ꆡ1998쓪12퓂쾵춳릤돌샭싛폫쪵볹뗚12웚ꆡ늻좷뚨탔뻶닟훐췪좫탅쾢믱뗃뗄쫂잰럖컶α헔뫣럥ꆡ쟱?뮪ꆡ몫샶쏴(놱뺩몽뿕몽쳬듳톧맜샭톧풺,놱뺩100083)햪튪ꆡ쏷좷쇋맦랶뻶닟럖컶훐탅쾢뗄룅쓮,뷩짜쇋탅쾢믱뗃폫럱뗄볛횵에뛏램ꆣ좻뫳훷튪헫뛔늻좷뚨탔뻶닟췪좫탅쾢믱뗃뗄쫂잰럖컶뷸탐쇋쳖싛,룸돶쇋떥ힴ첬췪좫탅쾢믱뗃뗄룅쓮뫍튻룶쪵볊럖컶샽ퟓ;춬쪱뛔췪좫탅쾢폫럧쿕첬뛈뗄맘쾵뷸탐쇋볲떥뗄럖컶ꆣ맘볼듊ꆡ췪좫탅쾢믱뗃ꆡ떥ힴ첬췪좫탅쾢믱뗃ꆡ늻좷뚨탔뻶닟Theex2anteAnalysisofPerfectInformationAcquiringinDecisionMakingunderUncertaintyZhaoHengfengꆡQiuWanhuaꆡHanLimin(SchoolofManagement,BeijingUniversityofAeronauticsandAstronautics,Beijing100083)Abstractꆡꆡperfectinformation;perfectinformationofsingle2state;decisionmakingunderuncertainty1ꆡ틽퇔뻶닟쫇틔탅쾢캪믹뒡뗄,퓚맦랶뻶닟럖컶훐,뻶닟탅쾢튻냣횸ힴ첬뿕볤뗄룅싊탅쾢,뛸뻶닟탅쾢볛횵뗄퇐뺿튲훷튪뻖쿞폚놴튶쮹뻶닟컊쳢훐,춨맽웚췻탅쾢볛횵EVSI(ExpectedValueofSamplingInforma2tion)뫍뺻웚췻탅쾢쫕틦ENGSI(ExpectedNetGainfromSamplingInformation)살에뇰탅쾢쫇럱믱뗃,떫쫇헢튻랽램횻쓜뛔탅쾢믱뗃뷸탐쫂뫳럖컶,늻쓜뛔탅쾢뷸탐쫂잰럖컶ꆣ쿂쏦컒쏇뻍늻좷뚨뻶닟훐뗄췪좫탅쾢믱뗃뷸탐쫂잰럖컶ꆣ2ꆡ뻶닟폫탅쾢뗄믹놾룅쓮ꆡ뻶닟럖컶뗄튻냣쒣탍맦랶뻶닟컊쳢평ힴ첬뿕볤(ꆢ탐뚯뿕볤A뫍횧뢶뿕볤Xퟩ돉,벴뻶닟컊쳢G={(,A,X},웤훐A={a1,a2,...,am},평m룶탐뚯ퟩ돉,(={Η1,Η2,ꆭ,Ηn}평n룶ힴ첬ퟩ돉,횧뢶뿕볤X=(xij)mꇁn,xij평aiꇊA뫍Ηjꇊ(뻶뚨,떱xij>0쪱뇭쪾쫕틦,xij<0뇭쪾쯰쪧ꆣ뻶닟컊쳢뗄뻘헳뇭쪾죧뇭1쯹쪾ꆣ죴뻶닟헟뛔ힴ첬뿕볤(뗄탅쾢췪좫쇋뷢,돆캪좷뚨탍뻶닟컊쳢;뛔(뗄탅쾢늿럖쇋뷢,돆캪럧쿕탍뻶α놾컄폚1997쓪7퓂2죕쫕떽' 1994-2009 China Academic Journal Electronic Publishing House. All rights reserved.
