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

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

If we call *χ*_{S} as a *membership function*, then, in standard set theory, the membership ...