One, the membership function of the set
Each set A can correspond to a function, f: S -> {0,1}, S is a superset, and the value range has only 2 elements
but
Second, fuzzy sets
As the name implies, each element is part of the set and part of it is not.
The membership function is changed to, f : S -> [0,1], and the value range is a closed interval.
An extension of the basic concept of collections: