一种群体评价一致性合成方法

2000 M 7 “ d L l 7 c I | : 1000-6788(2000) 07-0052-06B 8 N B Z E赵海燕, 曹 健, 张友良( 2 v CIMS , 2 210094)K 1 : s Y 8 N T y , V r N i n $ ,4 8 N B V E ,s Z E + . L V Z E ? z 8 8 i n , Q 8 N 8 I n y .1 o M : 8 N ; B ; N m s | :N94nullAn Aggregating Method of Group EvaluationBased on Consensus DegreeZHAO Hai-yan, CAO Jian, ZHANG You-liang(CIMS Institute, Nanjing University of Science consensus degree; weight of evaluation1 C 5 T , 1 % H , 1 “ E i n , S % , 8 N . 7 , E M , B (Z a 5 ) V ? i % . y N , 8 N pB N 8 N 1 o 5 .K 8 N Z E F p E , | E N E F p 8 8 N . I n E N N T Y , I n E W N B Y , ? N T . D 1 y % 5 , B N “ l 9 N B ,Y V x , B E N ,K y 8 8 N . “ v i n , I n E N B . Z E E 7 8 8 N T Y . D 2Y V E N M E N B , | E B L T E N ,i N $ E N F 8 N T . HI n E E N B N T Y . 7 , B ? 7 ) . L = , v E W N B 1 l E N B null l : 1998-12-04 T v Y . B E , T N E N B l E N B M , * , - B 1 B T v Y . X , V U N $ 4 B | B Z E , P K N T .2 8 N B Z E N 4 a , % N V ? B M L m, m P V U , B ( l, m, r), l P ,r , Z L , N N F u Y . 6 , . (Z a 5 ) 8 N 5 , V E, W, R, f , ! E= Ei null i= 1,l,n N E “ ,W= Winulli= 1,l,n N E “ ,R= Ri nulli= 1,l,n E N “ . B Z E / B f f , P E N R i(i= 1,l,n)7 8 B N R.2.1 N ) C I n m 1(a) U f , T R1= ( 1, 2, 3) ,R2= ( 5, 6, 7), N “ , e M F | ( Z E 8 N ( , T 4 $ E s , T , E f , ? E N null “ H , m 1(b) U , N T r . i Ri Rj null “ ,5 E 1 | + Z E DelphiZ E 3 N , P H q .a) E N “ b) E N null / m 1 E N M f 2.2 8 N B E N 8 N T Y . ) Y y ,i M 1 l .2.2. 1 Y N , / N E , , E 5 5 ,5 v ,M , N T Y 1 l E v . E i : Wi.2.2. 2 N B Yn 5 l M . l 2.1 ! Ri= ( li, mi, ri) , Rj = (lj , mj , rj ) ,5 S(R i, Rj ) =xmin(Ri(x) , Rj (x )xmax( Ri(x ), Rj (x) ) ( 1) M .A , M “ s i “ s 1 , m 2 U . E N V V r ,y N / l: l 2. 2 ! E Ei Ej N s Y R i= (li, mi, ri) , Rj = ( lj, mj,53 7 B 8 N B Z Em 2 M rj) , l E N W B S ij R i R j M , Sij = S(Ri, Rj ). B E N E N B , / l: l 2. 3B E Ei N E N B l E ( B S i, 9 Z E / T U :S i = 1n - 1 nullnj= 1, jiSij (2) L 1 , | ( B B B ,V 7 E M B , l / : l 2.4| E ( B B B V E M B , E i N M B S ri T / :Sri = S i nullni= 1Si ( 3) E Ei N M B Q E N B , v N ? V v i n . “ i n , 8 B 8 N T , I n E M B Y .2.2. 3 E N B 8 Y v E B f / N 1 , N F y , 8 B Q N , v E i n A d ,y 7 1 8 I n 8 N i n Y .m 3 B N T 8 YL ! E N V , , W1=W4,W2 W 3. E N m 3 U ,L E w L B “ . C In E E 1 E E4 N N T Y . m V , E E1 N E N M E E4 E NM M , M B l V E E 1 E E4 M M B , E E1 M B 1 v E E 2 N M ,7 E E4M B 1 l E E3 N M . B f / v E N 1 B t , E E 1 M B 1 E 3 M B o N p,y N , K 8 N T ,E1 N Y 1 E4 N Y v Q . r T E N B T / . E N T , M F B Q . l 2.5 ! S ij E Ei Ej B ,W j E E j (j = 1, 2,l,n).5 E Ei ( F B Ii :Ii = 1n - 1 nullnj= 1,jiW jS ij ( 4) l 2.6Ii E E i ( F B ,| ( F B B B E E i M F B Iri.Iri = Ii nullni= 1I i ( 5) T E M F B v , v E N B ,y N , N 8 N54 “ d L l 2000 M 7 T v Y . 8 C v E W N B 1 l E N B T Y v .2.2. 