A fuzzy graph is a pair of functions G = ([sigma], [mu]) where o is a

fuzzy subset of a non empty set V and p is a symmetric fuzzy relation on [sigma].

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].

A

fuzzy subset A of U is characterized by a membership function [[phi].

A fuzzy graph is a pair of functions G = ([sigma], [mu]) where a is a

fuzzy subset of a nonempty set V and [mu] is a symmetric fuzzy relation on [sigma].

As described by Tanaka and Watada [4], "A fuzzy number is a

fuzzy subset of the real line whose highest membership values are clustered around a given real number called the mean value; the membership function is monotonic on both sides of this mean value" Hence, fuzzy number can be decomposed into position and fuzziness, where the position is represented by the element with the highest membership value and the fuzziness of a fuzzy number is represented by the membership function.

Definition 2 (fuzzy number): A fuzzy number is a

fuzzy subset of the universe of discourse X that is both convex and normal.

In 1965, Zadeh defined

fuzzy subset of a non-empty set as a collection of objects with grade of membership in continum, with each object being assigned a value between 0 and 1 by a membership function [1].

If Q is a finite set and h : Q [right arrow] [0, 1] a

fuzzy subset of this set, then the fuzzy integral of the function h on Q defined in relation to the fuzzy measure g, is given by:

x) be the

fuzzy subset in the space X = {x}, if the membership degree [[mu].

MURALI, 2004) defined the concept of belongingness of a fuzzy point to a

fuzzy subset under a natural equivalence on a

fuzzy subset.

j] is the top of m -th

fuzzy subset for j -th variable; [[tau].