Fuzzy sets are sets whose elements have degrees of membership. Fuzzy sets were introduced simultaneously by Lotfi A. Zadeh

Lotfi Asker Zadeh

Lotfali Askar Zadeh , better known as Lotfi A. Zadeh, is a mathematician, electrical engineer, computer scientist, artifical intelligence researcher and professor emeritus of computer science at the University of California, Berkeley...

 and Dieter Klaua in 1965 as an extension of the classical notion of set. In classical set theory

Set theory

Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...

, the membership of elements in a set is assessed in binary terms according to a bivalent condition

Principle of bivalence

In logic, the semantic principle of bivalence states that every declarative sentence expressing a proposition has exactly one truth value, either true or false...

 — an element either belongs or does not belong to the set. By contrast, fuzzy set theory permits the gradual assessment of the membership of elements in a set; this is described with the aid of a membership function

Membership function (mathematics)

The membership function of a fuzzy set is a generalization of the indicator function in classical sets. In fuzzy logic, it represents the degree of truth as an extension of valuation. Degrees of truth are often confused with probabilities, although they are conceptually distinct, because fuzzy...

 valued in the real unit interval [0, 1].