Fuzzy logic

Fuzzy logic allows propositions to have degrees of truth rather than only true or false. It models vague categories using graded membership, commonly represented by values from zero to one.

Membership function: A function assigning each element a degree of membership in a fuzzy set. It converts a measured input, such as temperature, into a fuzzy truth value.
Classical logic: A family of formal systems in which propositions are evaluated using sharply defined logical rules. Fuzzy logic relaxes classical logic’s two-valued treatment of proposition truth.
Lotfi A. Zadeh: An Azerbaijani-American mathematician and engineer who introduced fuzzy sets in 1965. Zadeh’s fuzzy-set work supplied the foundation for fuzzy logic.
Fuzzy logic controller: A controller that uses fuzzy sets and rules to select control actions. It applies graded reasoning directly to machinery and process control.
Many-valued logic: A family of logics with more than two truth values. Fuzzy logic belongs to this broader family but typically uses a continuous range of values.
Fuzzy rule: A conditional statement that relates fuzzy linguistic variables, often in an if–then form. Fuzzy systems combine rules such as “if temperature is high, then fan speed is fast.”
Boolean algebra: An algebraic system built around the values true and false and operations such as AND, OR, and NOT. Fuzzy logic generalizes familiar Boolean operations to graded values.
Fuzzy Sets: A 1965 paper by Lotfi A. Zadeh that introduced sets with graded membership. This paper established the mathematical idea from which fuzzy logic developed.
Mamdani method: A fuzzy inference method that uses fuzzy sets for both rule inputs and outputs. It is a widely used way to turn linguistic rules into fuzzy control outputs.
Łukasiewicz logic: A many-valued logic with truth values commonly represented on the interval from zero to one. Its formal operations provide one influential basis for fuzzy logical connectives.

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