뗚35뻭뗚2웚2005쓪3퓂ꆡ뚫쓏듳톧톧놨(ퟔ좻뿆톧냦)JOURNALOFSOUTHEASTUNIVERSITY(NꆡVol135No12aturalScienceEdition)ꆡꆡꆡꆡꆡꆡ좺뻶닟훐믹폚늻춬욫뫃탅쾢뗄쿠뛔벯돉랽램돂뮪폑1,2ꆡꆡ쇵뒺쇖31(쓏뺩듳톧릤돌맜샭톧풺,쓏뺩210093)2(낲믕듳톧쫽톧쾵,뫏럊230039)3(쓏뺩듳톧짌톧풺,쓏뺩210093)햪튪:퇐뺿쇋믹폚늻춬탎쪽욫뫃탅쾢뗄좺뻶닟컊쳢.퓚좺뻶닟훐볒룹뻝룶죋뗄욫뫃,뎣뎣뛔뻶닟랽낸벯룸돶4훖늻춬탎쪽뗄욫뫃탅쾢,냼삨횱뷓랴펳뻶닟랽낸폅쇓듎탲뗄탲맘쾵횵뫍킧폃횵,틔벰2룶뻶닟랽낸돉뛔뇈뷏뮥랴에뛏뻘헳뫍쒣뫽뮥늹에뛏뻘헳.쫗쿈룸돶쇋탲맘쾵횵ꆢ뮥랴에뛏뻘헳뫍쒣뫽뮥늹에뛏뻘헳3훖욫뫃탅쾢뻹뮯캪킧폃횵탎쪽뗄볆쯣릫쪽,좻뫳듓쿠뛔뗄룅쓮돶랢,쳡돶쇋튻훖쿠뛔ퟮ폅뮯뗄벯돉쒣탍,룸돶쇋쒣탍뗄뷢.ퟮ뫳뷸탐쇋2룶쪵샽럖컶,뷡맻뇭쏷쯹쳡돶벯돉랽램쫇폐킧뗄.맘볼듊:좺뻶닟;쿠뛔;욫뫃탅쾢;튻훂뮯;ퟮ폅뮯쒣탍훐춼럖샠뫅:N945125ꆡꆡ컄쿗뇪쪶싫:Aꆡꆡ컄헂뇠뫅:1001-0505(2005)0220311205RelativeentropyaggregationmethodingroupdecisionmakingbasedondifferenttypesofpreferenceinformationC1,2henHuayouꆡꆡLiuC3hunlin1(SchoolofManagementScienceandEngineering,NanjingUniversity,Nanjing210093,China)2(DepartmentofMathematics,AnhuiUniversity,Heifei230039,China)3(BusinessSchool,NanjingUniversity,Nanjing210093,China)Abstract:,whichincludespreferenceorderingandutilityvaluegivingtheordersofalternativesdirectly,,,recipro2caljudgementmatrixandfuzzycomplementaryjudgementmatrix,,:groupdecisionmaking;relativeentropy;preferenceinformation;uniformity;optimalmodelꆡꆡ쯦ퟅ짧믡뗄뷸늽폫뺭볃뗄랢햹,죋쏇뺭뎣폶훐,튻냣튪쟳뻶닟헟룸돶쿠춬훖샠뗄욫뫃탅쾢.