**Fuzzy Logic** is a superset 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 which are very similar to probabilities (except that they need not sum to one). This allows for values between 0 and 1, shades of gray, and maybe; it allows partial membership in a set. It is highly related to fuzzy sets and possibility theory. It was introduced in the 1960s by Dr. Lotfi Zadeh of UC Berkeley.

Fuzzy logic is used to control household appliances (such as washing machines which sense load size and detergent concentration and auto-adjust their wash cycles accordingly; and refrigerators)

Another applications are passenger elevators, automobile subsystems (like ABS) and cameras.

A basic application might quantify where a limited range applies to a smooth spectrum -- as in temperature measurement for anti-lock brakes to function properly. Truth values derived from the specific temperature are mapped to a series of candidate quantities. These quantities can then be used to determine a separate function in accordance with the graduated value scheme.

In this image, cold, warm, and hot are identities mapped to a temperature scale. A point on that scale is represented by two "truth values" -- one in each of the two nearest identities. As the temperature rises, its "truth value" in the cold category declines, while its "truth value" in the warmer category rises.

The AND, OR, NOT operators of boolean logic have their fuzzy analogs in MIN, MAX, and COMPLEMENT.

See also: Dynamic logic, control system.