Discrete Mathematics

130 DISCRETE MATHEMATIC..._

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Definition Let S

be

a linear space. Then a fuzzy subset A e S is convex

iff

all its a-cuts are convex subsets

of

S (Fig. 2.7).

2.6.4

Fuzzy Relations

A relation between two sets S and

Tis

best defined as a subset

of

the Cartesian product S x

T.

Thus, a fuzzy

relation is defined as a fuzzy subset

of

the Cartesian product. Our intention is to consider only binary relations

since

n-ary relations follow in a straightforward manner. We have also decided to give only fundamental

definitions for the development

of

the application

we

have chosen to deal with next.

Definition

LetS,

Y

be

two

reference ...