1.
2.
3.
4.
, - , , . , -, , - . , - , , . , - , . , -, - , .
6 . , 9, - . - , , . - , .. . , .
( ) . - , - , .. - . , - , -, , -.
, , . , : , - , , . .
( ). , , . , , -, , .
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1. , .. = { m 1, m 2, m 3}, W = { w 1, w 2, w 3} :
P (m 1) = w 2, w 1, w 3; P (w 1) = m 1, m 2, m 3
P (m 2) = w 1, w 3, w 2; P (w 2) = m 3, m 1, m 2;
P (m 3) = w 1, w 2, w 3; P (w 3) = m 3, m 1, m 2.
, m 1 w 2, w 1 w 3; w 1 m 1, m 2 m 3, ..
μ =
m 1. μ w 1, , w 2. w 2 , μ, m 2, m 1 . (m 1, w 2) , - μ, , -. - μ, (m 1, w 2) ■
, 1, , (m, w) - μ. .
2. , 1,
ν = .
m 1 w 2. w 2 , -, m 1, (m 1, w 2) ν. (m 1, w 3) , m 1 w 1, w 3. (m 3, w 3) , m 3 w 2, w 3. , (m 3, w 1). , w 1 - , , m 1. (m 2, w 1) ( w 1 , , m 1). , (m 2, w 2) , w 2 , , m 3.
, 6 , ν ( 6 3- 3- -). ■
, , . 2 -, ν . - , . - ν 2- , w 1 w 2 , w 3 m 2, - . , , .
. ? , - ? 1-
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1. , -, ■
. 1 ( ) , , - , . .
3. . , .. = { m 1, m 2, m 3}, W = { w 1, w 2, w 3, w 4} :
P (m 1) = w 2, w 1, w 4, w 3; P (w 1) = m 2, m 1, m 3;
P (m 2) = w 2, w 3, w 4, w 1; P (w 2) = m 3, m 2, m 1;
P (m 3) = w 1, w 4, w 3, w 2; P (w 3) = m 3, m 1, m 2;
P (w 4) = m 1, m 3, m 2.
1, 2, 3, . - : () (). , , , , ( ) . ( 1 - .)
- -, . .
, , - , . - , ( ).
, .
1.
. .
.
. w 2 : m 1 m 2. m 2 - m 1, m 1.
.
, m 1 w 2.
2.
. m 1 . , w 2. - w 1.
.
. w 1 : m 1 m 3. m 1 - m 3, m 3.
.
, m 3 w 1.
3.
. m 3 . , w 1. - w 4.
.
, . m 2 , m 1 m 3 w 1 w 4, . - w 1, w 2 w 4 m 1, m 2 m 3, . w 3 ■
1- . , , , .. 1- , - , , , - , .. , - - , . ( ) .
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, , : ( ), -, . ( ) - , , , .
1. , , - :
P (m 1) = w 2, w 3, w 1; P (w 1) = m 2, m 1, m 3; P (m 2) = w 2, w 1, w 3; P (w 2) = m 3, m 2, m 1; P (m 3) = w 1, w 3, w 2; P (w 3) = m 3, m 1, m 2. | P (m 1) = w 2, w 3, w 1; P (w 1) = m 2, m 1, m 3; P (m 2) = w 1, w 3, w 2; P (w 2) = m 3, m 2, m 1; P (m 3) = w 2, w 1, w 3; P (w 3) = m 3, m 1, m 2. |
P (m 1) = w 2, w 1, w 3; P (w 1) = m 2, m 1, m 3; P (m 2) = w 2, w 3, w 1; P (w 2) = m 3, m 2, m 1; P (m 3) = w 1, w 3, w 2; P (w 3) = m 3, m 1, m 2. | P (m 1) = w 2, w 1, w 3; P (w 1) = m 2, m 1, m 3; P (m 2) = w 1, w 3, w 2; P (w 2) = m 3, m 2, m 1; P (m 3) = w 2, w 3, w 1; P (w 3) = m 3, m 1, m 2. |