떫떽튻킩뫍훚뛠튵쇬폲폐맘뗄훘듳뗄뻶닟컊쳢,틲퓚쪵볊뗄좺뻶닟맽돌훐,평폚쫂컯놾짭뗄쒣뫽탔ꆢ듋탨튪뛠룶볒뷸탐좺쳥뻶닟.퓚좺뻶닟뗄퇐뺿늻좷뚨탔틔벰볒횪쪶뷡릹뫍룶죋욫뫃뗈훷뿍맛틲쯘뗄펰쿬,볒뛔춬튻뻶닟컊쳢뿉쓜룸돶늻춬쫕룥죕웚:2004207221.훖샠뗄욫뫃탅쾢,샽죧탲맘쾵횵(믲돆욫뫃듎탲믹뷰쿮쒿:맺볒ퟔ좻뿆톧믹뷰훺쿮쒿(70101003)ꆢ훐맺늩쪿뫳뿆톧믹뷰훺쿮쒿횵),킧폃횵,뮥랴에뛏뻘헳,쒣뫽뮥늹에뛏뻘헳(2004035209).ퟷ헟볲뷩:돂뮪폑(1969ꆪ),쓐,늩쪿,뷌쫚,huayouc@.뗈.쯦ퟅ믹폚뮥솪췸뗄좺뻶닟횧돖쾵춳뗄랢햹,웈cn.쟐탨튪뷢뻶뻟폐뛠훖욫뫃탅쾢뗄좺뻶닟샭싛[1].
312뚫쓏듳톧톧놨(ퟔ좻뿆톧냦)ꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡ뗚35뻭뷼쓪살,폐맘헢랽쏦뗄뿎쳢퇐뺿틑틽웰쇋훘쫓,늢뛔뇈랽낸kkaj뗄훘튪돌뛈,쟒kbijꇊ[1/9,9],bijbji=좡뗃쇋튻킩퇐뺿돉맻[1ꆫ10].컄쿗[1]퇐뺿쇋좺뻶1;i,j=1,2,ꆭ,n.닟훐뻟폐뮥랴에뛏뻘헳뫍쒣뫽뮥늹에뛏뻘헳2훖4)쒣뫽뮥늹에뛏뻘헳[2]ꆡ퓚쒳튻ힼ퓲쿂뻶탎쪽욫뫃탅쾢뗄뮯랽램.컄쿗[3ꆫ5,7]퇐뺿킧닟헟dk뛔랽낸벯A훐랽낸뷸탐솽솽뇈뷏뗄쒣뫽욫폃횵ꆢ탲맘쾵횵뫍쒣뫽뮥늹에뛏뻘헳뮯캪뮥랴에뫃맘쾵,뿉평튻룶쒣뫽뮥늹에뛏뻘헳kkP=(p)ijnꇁn뛏뻘헳뗄욫뫃탅쾢뗄벯뷡랽램.컄쿗[2,6]퇐뺿킧<AꇁA뇭듯,쿠펦뗄솥쫴몯쫽ꛌPk:AꇁAꇺ[0,폃횵ꆢ탲맘쾵횵뫍뮥랴에뛏뻘헳뮯캪쒣뫽뮥늹에kk1],웤훐ꛌPk(ai,a)j=pij,pij뇭쪾랽낸ai폅폚랽낸뛏뻘헳뗄욫뫃탅쾢뗄벯뷡랽램.컄쿗[8]퇐뺿뛠aj뗄돌뛈k,pijꇝkkk0,pij+pji=1,pii=015;i,j=1,룶뻶닟헟룸돶맘폚Fuzzy에뛏뻘헳뫍AHP에뛏뻘2,ꆭ,n.헳,붨솢쇋쓜릻벯돉헢2샠욫뫃탅쾢뗄ퟮ폅뮯쒣탍.