A fuzzy set is a set in which elements can belong to the set to varying degrees rather than only fully belonging or not belonging. Membership is represented by values on a continuum, commonly between 0 and 1.
In classical set theory, the membership of elements in a set is assessed in binary terms according to a bivalent condition β 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 valued in the real unit interval [0, 1]. Fuzzy sets generalize classical sets, since the indicator functions (aka characteristic functions) of classical sets are special cases of the membership functions of fuzzy sets, if the latter only take values 0 or 1