P (m 1) = w 1, w 3, w 2; P (w 1) = m 2, m 1, m 3; P (m 2) = w 2, w 3, w 1; P (w 2) = m 3, m 2, m 1; P (m 3) = w 2, w 1, w 3; P (w 3) = m 3, m 1, m 2. | P (m 1) = w 1, w 3, w 2; P (w 1) = m 2, m 1, m 3; P (m 2) = w 2, w 1, w 3; P (w 2) = m 3, m 2, m 1; P (m 3) = w 2, w 3, w 1; P (w 3) = m 3, m 1, m 2. |
P (m 1) = w 2, w 3, w 1; P (w 1) = m 2, m 3, m 1; P (m 2) = w 2, w 1, w 3; P (w 2) = m 3, m 1, m 2; P (m 3) = w 1, w 3, w 2; P (w 3) = m 3, m 2, m 1. | P (m 1) = w 2, w 3, w 1; P (w 1) = m 2, m 3, m 1; P (m 2) = w 1, w 3, w 2; P (w 2) = m 3, m 1, m 2; P (m 3) = w 2, w 1, w 3; P (w 3) = m 3, m 2, m 1. |
P (m 1) = w 2, w 1, w 3; P (w 1) = m 2, m 3, m 1; P (m 2) = w 2, w 3, w 1; P (w 2) = m 3, m 1, m 2; P (m 3) = w 1, w 3, w 2; P (w 3) = m 3, m 2, m 1. | P (m 1) = w 2, w 1, w 3; P (w 1) = m 2, m 3, m 1; P (m 2) = w 1, w 3, w 2; P (w 2) = m 3, m 1, m 2; P (m 3) = w 2, w 3, w 1; P (w 3) = m 3, m 2, m 1. |
P (m 1) = w 1, w 3, w 2; P (w 1) = m 2, m 3, m 1; P (m 2) = w 2, w 3, w 1; P (w 2) = m 3, m 1, m 2; P (m 3) = w 2, w 1, w 3; P (w 3) = m 3, m 2, m 1. | P (m 1) = w 1, w 3, w 2; P (w 1) = m 2, m 3, m 1; P (m 2) = w 2, w 1, w 3; P (w 2) = m 3, m 1, m 2; P (m 3) = w 2, w 3, w 1; P (w 3) = m 3, m 2, m 1. |
P (m 1) = w 2, w 1, w 3; P (w 1) = m 3, m 2, m 1; P (m 2) = w 2, w 3, w 1; P (w 2) = m 2, m 3, m 1; P (m 3) = w 1, w 3, w 2; P (w 3) = m 2, m 3, m 1. | P (m 1) = w 2, w 1, w 3; P (w 1) = m 3, m 2, m 1; P (m 2) = w 1, w 3, w 2; P (w 2) = m 2, m 3, m 1; P (m 3) = w 2, w 3, w 1; P (w 3) = m 2, m 3, m 1. |
P (m 1) = w 1, w 3, w 2; P (w 1) = m 3, m 2, m 1; P (m 2) = w 2, w 3, w 1; P (w 2) = m 2, m 3, m 1; P (m 3) = w 2, w 1, w 3; P (w 3) = m 2, m 3, m 1. | P (m 1) = w 2, w 3, w 1; P (w 1) = m 2, m 1, m 3; P (m 2) = w 2, w 1, w 3; P (w 2) = m 3, m 2, m 1; P (m 3) = w 1, w 3, w 2; P (w 3) = m 3, m 1, m 2. |
P (m 1) = w 2, w 3, w 1; P (w 1) = m 2, m 1, m 3; P (m 2) = w 1, w 3, w 2; P (w 2) = m 3, m 2, m 1; P (m 3) = w 2, w 1, w 3; P (w 3) = m 3, m 1, m 2. | P (m 1) = w 2, w 1, w 3; P (w 1) = m 2, m 1, m 3; P (m 2) = w 2, w 3, w 1; P (w 2) = m 3, m 2, m 1; P (m 3) = w 1, w 3, w 2; P (w 3) = m 3, m 1, m 2. |
P (m 1) = w 2, w 1, w 3; P (w 1) = m 2, m 1, m 3; P (m 2) = w 1, w 3, w 2; P (w 2) = m 3, m 2, m 1; P (m 3) = w 2, w 3, w 1; P (w 3) = m 3, m 1, m 2. | P (m 1) = w 1, w 3, w 2; P (w 1) = m 2, m 1, m 3; P (m 2) = w 2, w 3, w 1; P (w 2) = m 3, m 2, m 1; P (m 3) = w 2, w 1, w 3; P (w 3) = m 3, m 1, m 2. |
