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,

As it is well known in the fuzzy theory established by Zadeh [23], a

fuzzy subset g of [Q.sub.t] is defined as a map from [Q.sub.t] to the unit interval [0,1].

The nine

fuzzy subsets that can be applied to the multiresponse output and the

fuzzy subset ranges are presented in Table 7.

A

fuzzy subset A of X is defined by a function called the membership function and is denoted as [[mu].sub.A](x).

A

fuzzy subset [mu] of a ring R is called a fuzzy ideal of R if for all x, y e R the following conditions are satisfied:

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].