The support of a
fuzzy subset A of E is the sharp set that contains all the elements of the reference E whose membership function is non-zero: S (A) = {x [member of] E / [[micro].sub.A] (x)> 0}
Murali [14] defined the concept of belongingness of a fuzzy point to a
fuzzy subset under a natural equivalence on a
fuzzy subset.
The notion of a
fuzzy subset was introduced by Zadeh [2] and later applied in various mathematical branches.
The subscript A represents the
fuzzy subset of the fuzzy variable.
A
fuzzy subset v : E x R [right arrow] R of E x R is called a fuzzy antinorm on E with respect to the t-conorm [??] if, for all x, y [member of] E,
The nine
fuzzy subsets that can be applied to the multiresponse output and the
fuzzy subset ranges are presented in Table 7.
A fuzzy number [??] = (a, b, c, d; w) is described as any
fuzzy subset of the real line R with the membership function [[xi].sub.[??]](x) which is given by
where [mathematical expression not reproducible] is the center of gravity of the
fuzzy subset, which converts the
fuzzy subset into an exact value.
A
fuzzy subset A of U is characterized by a membership function [[phi].sub.A] that assigns to each element x of U a number [[phi].sub.A] (x) in the interval [0,1].