컄쿗[9]룸돶붫늻춬탎쪽뗄욫뫃탅쾢뮯캪쒣2ꆡ늻춬욫뫃탅쾢뗄튻훂뮯랽램뫽에뛏뻘헳탎쪽뗄볆쯣릫쪽,좻뫳믹폚OWA쯣ퟓ떱좺뻶닟훐폐늻춬탎쪽뗄욫뫃탅쾢,튻냣탨튪룸돶벯뷡룷뻶닟헟욫뫃탅쾢뫍랽낸폅톡뗄랽램.쒿붫늻춬훖샠뗄욫뫃탅쾢뚼뮯캪춬튻훖욫뫃탅쾢,잰,폐맘탲맘쾵횵ꆢ뮥랴에뛏뻘헳뫍쒣뫽뮥늹에뛏벴횻폐뷸탐늻춬훖샠뗄욫뫃탅쾢뗄튻훂뮯뫳닅쓜뻘헳쫇럱뿉틔뮯캪킧폃횵뗄욫뫃탅쾢탎쪽벰웤뷸탐좺뗄벯뷡뫍랽낸톡폅,쿂쏦룸돶뮥랴에뛏뻘벯뷡랽램뗄퇐뺿짐캴볻놨뗀.놾컄쫗쿈룸돶뮥랴헳ꆢ쒣뫽뮥늹에뛏뻘헳뫍탲맘쾵횵뮯캪킧폃횵뗄에뛏뻘헳ꆢ쒣뫽뮥늹에뛏뻘헳뫍탲맘쾵횵뮯캪킧랽램.폃횵뗄튻훖랽램,좻뫳듓쿠뛔[11,12]뗄룅쓮돶랢,ꆡ뮥랴에뛏뻘헳뮯캪킧폃횵뗄랽램붨솢쓜릻벯뷡늻춬뗄욫뫃탅쾢튻훂뮯캪킧폃횵뗄뻶닟헟룸돶뛔랽낸벯A훐랽낸뷸탐솽솽뇈뷏좺뻶닟뗄ퟮ폅뮯쒣탍,ퟮ뫳틔쪵샽뇭쏷룃랽램뗄폐뗄뮥랴에뛏뻘헳Bk,뿉내쳘헷룹램[13]볆쯣Bk뗄좨킧탔뫍쪵폃탔.쿲솿W={wk(1),wk(2),ꆭ,wkꚳ(n)},쯼쪵볊짏쫇Bk뗄ퟮ듳쳘헷룹ꛋmax쯹뛔펦뗄맩튻뮯쳘헷쿲1ꆡ4훖욫뫃탅쾢뗄볲떥쏨쫶솿.좨쿲솿쳥쿖쇋뻶닟헟dk내룶죋욫뫃뛔A훐룷짨A={a1,a2,ꆭ,an}캪뻶닟랽낸벯,웤훐ai랽낸훘튪탔돌뛈뗄죏쪶,틲듋뿉틔ퟷ캪룷랽낸뗄킧뇭쪾뗚i룶뻶닟랽낸,i=1,2,ꆭ,n;D={d1,d2,폃횵,벴ꆭk,dm}캪좺쳥뻶닟벯,웤훐dk뇭쪾뗚k룶뻶닟헟,u(i)=wk(i)ꆡꆡi=1,2,ꆭ,n(1)k=1,2,ꆭ,m.죴퓚뺫뛈튪쟳늻룟뗄쳵볾쿂,튲뿉틔내랽룹램볆쯣1)탲맘쾵횵[2]ꆡ뻶닟헟dk룹뻝룶죋뗄욫뫃뮥랴에뛏뻘헳뗄맩튻뮯좨쿲솿,웤볆쯣릫쪽[13]캪횱뷓룸돶뻶닟랽낸벯A뗄듎탲:Okk={o(1),kꇇn1knbijo(2),ꆭk,o(n)},웤훐,Ok쫇{1,2,ꆭ,n}뗄튻룶kj=1u(i)=wk(i)=ꆡꆡi=1,2,ꆭ,n훃뮻k,o(i)뇭쪾뗚i룶뻶닟랽낸ai뗄캻훃듎탲,튻ꇆn냣짨ꇇn1knbijki=1j=1o(i)풽킡,퓲랽낸ai풽폅.2)킧폃횵[2]ꆡ뻶닟헟dk룹뻝룶죋뗄욫뫃룸(2)돶뻶닟랽낸벯A뗄킧폃횵:Ukkk쿔좻평쪽(1)(믲쪽(2))뗄뮯,뮥랴에뛏뻘={u(1),u(2),ꆭ헳뗄욫뫃탅쾢튻훂뮯캪킧폃횵싺ퟣku(i)ꇊ(0,kk,u(n)},웤훐,u(i)뇭쪾뗚i룶뻶닟랽낸ai뗄킧폃횵,튻냣짨ku(i)풽듳,퓲랽낸ai풽폅.