05.13.01 “ , ” - - 2006 ! " ! # $ % , c " & - $ ' $ " ! ( ' 26 " " , 117312, " ) ! . 60- 2006 ". 11 &.002.086.02 : % , 9. * ! . 2006 ". + " &.002.086.02 . .# * )' , " – , * . . # * " , .& ' ,#! , " " . . " " ) , ) : . – " ) % , * ! " , " * , , % )' * . " " - - , . " . * * " , , ) ) , ) * ' ,.( &*. 0. " , !.,.. , #.1 , %. ., , .&. " , ..2 " , , $./. . .# " . ) * ( ##!) ' . . , , %. " , " , /.! , $.! , . , . . ,#! ) , . % " ,#!. , " )' . 0 * 1 , " " ,#! )' " 4 , - " 3 , ,#!. ) " " " " " ,#!, - " ##!. & )' • * : ' )' . " • # " ,#!. " ,#!. • ! • ! ,#! * ! • , " , " . " " " * * ,#!. • ! ,#! 3 . • ! ##! . " , " , , " " " * , " " " , 2 , , . .% # 1. # (.% ), * " 2. 3. 4. " ,#!. 5. # " / 6. # * ,#!. . " ,#!. - " ,#! . 3 ,#! , . * 7. .% # )' UniComBOS, . 1. ! " " " ,#!. 2. ,#! . & * ' , ,#!. 3. ! * )' " - , 4. ! ' 5. # ) ,#! " * ,#! )' , " ,#!, ) " . ' . " " * . 3 .% # 2001-2003 " ##! UniComBOS «# + ". 5 UniComBOS 0 ) ,, , . . " / , " ! 2.21 " « (2001-2005 » , 1 , " ! » " ), % 0 1.2 ! " 00290 ! " # ! 61964.2003.1. " «1 », 1 01-01-00514, 04-01, " * ' ! * * " ' « ##! # , 2003; 58«# ' " 2003; 17* ) * 7 (MCDM 2004), ( % 2004)», » (AIS’05), & * « # * 7- * " * » (ISDSS’03), + , ! / », ,! , " , . , 2004; « , + , 2004; « 0-2005), # » ( 4 ,! , 2005; -( , ! ! , 2005; ; + 1 ". 5 , . . # 11 ! ' , . . , , ' " 2.3 3 3.1 . ! & , (65 * , * . ) 17 5 " , .! ) * " 136 * )' ) , .% . % 1 , * ) * , , . ) # * * " * " ' . ! " . )' , . 0 " , " ) " , " * " .% ) 5 ' , ,#!. ) 3 . , " # ) . " , “ * - ) , 3 ,#!, ” ,#!, . ) - ,#! ,#!, ) “ " ) ) 3 )' , . ”, “ * ” ,#!. % (“ ”). # “' , , . . ” ) " )' ), ) ) , - . . . 3 ,#!, " )' , . " )' " )' " , " . " .% # # " (.% " ), " " ( " " * , 3 , , , ). . " , ( . 8 * ) ( " " " , A. . , 6 ) ,#! )' . % " C = {C 1 ,...,C k } , C (a ) – j K = {1,..,k } { ) Cj, a∈A * – * 6 . } S j = s1j ,s2j ,...,smj j , j ∈ K , * ) , ( * ) , C j (a ) . # Sj = ): - a∈A " . * ) k- k S = ∏S j , j =1 a∈ A .. * *) ( C (a ) A * A. % # * (C ( a ) ,C ( a ) ,...,C ( a ) ) , 1 2 k 1 j ' k C ,...,C . % , A⊆S. A, A. Sj C, 0 * ,#!. " , .! * ωj: Qj = Sj ) Q = ∏Q j , " Sj, " {ω } , j S = ∏S j . * j∈K ! j∈K ) ) a ∈Q J ⊆K. % a 7 J * ) , j- ω , j∈J , a, jj j∈K\ J . – ) , , . . " , , , & P I, ( a ,b ) ∈ P , a ( a ,b ) ∈ I , a ,#! * b, Q: b , R=P * I. # * ' ( x, y ) , * )P I, ωj, ω . # )' P– - j" j- j . . ) " * , P, I ) R : " ( I – - ( ), (1) ), (2) (3) (4) ). , R– ( P I =∅,R = P I . . ) 1. . , ). ) C ), * C* ⊂ C - * " , C* , * )' C \ C* . # P ) I, )' : ( a ,b ) ∈ P ( c ,d ) ∈ P , ( a ,b ) ∈ I ( c,d ) ∈ I , " ∀j ∈ K ,( a j = b j ) (c j (5) (6) = d j ) , (a j ≠ b j ) a j ,b j ,c j ,d j – j- cj = a j ∧d j = bj, a, b, c 8 d. # 2. ,#! P,I ,R , ) ) (1)-(6). P⊆P I⊆I. ,#! & . aJ 3 ) J = { j1 , j2 ,..., js } ⊆ K , a j1 ,...,a js b j1 ,...,b js (0 )' .