뗚12웚늻좷뚨탔뻶닟훐췪좫탅쾢믱뗃뗄쫂잰럖컶21닟컊쳢;뛔(뗄탅쾢쎻폐쇋뷢,돆캪늻좷뚨탍뻶닟ꆣ헢퇹뚨틥늻쫇쪮럖쏷좷,쿂쏦컒쏇붫폃탅쾢뗄룅쓮뛔뻶닟샠탍뷸탐뺫좷뗄쏨쫶ꆣꆡ뻶닟훐탅쾢뗄믹놾룅쓮뇭1ꆡ맦랶뻶닟뻘헳탅쾢뗄룅쓮튪뇈죋쏇웕뇩죏캪뗄뢴퓓뗄뛠,퓚늻춬뗄쇬폲(웤몬틥늻춬ꆣ퓚맦랶뻶닟럖컶훐뗄탅쾢쫇횸맘폚ힴ첬뿕볤뗄탅Η1Η2ꆭΗjꆭΗn쾢A,벴뛔폚ힴ첬뿕볤룅싊뗄탅쾢ꆣ뚨틥1ꆡ뛔뇭1쯹쪾뗄맦랶뻶닟컊쳢,죧맻뻶닟헟ힼ좷횪뗀a1x11x12ꆭx1jꆭx1n쓇튻룶ힴ첬랢짺퓲돆탅쾢쫇췪좫뗄믲췪쏀뗄;죧맻뻶닟헟횪뗀a2x21x22ꆭx2jꆭx2nힴ첬뿕볤뗄룅싊럖늼퓲돆탅쾢쫇췪헻뗄,죧맻뻶닟헟늻횪뗀룅싊럖늼떫횪뗀튻킩맘폚럖늼뗄탅쾢퓲돆탅쾢쫇늻췪헻뗄;죧맻amxm1xm2ꆭxmjꆭxmn뻶닟헟뛔ힴ첬뗄탅쾢튻뗣뚼늻횪뗀퓲돆탅쾢쫇캴횪뗄ꆣ퓚뻶닟럖컶훐췪쏀탅쾢(perfectinformation)뫍췪좫탅쾢(completeinformation)쎻폐퇏룱뗄쟸뇰,떫퓚늩?싛훐헢솽룶룅쓮뗄틢틥쫇늻춬뗄[5],놾컄뛔헢솽룶룅쓮뗈춬쪹폃;췪헻탅쾢뗄룅쓮퓚컄쿗[4]훐폐쿪쾸뗄뷩짜,웤훐펢컄뇭듯폃뗄튲쫇ꆰcompleteinformationꆱ,늻췪헻탅쾢펢컄폃ꆰincompleteinformationꆱ뇭듯ꆣ놾컄폃ꆰperfectinformationꆱ뇭쪾췪쏀탅쾢뫍췪좫탅쾢ꆣ듓뻶닟탅쾢뗄뷇뛈퇏룱뚨틥뗄뻶닟샠탍죧쿂:퓚맦랶뻶닟럖컶훐,떱뻶닟헟펵폐췪좫탅쾢쪱돆캪좷뚨탔뻶닟;떱뻶닟헟펵폐췪헻탅쾢믲늻췪헻탅쾢쪱돆캪럧쿕뻶닟;떱뻶닟헟뛔ힴ첬탅쾢튻컞쯹횪쪱쫇늻좷뚨탔뻶닟ꆣ3ꆡ췪좫탅쾢믱뗃뗄에뇰ꆡ탅쾢믱뗃뗄볛횵럖컶에뇰램퓚뻶닟럖컶훐튻룶훘튪뗄컊쳢쫇뛔폚믱좡탅쾢폫럱뗄에뛏:떱뻶닟헟춨맽횧뢶돉놾뛸뿉틔믱뗃탂뗄뻶닟탅쾢쪱,죧뫎에뛏쫇럱횵뗃믱뗃탅쾢?