Strictly speaking, a fuzzy set A is a collection of ordered pairs:

Fuzzy Singleton

Item x belongs to the universe and μ(x) is its grade of membership in A. A single pair (x,μ(x)) is called a fuzzy singleton; therefore the entire set can be considered as the union of its constituent singletons. It is often convenient to think of a set A just as a vector:

Fuzzy Singleton

It is understood then, that each position i (1,2,3,…,n) corresponds to a point in the universe of n points.

References & Resources

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