a general mathematical concept that describes how an element belongs to a particular notion (set) of some domain of definition

a just a set with a measure of the degree of membership for each element in the set

an extension of a classical set

a set of elements that have a degree of belonging or membership attached to each one

a set that is defined by a membership function

a set whose elements have degrees of membership

a set with imprecise boundaries in which the transition from membership to non membership is gradual rather than abrupt

a set without a crisp, clearly defined boundary

a term which originates in non-traditional logic, describing a set whose individual members do not all share the same set-defining attributes to the same degree, i

a very general concept that extends the notion of a standard set defined by a binary membership to accommodate gradual transitions through various degrees

A set that can contain elements with only a partial degree of membership.

A set of elements which may have a graded degree of membership between no membership and complete membership.

Fuzzy sets are an extension of classical set theory and are used in fuzzy logic. In classical set theory the membership of elements in relation to a set is assessed in binary terms according to a crisp condition — 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 relation to a set; this is described with the aid of a membership function \mu\ \to [0,1].