퓚춳볆뻶닟샭싛훐뛔헢튻컊쳢뗄뻶닟랽램훷튪쫇:춨맽볆쯣믱뗃탅쾢잰폫믱뗃탅쾢뫳뗄쫕틦뇈뷏볆쯣탅쾢볛횵,떱탅쾢돉놾듳폚0쪱,퓙볆쯣탅쾢믱뗃뗄뺻쫕틦,뻶뚨쫇럱믱뗃탅쾢(Gregory(1988),ꆫ180)ꆣ뛔폚췪좫탅쾢뗄믱뗃폫럱뗄에뇰튲폃헢튻랽램,웤룹뻝쫇탅쾢믱뗃잰늢늻횪뗀뻟쳥쓄튻룶ힴ첬랢짺,틲듋탅쾢믱뗃잰뗄뻶닟컊쳢뗄탔훊늻뇤,럧쿕뻶닟죔좻쫇럧쿕뻶닟,횻쫇퓶볓쇋튻룶믱뗃췪좫탅쾢뗄탐뚯a0,죧뇭2쯹쪾ꆣ헢쪱뻶닟죔탨춨맽웚췻쫕틦ힼ퓲살뻶닟ꆣ뛔폚럧쿕탍뻶닟컊쳢,쎻폐췪뇭2ꆡ췪좫탅쾢쾵춳뗄좫ힴ첬탅쾢믱뗃탐캪뗄뻶닟컊쳢좫탅쾢쪱,내헕웚췻횵램퓲,ퟮ폅탐(뚯뗄웚췻쫕틦(expectedvalue)캪Η1Η2ꆭΗjꆭΗnnAEVmax=max6pjxij(1)ij=1뛸좡뗃췪좫탅쾢뫳뗄웚췻쫕틦a0maxxi1maxxi2ꆭmaxxijꆭmaxxiniiiiEVUC(expectedvalueundercer2a1x11x12ꆭx1jꆭx1ntainty)캪a2x21x22ꆭx2jꆭx2nnEVUC=6pjmaxxij(2)ij=1틲듋췪좫탅쾢웚췻쫕틦EVPI(ex2amxm1xm2ꆭxmjꆭxmnpectedvalueofperfectinformation)캪nnEVPI=EVmax-EVUC=6pjmaxxij-max6pjxij(3)iij=1j=1EVPI뗄쇭튻훖볆쯣랽램쫇샻폃믺믡돉놾,룹뻝짏쏦EVPI뗄뚨틥' 1994-2009 China Academic Journal Electronic Publishing House. All rights reserved.
22쾵춳릤돌샭싛폫쪵볹1998쓪12퓂nnnnEVPI=6pjmaxxij-max6pjxij=min6pj(maxxij-pjxij)=min6pjsij(4)iiij=1j=1j=1j=1웤훐sij=(maxxij-pjxij)뇭쪾뻶닟헟쎻폐닉좡ퟮ폅탐뚯뗄믺믡돉놾ꆣi춨맽EVPI에뛏탅쾢쫇럱믱뗃,죴탅쾢믱뗃뗄돉놾룟폚EVPI,퓲쎻뇘튪뷸탐췪좫탅쾢믱뗃,뛔폚늻좷뚨탔뻶닟,뿉틔폃쿠춬뗄랽램럖컶,횻쫇뻶닟ힼ퓲늻춬,헢샯늻퓙쿪쫶ꆣ탅쾢볛횵램횻쓜폃폚탅쾢믱뗃뗄쫂뫳럖컶,벴퓚뗃떽쇋탅쾢뫳럖컶웤볛횵,뛸쟒퓚럖컶늻좷뚨탔뻶닟뗄췪좫탅쾢믱뗃쪱튲폫쪵볊뻶닟탐캪늻튻훂:틲캪췪좫탅쾢믱뗃룄뇤쇋뻶닟헟뗄탐캪,벴쪹EVPI<0,떫떱뻶닟헟횪뗀쇋ힴ첬Ηi랢짺,쯻뮹믡톡퓱(öΗi쯹뻶뚨뗄탐뚯싰?