P (m 1) = w 1, w 3, w 2; P (w 1) = m 2, m 1, m 3; P (m 2) = w 2, w 1, w 3; P (w 2) = m 3, m 2, m 1; P (m 3) = w 2, w 3, w 1; P (w 3) = m 3, m 1, m 2. | P (m 1) = w 2, w 3, w 1; P (w 1) = m 2, m 3, m 1; P (m 2) = w 2, w 1, w 3; P (w 2) = m 3, m 1, m 2; P (m 3) = w 1, w 3, w 2; P (w 3) = m 3, m 2, m 1. |
P (m 1) = w 2, w 3, w 1; P (w 1) = m 2, m 3, m 1; P (m 2) = w 1, w 3, w 2; P (w 2) = m 3, m 1, m 2; P (m 3) = w 2, w 1, w 3; P (w 3) = m 3, m 2, m 1. | P (m 1) = w 2, w 1, w 3; P (w 1) = m 2, m 3, m 1; P (m 2) = w 2, w 3, w 1; P (w 2) = m 3, m 1, m 2; P (m 3) = w 1, w 3, w 2; P (w 3) = m 3, m 2, m 1. |
P (m 1) = w 2, w 1, w 3; P (w 1) = m 2, m 3, m 1; P (m 2) = w 1, w 3, w 2; P (w 2) = m 3, m 1, m 2; P (m 3) = w 2, w 3, w 1; P (w 3) = m 3, m 2, m 1. | P (m 1) = w 1, w 3, w 2; P (w 1) = m 2, m 3, m 1; P (m 2) = w 2, w 3, w 1; P (w 2) = m 3, m 1, m 2; P (m 3) = w 2, w 1, w 3; P (w 3) = m 3, m 2, m 1. |
P (m 1) = w 1, w 3, w 2; P (w 1) = m 2, m 3, m 1; P (m 2) = w 2, w 1, w 3; P (w 2) = m 3, m 1, m 2; P (m 3) = w 2, w 3, w 1; P (w 3) = m 3, m 2, m 1. | P (m 1) = w 2, w 1, w 3; P (w 1) = m 3, m 2, m 1; P (m 2) = w 2, w 3, w 1; P (w 2) = m 1, m 3, m 2; P (m 3) = w 1, w 3, w 2; P (w 3) = m 2, m 3, m 1. |
P (m 1) = w 2, w 1, w 3; P (w 1) = m 3, m 2, m 1; P (m 2) = w 1, w 3, w 2; P (w 2) = m 1, m 3, m 2; P (m 3) = w 2, w 3, w 1; P (w 3) = m 2, m 3, m 1. | P (m 1) = w 1, w 3, w 2; P (w 1) = m 3, m 2, m 1; P (m 2) = w 2, w 3, w 1; P (w 2) = m 1, m 3, m 2; P (m 3) = w 2, w 1, w 3; P (w 3) = m 2, m 3, m 1. |
P (m 1) = w 1, w 3, w 2; P (w 1) = m 3, m 2, m 1; P (m 2) = w 2, w 1, w 3; P (w 2) = m 1, m 3, m 2; P (m 3) = w 2, w 3, w 1; P (w 3) = m 2, m 3, m 1. | P (m 1) = w 2, w 3, w 1; P (w 1) = m 2, m 1, m 3; P (m 2) = w 2, w 1, w 3; P (w 2) = m 3, m 2, m 1; P (m 3) = w 1, w 3, w 2; P (w 3) = m 3, m 1, m 2. |
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1990- (. ). (), , , . - , , . , , , -, - ( , ), - , ,
4. . , . , - . , , , , . - :
(%) | (%) | |
3 | ||
1953 | ||
() | ||
, , , - . , - , - - . , , . , , , . - ( ) - , .
, ( , ):
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: (17%), (17%), (4%), (6%),
(17%) 61%.
: (14%), (14%), (21%), (14%), (14%) 77%.