틔쿂늻1),ꇆnku(i)=1.럁볙짨뻶닟헟dk룸돶뗄쒳룶뻶닟랽낸킧폃횵싺ퟣi=1럇뢺탔뫍맩튻뮯쳵볾ꆡ쒣뫽뮥늹에뛏뻘헳뮯캪킧폃횵뗄랽램,벴ku(i)ꇊ(0,1),ꇆnkꆡꆡ쒣뫽뮥늹에뛏뻘헳뗄업탲랽램폐뫜뛠,컄쿗u(i)=1,럱퓲,뛔킧폃횵뷸탐맩튻뮯뒦샭벴i=1[10]룅삨뫍움쫶쇋쒣뫽에뛏뻘헳뗄업탲랽램.헢뿉.샯닉폃컄쿗[14]쳡돶뗄쒣뫽뮥늹에뛏뻘헳kP뛔3)뮥랴에뛏뻘헳[13]ꆡ퓚쒳튻ힼ퓲쿂뻶닟헟펦뗄업탲쿲솿뗄튻룶볲뷝볆쯣릫쪽,춬샭뿉냑헢룶dk뛔A훐랽낸뷸탐솽솽뇈뷏,룸돶뮥랴에뛏뻘헳업탲쿲솿W={wk(1),wkꚳ(2),ꆭ,wk(n)}ퟷ캪Bkkk=(b)ijnꇁn,웤훐,bij뇭쪾뻶닟헟dk죏캪랽낸ai룷랽낸뗄킧폃횵,벴
뗚2웚돂뮪폑,뗈:좺뻶닟훐믹폚늻춬욫뫃탅쾢뗄쿠뛔벯돉랽램313ꇆnkn틔폃쿠뛔살뛈솿솽헟뗄럻뫏돌뛈.pij+-1kj=12u(i)=wk(i)=i=1볈좻3훖욫뫃탅쾢튻훂뮯캪킧폃횵뫳,뛔펦뗄,2,ꆭ,nn(n-1)킧폃횵뻹싺ퟣ럇뢺탔뫍맩튻뮯뗄쳵볾,뻍뿉틔붫헢(3)힢틢떽킩킧폃횵ퟷ캪뻶닟헟뛔룷랽낸뗄욫뫃탅쾢움에횵kkkkpijꇝ0,pij+pji=1,pii=015,i,j=1,2,ꆭ,n,틗횤뺭맽쪽(3)뗄뮯,쒣뫽뮥늹에뛏뻘헳뗄룅싊,쎿튻룶뻶닟헟뛔랽낸벯A={a1,a2,ꆭ,뗄욫뫃탅쾢튻훂뮯캪킧폃횵튲싺ퟣakn}훐쯹폐랽낸뗄샫즢룅싊뻍ퟩ돉쯼뗄튻룶룅싊u(i)ꇊ(0,럖늼.볙짨룷뻶닟헟룸돶뗄룅싊럖늼쫇쿠뮥뛀솢.1),ꇆnku(i)=1.짨좺쳥킧폃횵쿲솿캪Ug={u(1),u(2),ꆭ,i=1u(n)},붫웤쫓캪좺쳥욫뫃탅쾢움에횵뗄튻룶룅싊ꆡ탲맘쾵횵뮯캪킧폃횵뗄랽램짨ko(i)캪뻶닟헟dk룸돶뗄뗚럖늼.웤훐u(i)뇭쪾뗚i룶뻶닟랽낸ai뗄좺킧폃i룶뻶닟랽낸ai뗄캻훃듎탲k횵,i=1,2,ꆭ,n.짨W={w1,w2,ꆭ,wm}쫇좺뻶,u(i)캪웤킧폃횵k,o(i)풽킡,뗚i룶랽낸ai풽폅,퓲웤뛔펦뗄킧폃횵k닟벯D={d1,d2,ꆭ,dm}뗄좨훘쿲솿,웤훐wkꇊu(i)풽듳,벴ku(i)캪ko(i)뗄떥뗷쿂붵몯쫽,뿉틔좡ku(i)캪죧[0,1],ꇆmwk=1,wk뇭쪾뻶닟헟dk뗄좨훘,wk풽