4 N Y V s V , E N 8 N T Y v l E a E M B E M F B 1 . B 7 , - Y v B Y . y N . | E N , T / :Ci = null1W i + null2S ri + null3Iri ( 6) null1+ null2+ null3= 1, null1 null3, null2 null3 ( 6) “ | , I n T 7 I n E N B Y ,5 null1= 1,null2= null3= 0. I n E N B Y ,5 null2= 1,null1= null3= 0. null2, null1.Ci / : 2.1nullni= 1Ci = 1 nullni= 1Ci= nullni= 1(nullW i + null2S ri + null3Iri)= nullnullni= 1Wi + null2nullni= 1Sri + null3nullni= 1Iri = null1 + null2 + null3 = 1 82.3 8 N B Ci Q N E E i N Ri Y 8 8 N T y ,Ci v , Ri T Y v . y N , | E N E N V 8 N T , T / :R = nullni= 1CiRi ( 7)3 8 N B Z E D 44 8 N Z E r B t 5 ,/ V t 5 ? I Z E . 3.1B = : T 8 i E Ei Ej, Ri= Rj , * R= Ri. , T N E N M , * 8 N E N M . :R= nullni= i= 1Ci* Ri = Rinullni= 1Ci= R inull (null1W i + null2S i + null3Ii)= R i null1nullni= 1Wi + null2nullni= 1Si + null3nullni= 1Ii nullni= 1W i = 1, nullni= 1S i = 1, nullni= 1Ii = 15 R= Ri(null1+ null2+ null3) = Ri 3.2 E N “ A R , :ni= 1RnullinullR L E N i null(0,1) “ ni= 1Rnulli55 7 B 8 N B Z Eni= 1Rnulli = ni= 1Rnulli(anulli, bnulli) = ( maxni= 1(anulli) , minni= 1( bnulli) )R null= nullni= 1Ci R nulli = nullni= 1Ci anulli, nullni= 1Ci bnulliminni= 1( anulli) nullni= 1Ci bnulli maxni= 1(bnulli) , minni= 1( bnulli) nullni= 1Ci bnulli maxni= 1(bnulli)ni= 1Rnulli null R 8 3.3 T E N Ri H ( Ri) l , T ( 8) U ,H ( Ri) =+ - Ri(x) dx ( 8)5 minni= 1( H (R i) H (R) maxni= 1(H (Ri) ) H (R) = H nullni= 1Ci Ri = nullni= 1H (Ci Ri) = nullni= 1(Ci H (Ri) ) minni= 1H (Ri) ) H (Ri) maxni= 1H (Ri) minni= 1H (Ri)cnullni= 1Ci H (R) maxni= 1H (R i)cnullni= 1Ci# minni= 1H (Ri) ) H (R) maxni= 1H (Ri) 3.4 A , N T E N F . , T (1),( 2),l,( n) 1, 2,l,n M , * R= f ( R1,R 2,l, R n)= f (R( 1), R( 2),l,R( n).4 0C L ! N E E 1,E2, E3, N s Y R1= (1,2,3), R2= ( 1. 5, 2. 5, 3. 5) ,R 3=( 2,3,4), m 4(a) . ! null 0.2, V _ , V N .C s f s :1) I n E , null2= 1,null1= null3= 0. T ( 1) V 9 i E N M / :(S ij =1 0.391 0.1420. 391 1 0.3910. 142 0.391 1 T ( 2)a( 3) V E M B , ! S r M B _ :S r =Sr1Sr2Sr3=0.2880.4240.288 I n E , T ( 6) V E N E B , ! C N _ , :C =S1S2S3= Sr =0. 2880. 4240. 288 V n , I n N ,7 E1 E3 N M M ,# C1= C3, E 1 N 8 N T Y E 3 M . T ( 7) 8 N R( 1) = null3i= 1Ci Ri = (1.5, 2.5, 3.5)2) I n E 56 “ d L l 2000 M 7 ! null1= 0.6,null2= 0.3,null3= 0.1, W 1= 0. 5, W 2= 0.3, W3= 0.2Y V T ( 1)j(7) 9 V M B _ S raF M B _ Ira E N _ C 8 N T R (2) / :Sr =Sr1Sr2Sr3=0. 2880. 4240. 288I r =Ir1Ir2Ir3=0. 2400. 4500. 310c= (null1null2null3) W1 W 2 W3S r1 Sr2 S r3Ir1 Ir2 Ir3= (0.4100.3500. 240)R( 2) = null3i= 1(ci Ri) = ( 1. 4152.4153.415) f N T m 4(b) U . f 2 f 1M 1 ,8 N T _ N E1 M , L = f B ,y I n E1 1 v , T Y 9 3 v Y .a) E N b) 8 N Tm 4 E 8 N L 5 4 B 8 N Z E . V r N z C L , N $ ,Y V N s , N V aB Y B 8 Y s F , H 9 N Z E . Z E ? 8 I n Y N y ,y 7 8 N i n ; ? Q i n ? 8 C E . H ,Y V 8 N Z E B = a . L V , E ? Q L = f . I D : 1 . x % # ? 9 “ d ! 9 J. 9 ,1995, 6( 5) :59j63. 2Hsi- Mei Hsu et al. Aggregation of Fuzzy Options