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Elements of Fuzzy Logic

According to Georg Cantor, a set may be viewed as a well-defined collection of objects, called the element or member of the set. The term ‘well defined’ means that it is possible to decide if a given object belongs to the collection or not. Thus, if S is a set, then an element s is either a member of S or it is not.

Let χS be a characteristic (indicator) function of S. Then, by definition, χS is a function from universe of discourse to the set {0, 1} such that

 

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Hence, a set S can be represented in term of ordered pairs as

 

 

If we call χS as a membership function, then, in standard set theory, the membership ...

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