샭탔뗄뻶닟헟쿔좻늻믡뗄ꆣ쿂쏦훷튪뻍늻좷뚨탔뻶닟뷸탐췪좫탅쾢믱뗃뗄쫂잰쳖싛ꆣꆡ췪좫탅쾢쫂잰믱뗃뗄튻냣쳘탔뚨샭1ꆡa)뿉틔믱뗃췪좫탅쾢뗄맦랶뻶닟뗄럧쿕쯰쪧늻듳폚탅쾢믱뗃돉놾;b)믱뗃췪좫탅쾢뫳뗄뻶닟뗄믺믡쯰쪧뗈폚쇣ꆣ횤쏷ꆡa)틲캪떱뻶닟헟믱뗃췪좫탅쾢뫳,뻶닟컊쳢뇤돉튻룶좷뚨탔컊쳢,볙짨ힴ첬Ηj랢짺,퓲뻶닟헟붫톡퓱싺ퟣminxij뗄탐뚯ai,볙짨믱뗃탅쾢탐캪뗄럑폃캪C,퓲떱xij<-C쪱,뻶닟헟늻믡톡퓱Ηjힴ첬쿂뗄i죎뫎튻룶탐뚯,쯹틔,퓚췪좫탅쾢쾵춳쿂,C쫇뻶닟뗄ퟮ듳뿉쓜럧쿕쯰쪧ꆣb)틲캪믱뗃췪좫탅쾢뫳,뻶닟틑뺭돉캪튻룶좷뚨탔컊쳢,볙짨ힴ첬Ηj랢짺,맊뻶닟헟붫톡퓱싺ퟣmaxxij뗄탐뚯ai,듋쪱믺믡돉놾sij=maxxij-xij=0ꆣii뚨샭1쮵쏷쇋뻶닟헟ힷ쟳췪좫탅쾢뗄룹놾풭틲:탅쾢뿉틔쿞훆뻶닟헟뗄럧쿕쯰쪧,뛸쟒믱뗃탅쾢뫳뗄뻶닟탐캪늻믡퓬돉뫳믚ꆣꆡ늻좷뚨탔뻶닟뗄췪좫탅쾢쫂잰믱뗃퓚뻶닟헟믱뗃췪좫탅쾢뫳,늻좷뚨탔뻶닟뗄쓄튻룶ힴ첬랢짺틑뺭좷쟐횪뗀,헢쪱뻶닟돉캪튻룶좷뚨탔컊쳢,뛔폚늻춬뗄뻶닟ힼ퓲,탅쾢믱뗃뛔뻶닟뗄펰쿬쫇늻춬뗄ꆣ쿂쏦컒쏇뻍늻좷뚨탔뻶닟뗄5훖뻶닟ힼ퓲럖컶췪좫탅쾢뛔뻶닟뷡맻뗄펰쿬ꆣ뚨샭2ꆡ뛔폚뇭1쯹쪾뗄뻶닟컊쳢,폃ퟮ듳ퟮ킡램퓲뷸탐뻶닟,퓲췪좫탅쾢뗄믱뗃늻믡쪹뻶닟뷡맻룼닮ꆣ횤쏷ꆡ짨믱뗃뗄췪좫탅쾢쫇ힴ첬Ηj랢짺,벴pj=1쪱,듋쪱뗄뻶닟뷡맻쫇maxxij;믱뗃탅쾢잰뗄뻶닟뷡i맻쫇maxminxij,틲캪maxxijΕmaxminxij,맊뚨샭뗃횤ꆣijiij뚨샭2쮵쏷폃ퟮ듳ퟮ킡램퓲뻶닟,뻶닟헟늻믡캪췪좫탅쾢횧뢶죎뫎럑폃,틲캪뻶닟헟늻싛쓄튻룶ힴ첬뿕볤랢짺웤뻶닟뷡맻늻믡룼퓣ꆣ뚨샭3ꆡ뛔폚뇭1쯹쪾뗄뻶닟컊쳢,폃ퟮ듳ퟮ듳램퓲뷸탐뻶닟,퓲췪좫탅쾢뗄믱뗃늻믡쪹뻶닟뷡맻룼뫃ꆣꆡꆡ(횤싔)뚨샭3쮵쏷폃ퟮ듳ퟮ듳램퓲뻶닟,뻶닟헟튲늻믡캪췪좫탅쾢횧뢶럑폃,틲캪탅쾢늻믡룄짆뻶닟헟뗄뷡맻,쿠랴ퟜ쫇붵뗍뻶닟헟뗄쫕틦,틲듋뛔뻶닟헟살쮵쎻폐틢틥ꆣ듓뚨샭2뫍뚨샭3훐뿉틔뾴떽튻룶폐좤뗄ꆢ뾴쯆쎬뛜뗄쿖쿳:벫뛋샖맛헟(쾲뫃럧쿕헟)뫍벫뛋놯맛헟(퇡뛱럧쿕헟)뛔폚탅쾢뗄첬뛈쫇쿠춬뗄,벴뚼늻ힷ쟳탅쾢ꆣ떫쫇뛾헟뗄뚯믺늻춬:벫뛋놯맛헟쫇틲캪죏캪쎻폐뇘튪퓙뮯ꆰ풩췷잮ꆱ,뛸샖맛헟쫇죏캪럧쿕룼폐볛횵ꆣ뚨샭4ꆡ뛔폚뇭1쯹쪾뗄뻶닟컊쳢,룹뻝샖맛쾵쫽램퓲(Hurwitz램퓲),벴룹뻝뻶닟몯쫽f(ai)=Κmaxxij+(1-Κ)minxij뷸탐뻶닟,웤훐Κꇊ[0,1],짨jj(1={Ηj1-iûΗj1-i쫇maxxij쯹좷뚨뗄ힴ첬,i=1,ꆭ,m}j={Ηj2-iûΗj2-i쫇maxxij쯹좷뚨뗄ힴ첬,i=1,ꆭm}j웤훐((1ꇈ(2)Α(;' 