8.3. 
= {<0.6; x 1 >; <0.3; x 2 >; <0.8; x 4 >; <0.4; x 5 >} 
= {<0.2; x 2 >; <0.5; x 3 >; <0.7; x 4 >; <0.9; x 5 >} X = { x 1, x 2, x 3, x 4, x 5 }.
.
. n ( , ) = (0.6 0) & (0.3 0.2) & (0 0.5) & (0.8 0.7) & (0.4 0.9) = 0.4 & 0.7 & 1 & 0.7 & 0.9
: n ( , ) = 0.4.
8.4. = {<0.4; x 1 >; <0.7; x 2 >; <0.2; x 4 >; <0.9; x 5 >} = {<0.6; x 3 >; <0.3; x 4 >; <0.8; x 5 >} X = { x 1, x 2, x 3, x 4, x 5 }.
, , .
: Ç = {<0.2; x 4 >; <0.8; x 5 >};
È = {<0.4; x 1 >; <0.7; x 2 >; <0.6; x 3 >; <0.3; x 4 >; <0.9; x 5 >};
\ = {<0.4; x 1 >; <0.7; x 2 >; <0.2; x 4 >; <0.2; x 5 >};
ù = {<1; x 1 >; <1; x 2 >; <0.4; x 3 >; <0.7; x 4 >; <0.2; x 5 >}.
8.5. 
= (X, Y, 
).
:
) X = { x 1, x 2, x 3, x 4 }; Y = { y 1, y 2, y 3, y 4 }; = {<0.3; < x 1; y 1 >>; <0.2; < x 1; y 3 >>; <0.4; < x 2; y 2 >>; <0.6; < x 3; y 2 >>; <0.1; < x 4; y 1 >>; <0.8; < x 4; y 4 >>}. , = (X, Y, ) .
) , , :
,
X, Y. , X ´ Y .
) (. 8.7). , .
. 8.7.
8.6. = (X, Y, ) 
= (Y, Z, 
). . 8.7, - . 8.8. .
. 8.8.
: . 8.9.
. 8.9.
8.7. 
.
: ) . = (X, ); X = { x 1, x 2, x 3, x 4 }; = {<0.4; < x 1, x 2 >>; <0.7; < x 1, x 3 >>; <0.2; < x 2, x 1 >>; <0.5; < x 2, x 4>>; <0.7; < x 3, x 2 >>; <0.3; < x 3, x 4 >>; <0.8; < x 4, x 2 >>; <0.1; < x 4, x 3 >>}.
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) .
X. , X 2 .
) . (. 8.10), .
. 8.10.
8.8. = (X, ) (. 8.10) 
= (X, ) (. 8.11) , .
. 8.11.
:
) (. 8.12).
. 8.12.
) (. 8.13).
. 8.13.
) (. 8.14).
. 8.14.
, . . , ( ) .. . . , . , . . , .
X j = < , X >, Í X ´ X. , X . Q = <j, X > . = { Q 1, Q 2,, Ql }, .
j Q. Q Q. .. ., j*(D) = { e 1, e 2, , en }, D .
. Q .
X Q Q, X, X Q Q, X. X Q 
X . () = X - X Q.
. 8.1.
8.1
D = { }, :
R *(D) ={{, }, {}, {}, {}}.
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1 = {, }, 2 = {}, 3 = {}, 4 = {}.
. , { 2, 3} = {, } - .
X .
= {, }
= {, , , }
() = X - 
={, }.
.
Y Z , : Y = Z.
Y Z , : Y = Z.
, Y Z.
:
1. Y Ì Y Ì Y
2. 1 = l = 1
3. 0 = 0 = 0
4. (Y Ç Z) = Y Ç Z
5. (Y È Z) = Y È Z
6. Y = - (- Y)
7. Y = - (- Y)
0 , 1 X.
1. ?
2. .
3. ? .
4. ?
5. ?
6. ?
7. , , ?
8. ?
9. ?
10. ?
11. ?
12. ?
13. .
14. .
1. X = {0, 1, 2,..., 10}. , , , , , , , , , , .
2. , , 
- , = 0.3, = 0.8, = 0.1.
, :
a) = ( ) ;
) = (ù Ú ù ) & ù ;
) = (ù ) Ú ù ;
) = ù ((ù ù ) & (ù ù ));
) = ù (( Ú ù ) ) & ;
) = (ù (ù Ú ) & ù ( Ú ù ) Ú ( & ù )) & & ;
3. :
= {<0.8; x 1 >; <0.4; x 2 >; <0.3; x 3 >; <0.6; x 4 >};
= {<0.7; x 2 >; <0.6; x 3 >; <0.2; x 4 >; <0.1; x 5 >}
X = { x 1, x 2, x 3, x 4, x 5 }.
, :
) = Ç ;
) = ù Ç ;
) = ù (ù Ç ù );
) = È ;
) = È ù ;
) = ù (ù È );
) = \ ;
) = ù \ ù ;
) = ù ( \ ù ).
4. = (X, Y, ), X = { x 1, x 2, x 3, x 4 }, Y = { y 1, y 2, y 3, y 4, y 5 }, = {<0.7,< x 1, y 2 >>, <0.9,< x 1, y 5 >>, <0.1,< x 2, y 1 >>, <0.3,< x 2, y 2 >>, <0.6,< x 2, y 3 >>, <1,< x 3, y 4 >>, <0.8,< x 4, y 2 >>, <0.4,< x 4, y 3 >>}.
R G, .
5. = (X, Y, ) = (Y, Z, ), X = { x 1, x 2, x 3, x 4 }, Y = { y 1, y 2, y 3, y 4, y 5 }, = {<0.7, < x 1, y 2 >>; <0.9, < x 1, y 5 >>; <0.1, < x 5, y 1 >>; <0.3, < x 2, y 2 >>; <0.6, < x 2, y 3 >>; <1, < x 3, y 4 >>; <0.8, < x 4, y 2 >>; <0.4, < x 4, y 3 >>}, Y = { y 1, y 2, y 3, y 4 }, Z = { z 1, z 2, z 3 }, = {<0.6, < y 1, z 1 >>; <0.3, < y 1, z 2 >>; <1, < y 3, z 3 >>; <0.8, < y 4, z 1 >>}. :
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) -1;
) -1;
) ;
) -1 -1.
6. = (X, ) = (X, ), X = { x 1, x 2, x 3, x 4, x 5 }, = {<0.4, < x 1, x 2 >>; <0.3, < x 1, x 3 >>; <0.5, < x 1, x 5 >>; <0.9, < x 2, x 1 >>; <0.8, < x 2, x 3 >>; <0.1, < x 3, x 2 >>; <0.6, < x 3, x 3 >>; <0.7, < x 5, x 1 >>; <0.2, < x 5, x 2 >>}, = {<0.3, < x 1, x 1 >>; <0.9, < x 1, x 4 >>; <0.1, < x 2, x 3 >>; <0.4, < x 3, x 1 >>; <0.5, < x 4, x 2 >>}.
, , .
7. ( ) :
a) ;
b) ;
c) ;
d) .
1
1. , ,
2. ù (" x Î X) (x Î Y) :
x, X, Y
x, X, Y
X Y
x, X Y
X Y
3.