, , - : (100) . ■
2.1. . - . , N ( , , .), - A B. (.. -) a 1, , aN b 1, , bN , , A B. ,
= = 100, (1)
.
x = (x 1, , xN), xi , 0 ≤ xi ≤ 1 (i = 1, , N). xi i - , - x A ( B (1 xj) ). i - ( , .), - . . , , , , xi , A. , - , , 0,75 0,25. xi 1 xj , i - -.
G A(x) G B(x) A B x = (x 1, , xN) -
G A(x) = , G B(x) = ). (2)
0 100 100- x . , A, G A(x) = 100, G B(x) = 0, B, G A(x) = 0, G B(x) = 100. - , - . (2) (1) , B A (.. A)
= 100 G A(x), (3)
A B (.. B)
= 100 G B(x). (3b)
, - G A(x) G B(x) A B. G (x) = (G A(x), G B(x)) G (x) (- ) x.
x ,
G A(x) ≥ 50 (4a)
G B(x) ≥ 50. (4b)
(4a) (3a) , A B
, .. , B x; B A, -.
x ,
G A(x) = G B(x), (5)
.. x.
x ( -),
G (x) . , y G A(x) > G A(y) , G B(x) < G B(y), G B(x) > G B(y) , G A(x) < G A(y). , x , , y.
2.2. (). x , , -. , , - , : ? , ? - ( ) ? , ? , - ? ..
- , . a 1, , aN b 1, , bN. (). : (, , , ) , .
. ,
= 0, q < p ( ).
. , , , -
a 1 ⁄ b 1 ≥ a 2 ⁄ b 2 ≥... ≥ aN ⁄ bN. (6)
1. r = 0.
2. r = r +1.
3.
≥ . (7)
(7) , .
3.1.
xr = ( ) ⁄ (ar + br). (8)
3.2. xi = 1 (i = 1, , r 1), xi = 0 (i = r +1, , N).
3.3. . .
2.
(1) , (7) -- r. , xr, (8), 0 1.
2. , , - a 1, , aN b 1, , bN. , r - , r , (7) ■
5. , 1.
1
| 2
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(6) , - 2 ( 1- ).
, r = 1, (7), 2. r = 1
= a 1 = 27, = b 2 + b 3 + b 4 + b 5 = 12 + 29 + 21 + 28 = 90. 27 < 90, (7) .
, r = 2,
= a 1 + a 2 = 27 + 26 = 53, = b 3 + b 4 + b 5 = 29 + 21 + 28 = 78. 53 < 78, (7) .
, r = 3,
= a 1 + a 2 + a 3 = 27 + 26 + 23= 76, = b 4 + b 5 = 21 + 28 = 49. 76 ≥ 49, (7) . , 3,
xr = ( ) ⁄ (ar + br) = (78 53) ⁄ (23 + 29) = 25 ⁄ 52 = 0,48.
, : x = (1; 1; 0,48; 0; 0). , 1- 2- A, 4- 5- B; 3- 0,48:0,52. , - 2, . A 1- 3- , B 2- 4- , 5- 0,48:0,52. : x = (1; 0; 1; 0; 0,48).
x, (2) .
G A(x) = = 261+110+271+130+230,48 ≈ 64,06;
G B(x) = ) = 120+281+100+211+290,52 ≈ 64,06.
, 2. , , . - , - . (5) , - . 2 x - ■
6. , 3.
3
| 4
|
(6) , - 4 ( 1- ). , r = 1, (7), 4. r = 1 = a 1 = 90, = b 2 + b 3 + b 4 + b 5 = 20 + 20 + 20 + 20 = 80. 90 ≥ 80, (7) . , 3,
x 1 = ( ) ⁄ (ar + br) = (100 0) ⁄ (90 + 20) = 100 ⁄ 110 = 10 ⁄ 11; x 2 = x 3 = x 4 = x 5 = 0.
, 4, . A 10 ⁄ 11 4- , B 1 ⁄ 11 4- . - : x = (0; 0; 0; 0,91; 0). x, (2) -.
G A(x) = = 20+ 30+ 20+90(10 ⁄ 11)+30 = 81 ;
G B(x) = ) = 201+201+201+20(1 ⁄ 11)+201 =.81 ,
5, , . , . - ■
2. . 5 6.
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: 2016-10-07; !; : 1289 | : : , . : 0.152 . |