关于均衡度与变权的注记_鲁风菊

2002 M1238 6 =Sv(1 S)Jo urnal o f Beijing N or mal U niv er sity ( N atura l Science)Dec. 2002V ol. 38 N o. 61 (M :*鲁风菊1, 2) 谷云东1)( 1) =Sv “, 100875,; 2) =S “, 471022, 2, BT37 , o, =)K1 YVB L (li),N1 (lZ; HgsT . (sW1“ Y,i O) (/.+Y,4 Y % ( z T ( zf Q,y y %F- (8 , HB + y M .1oM 8 %;M ; (;s;F - (8s | O 159*SE1 S “( 69974006, 60174013)l : 2002-05-200 L= 3,vs %5 “S %. % 5F 8 :Mm (x1 ,x2, ,xm ) mj= 1wjxj , ( 1)wj 0, 1( j= 1, 2, ,m) Omj= 1wj = 11-2 .y wj ,# 8“ ”8. W= (w1 ,w2, ,wm ) ,5W“ ”_ . “ ”Q y %M1,yN f / B 7$ b(Y ) , “ ” z,8C ( z1“.5bX (.l51 T dXn Rn 0, 1 740 =Sv(1 S)38 1)d( X )= d(Y ) , Y XB , y1y2y3yn;2)X0 H, d(x , ,x )= 0;3)X0 H, d(x1, , xn )1xj , j 1, 2, ,n;4)d( x1 , ,xn ) nj= 1xj9F7h , d(x1 , , xn ) nj= 1xj9F79F;5)X Y H,d( X ) M(X 2 ).Z1Z2, L= f M. 2 F -8 r X “ ”8 . I n %y M1,7 O ?v$ % ( z TY.3 L= ,F - (8 H B“M ”/ZE. n5 ( (f /B“ y0”; , F 8 _ ,iN Q % ( z %Y. “ y0” “S_ f | | % “S_ .yN, 9 B“ ”“M ”. X“ ” Z , D5-6 ZE “M ” r.“M ”9D54“M ” :M _ W (X ) y _ W M _ SXHarda rmard. Y L , / . 4 !b(X ) 3? (, g(x ) 0, ) 9f Og( 0) = 0,5 SX 0, 1m 0,)m , Sj ( X )= g(b( X ) ) (j= 1, 2, ,m); M , M . !SX ( X )= ( g(b( X ) ) ) 1m ? ,5 (l#5 ! V,l2s1) s3)A .7 i T( 2) _ W ,v T( 3)_ , ,yN9 V AT .4 M ; , M W (X )=SX (X ) W= (g(b(X ) ) w1 , , g(b(X ) ) wm )i 、 M . Y L , ,BBY ? ; . (f # M 8 J.“d Ll, 1997, 17( 4): 58 8 , . M 8“ (f / J.“d Ll, 1999, 19( 7): 116 9 -g, . M 8“ J.“d Ll, 2000, 20( 1): 106743 6 Z :1 (M : 10 Li Hong xing . M ultifa ctorial functions in fuzzy sets theo ry J. Fuzzy Sets and Sy stems, 1990, 35: 69 11 Li Ho ng xing . Facto r spaces theo ry a nd its applica tions to fuzzy info rmation pro cessing ( ) J. FuzzySets and Sy stems, 1998, 95( 2): 145 12 Li Ho ngx ing , Ye n V C, Lee E S. Fac tor space theo ry in fuzzy info rma tio n pro cessing: Composition ofstates of facto rs a nd m ultifac to rial decisio n making J. Com puter s and M a th ema tics w ith Applicatio n,2000, 39: 245 13 Li Hong xing . Fuzzy clustering methods based o n per turbatio n J. F SS, 1989, 32( 3): 291 14 Li Hongx ing . M ultifac to rial fuzzy sets and multifacto ria l deg r ee of nearess J. FSS, 1986, 19( 3): 291 15 Li Hongx ing , Li D X u. Featur e space th eor y a mathema tical fo undatio n fo r data mining J. Kno wl-edg e-Based Sy stems, 2001, 14: 253 16 .V e A J. “d , 1995, 9( 4): 1 17 . Yen V C.y bW % J. =Sv(1 S) , 1994, 30( 1): 41 18 .y bW MV U O( ) J. =Sv(1 S) , 1996, 32( 4):470 19 .y bW MV U O( ) J. =Sv(1 S) , 1997, 33( 2):151 20 , . l “ J. =Sv(1 S) , 1993, 29( 1): 1 21 , . Fuzzy9 !9 X J. =Sv(1 S) , 1995, 31( 2): 189 22 , . Fuzzy9 !9 X( ) J. =Sv(1 S) , 1995, 31( 3): 303 23 , . Fuzzy9 !9 X( ) J. =Sv(1 S) , 1995, 31( 3): 308 24 , . Fuzzy9 !9 X( ) J. =Sv(1 S) , 1995, 31( 4): 434NOTES ON BALANCE DEGREE AND VARIABLE WEIGHTLu Feng ju1, 2) Gu Yundong1)( 1) Department of M ath ematics , Beijing Normal Univ ersity, Beijing, 100875, Beijing, China;2) Department of M ath ematics, Luoyang Teach ers College, 471022, Luoyang, Henan , China)Abstract Some imperfect aspects in the definitio n o f balance deg ree introduced in theliterature are ex plained. New definitions of balance deg ree and difference deg ree are giv en.The relatio ns among them and the co nstructio n of balance degree are studied. A new kind ofm ultifactor decisio n-making m odel w eig hted-balance synthesis is intro duced. A sp