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].

be the

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

A is a

fuzzy subset of the factor set U,if B [subset or equal to] V, then the comprehensive evaluation result B can be defined as follows:

A fuzzy graph [1] is a pair G: ([sigma],([mu]) where [sigma] is a

fuzzy subset of a set S and [mu] is a fuzzy relation on [sigma] such that [mu].

If we let U represent a set (universe), A is called a

fuzzy subset of U if A is a set of ordered pairs; A= { [[mu], [[mu].

Zadeh [1] introduced the notion of a

fuzzy subset of a set as a method for representing uncertainty in real physical world.

The

fuzzy subset B of X is said to be fuzzy a-closed (resp.

Fuzzification is an interface that produces a

fuzzy subset from the measurement.

Then a

fuzzy subset of V is a mapping [mu]:V [right arrow] [0,1] which assigns to each element [member of] V, a degree of membership, 0 [less than or equal to] [mu](v) [less than or equal to] 1.

The

fuzzy subset that represents an interval of confidence associated with a 0.

In general, a generalized L-R type fuzzy number A can be described as any

fuzzy subset of the real line R whose membership function [[mu].