쿂탎쪽k=1:듳,쳥쿖뗚k룶뻶닟헟풽좨췾,k=1,2,ꆭ,(n+1-o(i))u(i)=ꆡꆡi=1,2,ꆭ,n룹뻝뚨샭1횪,튪쿫믱뗃튻훂뗄좺쳥킧폃횵n(n-1)쿲솿뗄룅싊럖늼,뻍튪ퟮ킡뮯폫쎿튻룶뻶닟헟룸돶(4)힢틢떽탲맘쾵횵kk뗄쯹폐랽낸킧폃횵쿲솿뗄룅싊럖늼뗄쿠뛔,틲듋{o(1),o(2),ꆭk,o(n)}쫇{1,ꆭ,n}뗄튻룶훃뮻,틗횤뺭맽쪽(4)뗄뮯좺뻶닟훐믹폚늻춬욫뫃탅쾢뗄쿠뛔벯돉랽램뿉,탲맘쾵횵뗄욫뫃탅쾢튻훂뮯캪킧폃횵튲싺ퟣku틔뇭쪾돉죧쿂ퟮ폅뮯쒣탍:(i)ꇊkminF(Ug)=(0ꇆmnwu(i)kꇆu(i)logk,1),ꇆnu(i)==1i=1u(i)i=13ꆡ믹폚늻춬욫뫃탅쾢뗄쿠뛔좺뻶ꇆn(7)u(i)==1닟벯뷡ퟮ폅뮯쒣탍u(i)>0ꆡꆡi=1,2,ꆭ,nꆡꆡ좺뻶닟컊쳢놾훊짏쫇튻룶벯뷡컊쳢[12]쪽훐k,u(i)뇭쪾뻶닟헟dk뛔뗚i룶뻶닟랽낸ai룸.캪쇋믱뗃튻훂뗄좺쳥뻶닟쒿뇪,뻍쫇튪ퟮ킡뮯좺뻶닟뷡돶뗄욫뫃탅쾢튻훂뮯뫳뗄킧폃횵;u(i)뇭쪾뗚i룶맻폫룶죋욫뫃탅쾢뗄늻튻훂뗄뿉쓜탔.퓚튻뚨뗄쳵뻶닟랽낸a뗄좺킧폃횵.뛔폚쪽(7)좷뚨뗄ퟮ폅뮯i볾쿂뿉틔뮯캪튻룶폅뮯컊쳢.뛸폅뮯샭싛헽뫃쒣탍폐죧쿂쇐뷡싛:쳡릩쇋튻훖뷏뫃뗄럖컶쫖뛎,캪듋틽뷸샫즢탎쪽뗄뚨샭2ꆡ쪽(7)좷뚨뗄ퟮ폅뮯쒣탍폐좫뻖ퟮ쿠뛔샫뚨틥벰탔훊폅뷢U333g={u(1),u(2),ꆭ3,u(n)},웤훐.뚨틥[11,12]1ꆡ짨xi,yiꇝ0,i=1,2,ꆭ,n.쟒ꇇmkwk(u(i))3k=11=ꇆnxu(i)=i=1,2,ꆭ,n(8ꇇm)iꇝꇆnxiyi,퓲돆h(X,Y)=ꇆnxilog캪i=1i=1i=1yiꇆnkwk(u(i))X쿠뛔폚Y뗄쿠뛔i=1k=1,웤훐X={x1,x2,ꆭ,xn},Y뚨샭2뗄횤쏷샠쯆폚컄쿗[11]훐뷡싛뗄횤쏷,맊={y1,y2,ꆭ,yn}.뚨샭[11,12]1ꆡ죴h(X,Y)캪X쿠뛔폚Y뗄쿠듓싔.뛔뚨샭2룸돶쇋ퟮ폅좺쳥킧폃횵쿲솿뗄볆쯣릫,퓲폐쪽.룹뻝뚨샭2,뿉틔뗃떽좺뻶닟훐믹폚늻춬욫뫃xh(X,Yi)=ꇆnxilogꇝ0(5)탅쾢뗄쿠뛔랽램볆쯣늽훨:ꋙ평쪽(1)ꆢ(3)ꆢi=1yiꇆnx(4)(믲쪽(2)ꆢ(3)ꆢ(4))붫뮥랴에뛏뻘헳ꆢ쒣뫽ixlog=0(6)i뮥늹에뛏뻘헳뫍탲맘쾵횵뗄욫뫃탅쾢뮯캪럇뢺i=1yi떱쟒뷶떱xi=yi;i=1,2,ꆭ,n.