
Boolean logic - Partial truth - Classical logic - Binary - Degrees of truth

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Degrees of truth are often confused with probabilities. However, they are conceptually distinct; fuzzy truth represents membership in vaguely defined sets not likelihood of some event or condition. To illustrate the difference, consider this scenario: Bob is in a house with two adjacent rooms: the kitchen and the dining room. In many cases, Bob's status within the set of things "in the kitchen" is completely plain: he's either "in the kitchen" or "not in the kitchen". What about when Bob stands in the doorway? He may be considered "partially in the kitchen". Quantifying this partial state yields a fuzzy set membership. With only his little toe in the dining room, we might say Bob is 0.99 "in the kitchen", for instance. No event (like a coin toss) will resolve Bob to being completely "in the kitchen" or "not in the kitchen", as long as he's standing in that doorway. Fuzzy sets are based on vague definitions of sets, not randomness.

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Fuzzy logic allows for set membership values between and including 0 and 1, shades of gray as well as black and white, and in its linguistic form, imprecise concepts like "slightly", "quite" and "very". Specifically, it allows partial membership in a set. It is related to fuzzy sets and possibility theory. It was introduced in 1965 by Prof. Lotfi Zadeh at the University of California, Berkeley.

Related Topics:
Set membership values - Fuzzy sets - Possibility theory - 1965 - Lotfi Zadeh - University of California, Berkeley

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Fuzzy logic is controversial despite wide acceptance: it is rejected by some control engineers for validation and other reasons, and by some statisticians who hold that probability is the only rigorous mathematical description of uncertainty. Critics also argue that it cannot be a superset of ordinary set theory since membership functions are defined in terms of conventional sets.

Related Topics:
Control engineers - Statisticians - Probability - Uncertainty - Ordinary set theory - Conventional set

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