fuzzy logic
In plain wordsA kind of logic that allows degrees of truth, so a statement like 'the room is warm' can be 70 percent true, which helps machines handle vague everyday categories.
A logic of graded truth, built on fuzzy set theory, in which a statement may hold to any degree between 0 (false) and 1 (true), just as an element belongs to a set to the degree given by a membership function: 24 °C might be 'warm' to degree 0.7. Connectives generalize the Boolean ones, commonly with AND as minimum (or another t-norm), OR as maximum and NOT as one minus the value. In fuzzy control, rules such as 'if temperature is high and rising, then fan speed is fast' fire in parallel to varying degrees, their outputs are combined, and the result is defuzzified into a crisp command. Such controllers suit systems that are hard to model precisely but easy to describe in words, and have run cameras, washing machines, subway braking and automatic transmissions. Fuzzy degrees express vagueness, not likelihood: they are not probabilities and need not sum to one.
The fuzzy controller eases the brakes gradually instead of switching between fixed levels.
Origin
Lotfi Zadeh of the University of California, Berkeley, introduced fuzzy sets in 1965 ('Fuzzy Sets', Information and Control) and developed fuzzy logic in the 1970s. Ebrahim Mamdani and Sedrak Assilian built the first fuzzy controller, for a laboratory steam engine, in 1974–1975, and the Sendai subway in Japan adopted fuzzy train control in 1987.
Usage note
Fuzzy logic was a commercial fashion in Japan in the late 1980s and 1990s; critics argued that probability theory already covered its uses. In everyday speech 'fuzzy logic' can simply mean muddled reasoning, a sense unrelated to the formal one.
Related
- propositional logicpropositional logic, n.: The simplest formal logic: whole statements that are either true or false, joined by 'and', 'or', 'not' and 'if… then', with exact rules for working out whether the combination is true.
- rule-based systemrule-based system, n.: A computer system that makes decisions by following a list of 'if… then…' rules written by people, rather than by learning from examples.
- expert systemexpert system, n.: A program that stores a human specialist's know-how as many if–then rules and uses them to give advice or make decisions in a narrow field, such as diagnosing infections or configuring computers.
- uncertainty quantificationuncertainty quantification, n.: Measuring how unsure an AI system's predictions are, and why, so that people know when to trust an answer and when to double-check it.
- non-monotonic reasoningnon-monotonic reasoning, n.: Reasoning in which new information can overturn earlier conclusions — you assume a bird can fly until you learn it is a penguin — as people do constantly but classical logic does not allow.
- propositional logicpropositional logic, n.: The simplest formal logic: whole statements that are either true or false, joined by 'and', 'or', 'not' and 'if… then', with exact rules for working out whether the combination is true.
- Bayesian inferenceBayesian inference, n.: Reasoning that treats unknowns as uncertain beliefs and updates them with evidence using Bayes' theorem. The result is not one answer but a range of answers, each with a probability.
Sources
- Zadeh, L. A. (1965). Fuzzy Sets. Information and Control 8(3), 338–353.
- Mamdani, E. H. & Assilian, S. (1975). An Experiment in Linguistic Synthesis with a Fuzzy Logic Controller. International Journal of Man-Machine Studies 7(1), 1–13.
Mentioned in
propositional logicpropositional logic, n.: The simplest formal logic: whole statements that are either true or false, joined by 'and', 'or', 'not' and 'if… then', with exact rules for working out whether the combination is true., rule-based systemrule-based system, n.: A computer system that makes decisions by following a list of 'if… then…' rules written by people, rather than by learning from examples., computational intelligencecomputational intelligence, n.: A family of AI methods inspired by nature, such as neural networks, fuzzy logic and evolutionary algorithms, that learn or adapt from numbers rather than following explicit logical rules., Dempster–Shafer theoryDempster–Shafer theory, n.: A theory of reasoning with uncertain evidence that lets you hold back belief — in effect saying 'I don't know' — instead of being forced to divide all your confidence among the possibilities., Lotfi ZadehLotfi Zadeh, prop. n.: An Azerbaijani-born American engineer who invented fuzzy logic, which lets computers reason with vague categories such as 'warm' or 'tall' that are true only to a degree., soft computingsoft computing, n.: A group of computing methods, including fuzzy logic, neural networks and evolutionary algorithms, that accept imprecise, approximate answers in exchange for being practical on messy real-world problems.