Fuzzy sets Operation

                   FUZZY  SET  OPERATIONS :
1. FUZZY  UNION :-
         A = {( x , 0.5) , (y , 0.7) , (z ,0)}  

          B={( x , 0.8) , (y , 0.2) , (z ,1)}
A U B = A UNION B
         = maximum of membership       
     degree among the sets
A U B = ( x , 0.8) , (y , 0.7) , (z ,1)}
 NOTICE -
          0.8 > 0.5
           0.7 > 0.2
            1 > 0

2. FUZZY  INTERSECTION :-
 A = {( x , 0.5) , (y , 0.7) , (z ,0)}         B={( x , 0.8) , (y , 0.2) , (z ,1)}
 A INTERSECTION B  = minimum of
membership degree among the sets
= ( x , 0.5) , (y , 0.2) , (z ,0)}

 NOTICE - 
          0.8 < 0.5
           0.7 < 0.2
            1 < 0

3.  A ' = COMPLEMENT OF A
A = {( x , 0.5) , (y , 0.7) , (z ,0)}         B={( x , 0.8) , (y , 0.2) , (z ,1)}
A ' = 1 - MEMBERSHIP DEGREE
A ' = {(x , 0.5), (y ,0.3) , (z,1)}
B ' ={(x , 0.2) , (y,0.8) , (z,0)}

4.  A - B = ? 
A = {( x , 0.5) , (y , 0.7) , (z ,0)}        
B={( x , 0.8) , (y , 0.2) , (z ,1)}
A - B = A INTERSECTION B'
         = minimum of membership       
     degree among the sets
A- B = {(x , 0.2) , (y , 0.7) , (z ,0)}

5. POWER OF  FUZZY SET = ? 
   IF "A " IS A FUZZY SET THEN
     POWER SET (A)  =  (membership
degree of set )^ $
       P(A) = (M. DEGREE)^$
NOTE -
        IF $ = 1/2 THEN IT IS CALLED
"DILATION"
       IF $ = 2 THEN IT IS CALLED
"CONCENTRATION "

EXAMPLE - 
A = {( x , 0.5) , (y , 0.7) , (z ,0)} 
$ = 2
A = {( x , 0.25) , (y , 0.49) , (z ,0)}