Soft Computing and Its Applications, Volume One

184 Soft Computing and Its Applications

FIGURE 76 Projection of R on the x axis is [a,b] and on the y axis is [0,c].

Denition 2.66 Let R be a fuzzy binary fuzzy relation on X Y. The projection

of R on X is dened as

( ) = sup {R (x,y)| y Y}

and the projection of R on Y is defined as

( ) = sup {R (x,y)| x X}.

Example 2.70 Consider the relation

R = “x is considerable larger than y”

=

Then the projection on X means that

•

is assigned the highest membership degree from the tuples ( , ), ( , ),

( , ), ( , ), that is ( = 1, which is the maximum of the first now.

•

is assigned the highest membership degree from the tuples ( , ), (