% K\J " ) . 7 ,#! a J P bJ , * ' 1). bJ , ( a J ,b J ) , aJ (a I aJ , ( b J ,a J ) . 0 ,#! bJ , " , J ,b J ) , bJ P aJ 1. bJ C j1 C j2 … C js a j1 a j2 … a js b j1 b j2 … b js # ,#! . ,#! * " * , . ) ) ,#!. " " - , , .% # . ( . & , 9 3 ,#!, )' , " " , ,#! ! . ' 3 ,#! ) ,#!. + -, * , # * ' " , ,#! " , , ) * 7 . " , . . ) , 2 3 ' ,#! " . ,#! * - " * " ,#! . " . ) / * , . 7 * * , ' * .% # * * . * ,#! 3 * " ,#!. + , ,#!, ' " " " ' , " * . $ ,#!, , )' " , ' * ,#!. # ) ) , * , , . .% # " , ,#! 10 " * ) - 3 * " . .% # )' : • * , . • + . • ,#! ) # • , ,#! , ,#! ,#!. . # * " . . ) ) , ) • . ! 3 " # . ,#! * . - • • + # - ) " ,#! " ' ,#! * " ' . " ,#!. • " , ) " , )' " ) ,#!. * ,#!, . # * . ,#! " I ( a ,b ) R ( a ,b ) ( a ,b ) ∈ P , ( a , b ) ∈ I 3) " P ( a ,b ) , . )' ( a ,b ) ∈ R . , 11 * + (1)-(6), ) * 3) Ω PI , ) R ' ) * . # P ⊆ P,I ⊆ I , # { * * )' - ( P = ( a1 ,b1 ) ,..., aN P ,bN P )} , - - { ( I = ( c1 ,d1 ) ,..., c N I ,d N I P, ,#!. : )} , " NP - - NI - I, * { Ω ( ) ( = P ( a1 ,b1 ) ,...,P aN P ,bN P ,I ( c1 ,d1 ) ,...,I c N I ,d N I PI )} . % , P I. 0 " " . - * , . , , - , . ) .+ )' * : a ,b ∈ Q 1. PI Ω ,Ω ! P ( a,b ) : Ω ,Ω ( a ,b ) ∈ P ; I ( a ,b ) : Ω ,Ω |− I ( a ,b ) , ( a ,b ) ∈ I . PI " PI |− P ( a ,b ) , PI " " PI - PI * ) * ,#!, 3) ) , ,#! " . 2. PI PI Ω ,Ω , " ! , PI Ω ,Ω PI !# |− , . $ % # ,#! 3 . - , " " ' NP- " , . . , 12 ' . # * . - ,#! 3 ) , " ' modus ponens, ) . % ' , .# " , " ,#! ' 3 , )' ,#! ,#!, ' Ω mp . * Ω ' ) Γ mp Ω |− Γ . modus ponens a ∈Q # δ (a) , - ' " , ' δ (a) |Q j | , M= j∈K a: T δ ( a ) = (δ11 ( a ) ,..,δ m1 ( a ) ,δ m1 +1 ( a ) ,δ12 ( a ) ,..,δ1k ( a ) ,..,δ mk ( a ) ,δ mk +1 ( a ) ) , 1 " δi ( a ) = j 1 k 1, i ≤ m j a j = sij 0, i = mj +1 # a j ≠ sij D E, P ,#! ( ( ( E = (δ ( c ,d ) ,δ ( c ,d ) ,...,δ ( c D = δ ( a1 ,b1 ) ,δ ( a2 ,b2 ) ,...,δ aN P ,bN P 1 1 2 2 NI ,d N I δ ( a ,b ) = δ ( a ) − δ ( b ) . )' k : 13 I ), )) , )) , )' : a ,b ∈ Q " 1. & P ( a,b ) mp Ω ,Ω PI ! # ! modus ponens Ω mp ,Ω PI|− mp P ( a ,b ) , Dy + Ez = δ ( a ,b ) , y ≥ 0 , y (7) z NP , NI y≠0. mp PI Ω ,Ω |− mp , I ( a,b ) : " I ( a ,b ) , y=0. (7) P ( a ,b ) ( " NP. . & - " * (7). 