A fuzzy set is a function A: U → L where U is an ordinary set of elements called universe and L is a scale which is usually supposed to have the structure of a residuated lattice (see “ Residuated Lattice”). The function A is at the same time called also membership function, i.e., fuzzy set is identified with its membership function.
If x ∈ U is an element then A(x) ∈ L is a membership degree of x in the fuzzy set A. It can also be interpreted as a degree of truth of the fact that the element x belongs to the fuzzy set A. If U is a universe and A a fuzzy set then it is convenient to write A ⫇ U.