탔뫍맩튻뮯뗄킧폃횵뗄욫뫃탅쾢;ꋚ룹뻝뚨샭2뚨샭1뇭쏷떱2룶샫즢룅싊럖늼X뫍Y췪좫쿠뗄쪽(8)볆쯣ퟮ폅뮯쒣탍뗄좫뻖ퟮ폅뷢U3g=뗈쪱33,X쿠뛔폚Y뗄쿠뛔듯떽쇋ퟮ킡횵,틲듋뿉{u(1),u(2),ꆭ3,u(n)};ꋛ룹뻝볆쯣돶뗄ퟮ
314뚫쓏듳톧톧놨(ퟔ좻뿆톧냦)ꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡ뗚35뻭폅좺쳥킧폃횵쿲솿U33g훐u(i)뗄듳킡뛔뻶닟랽샽[6]2ꆡ쒳튻뻶닟컊쳢뗄랽낸벯A={a1,a2,낸벯A뷸탐업탲,듓뛸믱뗃ퟮ병뻶닟랽낸.a3,a4},좺쳥뻶닟벯D={d1,d2,d3,d4},볙짨뻶닟헟뗄좨훘쿲솿W={w1,w2,w3,wꚳ4}={012,4ꆡ쪵샽럖컶ꚳ011,014,013},4캻뻶닟헟럖뇰뛔4훖랽낸룸돶캪쇋랴펳놾컄쳡돶뗄쒣탍뗄폐킧탔,놾컄펦폃탲맘쾵횵ꆢ킧폃횵ꆢ쒣뫽뮥늹에뛏뻘헳ꆢ뮥랴에뛏뻘컄쿗[5,6]뗄쫽뻝뷸탐쪵샽럖컶.헳4훖늻춬탎쪽뗄욫뫃탅쾢,벴샽[5]1ꆡ뛔폚쒳튻뻶닟컊쳢,볙짨뻶닟랽낸벯d1:O1={2,1,4,3}A={a1,a2,a3,a4},뻶닟좺쳥벯캪D={d1,d2,d2:U2={014,015,018,016}d01501201413,d4},늻럁볙뚨뻶닟헟뗄좨훘뚼쿠뗈,벴w1=w2=w3=w4=1/캻뻶닟헟럖뇰뛔4훖랽낸룸돶3018015018016탲맘쾵횵ꆢ킧폃횵ꆢ쒣뫽뮥늹에뛏뻘헳ꆢ뮥랴에뛏뻘d3:P=016012015017헳4훖늻춬탎쪽뗄욫뫃탅쾢,벴0014013015d11/8371:O1={3,1,4,2}d2:U2={015,017,019,011}8164B4d4:=0150110160171/31/6151/71/41/513019015018014d3:P=014012015019틀좻내헕3룶늽훨,쫗쿈붫늻춬욫뫃탅쾢튻훂뮯캪013016011015럇뢺탔뫍맩튻뮯뗄킧폃횵쿲솿,벴11U1={013,014,011,012}/9379181/2U2={011739,012174,013478,012609}d4:B4=U3={012583,013083,012500,011833}1/31/819U4={012117,016192,011208,010484}1/721/91웤듎평쪽(8)볆쯣ퟮ폅뮯쒣탍뗄좫뻖ퟮ폅뷢뗃1)쿈붫늻춬욫뫃탅쾢튻훂뮯캪럇뢺뫍맩튻뮯33뗄킧폃횵쿲솿.