2 " , * . 7 (7) * ' * ) , ' , I ( a ,b ) . P ( a ,b ) , ,) ) I ( a ,b ) ,#!, )' ) " " * , . Ω mp ,Ω PI * 2. & Ω mp ,Ω PI , ! , Dy + Ez = 0 , y ≥ 0 , y z y≠0. (8) NP # * ) * , NI 3 , * , ,#! 3 . & * 14 3 ) , ) , " )' . . * - ,#!, , , )' " " , , ' # 3 3 3 3 - . )' . & - )' . # b = ( s21 ,s22 ,s23 ) , ( s ,s 1 1 ( s ,s 1 2 b 2 2 2 1 ,s23 ) . & ((ω ,s ,s ) ,(ω ,s ,s ) ) . 2. 3. 4. 5. 6. 3 1 1 2 2 3 " , , ( : 2 3 a = ( s11 ,s12 ,s13 ) ,s13 ) , 1 P ( a ,b ) , " )' a 1. 3 ,#! 3 2 P * 2 3 1 2 ( s ,s1 ,ω ) ,( s2 ,s3 ,ω 3 ) 1 1 P ( a ,b ) 0 " )' P ( s11 ,s12 ,ω 3 ) ,( s12 ,s32 ,ω 3 ) , : ( ) P ( ( s ,s ,ω ) ,( s ,s ,ω ) ) ⊃ P ( ( s ,s ,s ) ,( s ,s ,s ) ) , P ( ( s ,s ,s ) ,( s ,s ,s ) ) , P ( (ω ,s ,s ) ,(ω ,s ,s ) ) , P ( (ω ,s ,s ) ,(ω ,s ,s ) ) ⊃ P ( ( s ,s ,s ) ,( s ,s ,s ) ) , P ( ( s ,s ,s ) ,( s ,s ,s ) ) , 1 1 2 1 1 1 2 1 3 3 1 1 2 1 2 2 3 2 3 3 2 3 3 1 1 2 2 3 2 1 2 3 3 1 1 2 2 3 2 2 3 3 1 1 2 2 2 2 1 3 1 1 2 2 3 3 1 1 2 2 3 3 1 1 2 2 2 3 2 3 1 1 1 2 1 1 3 2 15 )' ) 7. ( ) ( ⊃ P ( ( s ,s ,s ) ,( s ,s ,s ) ) , P ( ( s ,s ,s ) ,( s ,s ,s ) ) . 1 1 8. ) P ( s11 ,s12 ,s13 ) ,( s21 ,s32 ,s13 ) ∧ P ( s21 ,s32 ,s13 ) ,( s21 ,s22 ,s23 ) ⊃ 1 1 2 1 2 1 3 1 3 1 1 2 1 2 2 2 2 2 ( 3 2 1 4 2 P, ), ) ) 5– 2, ) 6 ' ) 8 3, 6 modus 5, 7 P, , , modus ponens 7. * 3 « ' ) 4 3 1 ponens 3 2 ) 3 ," " sij * : s11 ,s12 , C1 ,C 2 )' C j ,#! s21 ,s32 »; ) C3 * «# * s13 . # C 1 ,C 2 ,C 3 s11 ,s12 ,s13 : s21 ,s32 ,s13 »; « , C 2 ,C 3 s22 ,s23 »; s32 ,s13 ) C1 * «# * s21 . # s21 ,s32 ,s13 : C 1 ,C 2 ,C 3 s21 ,s22 ,s23 »; «( C 1 ,C 2 ,C 3 1 2 2 3 s21 ,s32 ,s13 , ) 1 2 3 C ,C ,C 3 1 s ,s ,s 1 2 2 2 3 2 s ,s ,s . s11 ,s12 ,s13 , " , s11 ,s12 ,s13 , s21 ,s22 ,s23 ». 16 , " C1 ,C 2 ,C 3 * " 3 ,#! * " - . . " " ) " , . 4 3 , , a " 3 – ,#!, , ,#!, ,#! , " * . " " " . " ,#! , " 3 ,#! . " u, a ∈Q * - . ( * " P,I . u ) u ( a ) = (δ ( a ) ,v* ) a δ (a) v* " " )' " : (" M , v ) → min N N DT v + # ≥ " P , ET v = 0 , # ≤ p* " P , v ,# ≥ 0 , " ( v = v11 ,v12 ,...,vm1 1 ,vm1 1 +1 ,v12 ,...,vij ,...,vmk −k −11 ,vmk −k −11 +1 ,v1k ,...,vmk k −1 ,vmk k ,vmk k +1 - "M M, # – " NP – M - " p* " . ' N DT v + # ≥ " P , ET v = 0 , # ≤ p" P , v ,# ≥ 0 . 17 – NP , ,0– p → min , N T ' , NP - - ) # N " P -DT v v. # " a , a " , b u (a) − u (b) . " % , )' * ' ) ( a′,b′ ) ) ,#! 1. ' ) * A * ( PI mp mp , A, . . ) P ( b ,a ) . { B = a ∈ A | ¬∃b ∈ A,Ω PI ) 2. " % } Ω mp|− mp P ( b ,a ) a∈B b′ a∈B \{a′} Ω mp|− mp I ( b′,a′) , B := B \ {b′} 5. . B \ {a′} u ( b′) : b′∈ arg max u ( a ) " Ω PI a B a′ u ( a′) : a′ ∈ arg max u ( a ) ) 3. 