# fuzzy subset

## fuzzy subset

In fuzzy logic, a fuzzy subset F of a set S is defined by a "membership function" which gives the degree of membership of each element of S belonging to F.
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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  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  and later applied in various mathematical branches.
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 , 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].

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