Soft Computing and Its Applications, Volume One

Fuzzy Sets, Fuzzy Operators, and Fuzzy Relations 59

Therefore,

( )

BA +

can be written as ,

( ) ( ) ( ) ( ){ }

7,0.5 ,6,0.5 ,1,5=+ BA

.

Example 2.12 Let’s consider

( )

BA −

between previously dened fuzzy sets A and

B. For

( )

B-AB, zAx ∈∈∈ y ,

, fuzzy set

( )

B-A

is represented as follows:

1. For

,2−<z

( )

( )

0=

−

Z

BA

µ

.

2.

2−=z

results from

42 −=− yx

( ) ( )

5.05.0142 =∧=∧

BA

µµ

( )

( )

5.02 =−

− BA

µ

.

3.

1−=z

results from x-y=2-3 or x-y=3-4

( ) ( )

11132 =∧=∧

BA

µµ

( ) ( )

5.05.05.043 =∧=∧

BA

µµ

( )

( ) ( )

15.0,11

431

321

=∨=−

−=−

−=−

− BA

µ

.

4

.

0=z

results from

33 −=− yx

( ) ( )

5.015.033 =∧=∧

BA

µµ

( )

( )

5.00 =

− BA

µ

.

5. For

1≥z

( )

( )

0=

−

z

BA

µ

.

Therefore,

( )

BA −

can be written as,

( ) {( 2,0.5),( 1,1),(0, 0.5)}.AB− =− −

60 Soft Computing and Its Applications

Example 2.13