평쪽u(1)=012591,u(2)=014156(4)붫뗚1캻뻶닟헟d1룸돶뗄33탲맘쾵횵뮯캪킧폃횵,볆쯣뗃u(3)=011859,u(4)=011393ퟮ뫳룹뻝볆쯣돶뗄ퟮ폅좺쳥킧폃횵뗄듳킡뛔뻶닟U1={012,014,011,013}뛔뗚2캻뻶닟헟d2룸돶뗄킧폃횵뷸탐맩튻뮯뒦샭랽낸벯A뷸탐업탲뗃죧쿂뷡맻:,캪쇋춳튻볇뫅,맩튻뮯뫳뗄킧폃횵죔볇캪a2:a1:a3:a4U2,퓲폐뿉볻ퟮ병뻶닟랽낸캪a2.샽1뫍샽2뗄ퟮ병뻶닟랽낸볆쯣뷡맻뫍컄쿗U2={012273,013182,014091,010455}평쪽(3)붫뗚3캻뻶닟헟d3룸돶뗄쒣뫽뮥늹[5,6]쫇쿠춬뗄,틲뛸뇭쏷놾컄쳡돶뗄쒣탍뗄폐킧에뛏뻘헳뮯캪룷랽낸킧폃횵탔.,볆쯣뗃U3={012417,013000,012500,012083}5ꆡ뷡ꆡ폯평쪽(2)붫뗚4캻뻶닟헟d4룸돶뗄뮥랴에뛏뻘헳뮯캪룷랽낸킧폃횵,볆쯣뗃듓쪵샽뿉틔뾴돶,놾컄뒦샭늻춬탎쪽욫뫃탅쾢뗄좺뻶닟랽램뗄쳘뗣냼삨2룶랽쏦:ꋙ룸돶쇋늻춬U4={012527,015009,011600,010863}욫뫃탅쾢뗄튻훂뮯캪킧폃횵뗄볲떥랽램;ꋚ듓쿠2)붫1)훐볆쯣돶뗄튻훂뮯뫳킧폃횵듺죫쪽뛔뗄룅쓮돶랢,붨솢벯뷡늻춬뗄욫뫃탅쾢튻훂뮯(8),볆쯣돶ퟮ폅뮯쒣탍뗄좫뻖ퟮ폅뷢U3g,벴캪킧폃횵뗄좺뻶닟뗄ퟮ폅뮯쒣탍,늢룸돶쇋ퟮ폅뮯33u(1)=012474,u(2)=014009쒣탍뷢뗄뷢컶쪽,듓뛸랽뇣볆쯣.뛸컄쿗[7]횸돶33u(3)=012168,u(4)=011349냑늻춬탎쪽욫뫃탅쾢뮯캪킧폃횵쫇늻랽뇣뗄,3)룹뻝볆쯣돶뗄ퟮ폅좺쳥킧폃횵3u(1),틲듋뿉틔쮵놾컄뗄퇐뺿뷸튻늽췪짆쇋믹폚늻춬탎333u(2),u(3),u(4)뗄듳킡뛔뻶닟랽낸벯A뷸쪽욫뫃탅쾢뗄좺뻶닟랽램.탐업탲뗃죧쿂뷡맻:a닎뾼컄쿗(References)2:a1:a3:a4틲듋ퟮ병뻶닟랽낸캪a2.[1]키쯄몺,랮훎욽,췵쏎맢.좺뻶닟훐솽샠욫뫃탅
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