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. , Q = {q1, q2 ,..., qk } - Q2 = { (qm , qn), m,n = 1,2,,k }. (qm , qn) , qm qn . , , || x(a, b) || 0 1 k x k. x(a, b) = 1 , a < b a = b. x(b, a) = 0, x(b, a) = 1. x(a, b) x(b, a) 1.
? , (a, b) (. , ) , , . || x(a,b) || || y(a, b) ||, , , x(a,b)y(a,b)=x(b,a)y(b,a)= 0.
, , , (, , ), , ( ). , || a(i,j) || 0 1, a(i,j) = 1 , qi qj , a(i,j) = 0 .
. , || a(i,j) || || b(i,j) || , D (A, B) = ∑ │ a(i,j) - b(i,j) │, i,j 1 k, .. , .
, - || a(i,j) || || b(i,j) ||. . [7], , [4, 6]. - , , [4].
. . 1 , 2 , 3 ,, - , . .. Arg min ∑ D (Ai ,A), Arg min - , , . , ∑ D (Ai ,A) = D (A1 ,A) + D (A2 ,A) + D (A3 ,A) ++ D (A ,A). , , D (Ai ,A) D2 (Ai ,A). - . , .. (.. - ), : Arg min ∑ D (Ai ,A) → Arg min D (A1 , A). - . , 1 , 2 , 3 ,, (.. ) , , . (., , [4, 6]).
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. ( 9) 9 1 , 2 , 3 ,..., 9 (. . 3). 5 { 2 , 4 , 5 , 8 , 9 }.
() = ∑ D(Ai ,A) = D(A2 ,A)+D(A4 ,A)+D(A5 ,A)+D(A8 ,A)+D(A9 ,A),
1 , 2 , 3 ,..., 9 . : (1) = 24, (2) = 13, (3) = 21, (4) = 27, (5) = 16, (6) = 23, (7) = 15, (8) = 25, (9) = 25. 13, = 2, , - 2.
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[9].
1. .. // . 1996. .62. 1. .54-60.
2. .., .., .. // . 2000. 3. . 159-167.
3. .. , , . .: , 1971.
4. .. - . - .: , 1979. - 296 .
5. . . / . .. . - .: , 2000. - 288 .
6. .. // . 1998. . 64. 3. .52-60.
7. ., . : . - .: , 1972. - 192 .
8. .. . . - .: - "", 2003. 576 .
9. .., .. . .: , 2003. -404 .
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1 < 3 < 2 < 5 < 6 < 7 < 4 | |
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