Abstract:
A fuzzy set is a class of objects with a continuum of grades of
membership. Such a set is characterized by a membership (characteristic)
function which assigns to each object a grade of membership
ranging between zero and one. The notions of inclusion, union,
intersection, complement, relation, convexity, etc., are extended
to such sets, and various properties of these notions in the context
of fuzzy sets are established. In particular, a separation theorem for
convex fuzzy sets is proved without requiring that the fuzzy sets be
disjoint.
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