4. 7 A, . ) ∃b ∈ A, Ω ,Ω |− * b ,#! B * b′ : ) " 3. - ( a′,b′ ) , )' P ( a′,b′ ) , Ω mp ,Ω PI # , I ( a′,b′ ) , * . . P ( b′ ,a ′ ) . * * , . & , " " 18 ,#!, " r1+ ,r1− ,...,rt + ,rt − M, ( v ,r * + 1 − 1 −r ). ri + ,ri − ,i = 1,...,t , ( gi ,hi ) , ) gi ,hi ∈ Q, i = 1,...,t δ ( gi ,hi ) = ri − ri . + " − ) * ( v ,r * + i a′ − r1− ) 1 g ( i ,hi ) ,i = 1,...,t , * " i = 1,...,t . P «1» + 1 − ri − ) ,i = 2 ,...,t , b′ ) # ( gi ,hi ) )' ( v ,r : , «-1» ri + ,ri − 3 ) ,#! u ( gi ) − u ( hi ) " ( gi ,hi ) . # * , * " )' , . 0 * * , 7 , 3 & ) . + − ri = ri = 0 , . - * 3 - , * ' ) ( .% # ,#! " . 19 . 1 )' , , . 100.00% 80.00% 60.00% 40.00% % 20.00% ! 51 49 47 45 43 41 39 37 35 33 31 29 27 25 23 21 19 17 15 13 9 11 7 5 3 1 0.00% 1& " ' ,#! ##! UniComBOS, " )' .% # . % * ,#!, " 3 , " , ,#!. % 2. ##! UniComBOS 9 ) " / ##! UniComBOS ,#! , . " * )' , ) , . , # - . " ", - * ,#! . . * , * . * ,#!, " * 20 2 ) ) , . $& % # # # 3 ,#! ! 2. . ' ##! UniComBOS , ! . * , * 3) " , 1, . 21 1. # ' " )' , " )' , ) . 2. ! " .% # ) , ,#!, , ) " * . 3. # ,#! " " . 4. ,#!. 5. ! " * " 6. # * ,#!. * ,#!, . 7. ! ,#! * 8. # ' 9. # ) , " , " - * . " ,#! . # . * 3 , * . 10. ! ##! .% # )' , . ., ! 1. ». .: 7 . ., ! 2. 3 , . . /. . " 3 * . // « +! , 2001 "., . 51-71. /. ., 1 7. . + * 22 . // 0 * " " " XXI ". .: 1 , 2001, 0.1, . 463-470. 3. Ashikhmin I.V., Furems E.M., Larichev O.I., Roizenson G.V. Decision Support System UniComBOS to Discreet Multi-Criteria Choice Problems // DSS in the Uncertainty of the Internet Age. Poland, The Karol Adamiecki University of Economics in Katowice, 2003, pp. 111-121. 4. , %. ., . ., ! /. ., 1 7. . # * " 3 . // " . 2003, :4, . 12-19. 5. Ashihmin I.V., Furems E.M. Decision Support System for the Best Object Selection with Inconsistency Control. // Abstracts of 58th Meeting of the European Working Group Multiple Criteria Decision Aiding. Moscow, URSS, 2003, pp. 5-6. 6. . . " 3 3 . // . 2004, :2, . 11-16. 7. . ., 1 7. . ##! UniComBOS " 3 " . // 2004, :2, . 243-247. 8. . . ,#! " 3 3 . // * . 0.12, .: 7 +! , 2005, . 7-15. 9. . ., 1 7. . UniComBOS * " 3 . // * . 0.12, .: 7 +! , 2005, . 16-25. 10. . ., 1 7. . ##! UniComBOS " 3 * ) 3 . // 0 * « » (IEEE AIS’05) « #!» (CAD-2005). 0.1, .: 1 , 2005, . 376-381. 11. . ., 1 7. . * " " UniComBOS. // # * « " » ( 0-2005): 0 . 0.1, .: . . " , 2005, . 236-239. 23