1994-2009 China Academic Journal Electronic Publishing House. All rights reserved.
뗚12웚늻좷뚨탔뻶닟훐췪좫탅쾢믱뗃뗄쫂잰럖컶23퓲É)ힴ첬ퟓ뿕볤(1ø((1ꇉ(2)뗄췪좫탅쾢믱뗃ꋙ,늻믡쪹뻶닟뷡맻룼닮;Ê)ힴ첬ퟓ뿕볤(2ø((1ꇉ(2)뗄췪좫탅쾢믱뗃,늻믡쪹뻶닟뷡맻룼뫃;Ë)ힴ첬ퟓ뿕볤(ø((1ꇈ(2)뗄췪좫탅쾢믱뗃,뛔뻶닟뷡맻쎻폐펰쿬;Ì)ힴ첬ퟓ뿕볤(1ꇈ(2뗄췪좫탅쾢믱뗃,뛔뻶닟뗄펰쿬늻쓜쫂잰좷뚨ꆣꆡꆡ(횤싔)짏쏦죽룶램퓲돆캪샖맛-놯맛램퓲,볲떥뗄ퟜ뷡뿉틔랢쿖췪좫탅쾢폫럧쿕횮볤뗄맘쾵:뛔놯맛ힴ첬뗄탅쾢믱뗃탐캪뎣뎣쓜릻룄짆뻶닟횵,뛔샖맛ힴ첬뗄탅쾢믱뗃탐캪튻냣붫붵뗍뻶닟횵,헢쮵쏷놯맛뻶닟헟튻냣ퟜ쫇뗍맀쪵볊뻶닟ힴ첬,뛸샖맛뻶닟헟ퟜ쫇룟맀쪵볊뻶닟ힴ첬;쇭튻랽쏦,평폚샖맛뻶닟뗄탅쾢믱뗃탐캪뎣뎣붵뗍뻶닟횵,맊뻶닟헟튻냣뛔탅쾢믱뗃탐캪늻룐탋좤,헢쮵쏷쯻쏇쫇쾲뫃럧쿕뗄ꆣ퓚뾪쪼쳖싛틔잰,컒쏇쿈뚨틥튻룶뛔쿂쏦뗄럖컶폐폃뗄룅쓮ꆣ뚨틥2ꆡ뛔폚뇭1쯹쪾뗄맦랶뻶닟컊쳢,죴ힴ첬뿕볤(훐뗄ힴ첬Ηk싺ퟣxikΦxij,ꆡj=1,2,ꆭ,n떫jꇙk(6)뛔쯹폐뗄i=1,2,ꆭ,m돉솢,컒쏇돆Ηk캪뻶닟ힴ첬뿕볤뗄쇓첬,죴(1)듦퓚퇏룱늻뗈쪽,돆Ηk캪퇏룱쇓첬;쿠랴,죴ힴ첬뿕볤(훐듦퓚ힴ첬Ηl,싺ퟣxilΕxij,ꆡj=1,2,ꆭ,n떫jꇙl(7)뛔쯹폐뗄i=1,2,ꆭ,m돉솢,컒쏇돆Ηl캪뻶닟ힴ첬뿕볤뗄폅첬,죴(2)듦퓚퇏룱늻뗈쪽,돆Ηl캪퇏룱폅첬;죴Ηj볈늻쫇폅첬,튲늻쫇쇓첬,돆캪뻶닟ힴ첬뿕볤뗄럇폅럇쇓첬;폅첬탎돉뗄벯뫏폃(뇭쪾,쇓첬탎돉뗄벯뫏폃(뇭쪾ꆣ뚨샭5ꆡ뛔뇭1쯹쪾뗄뻶닟컊쳢,폃뗈룅싊램퓲(Laplace램퓲)뷸탐뻶닟,췪좫탅쾢뗄믱뗃뛔폚뻶닟뷡맻뗄펰쿬쫇늻뚨뗄;죴ퟓힴ첬뿕볤(뫍(럇뿕,퓲맘폚(뗄췪좫탅쾢믱뗃늻믡쪹뻶닟뷡맻룼닮,맘폚(뗄췪좫탅쾢뗄믱뗃늻믡쪹뻶닟뷡맻룼뫃ꆣꆡꆡ(횤싔)뗈룅싊ힼ퓲뾼싇쇋쯹폐뗄ힴ첬,돽럇듦퓚벫뛋쇓첬뫍폅첬,췪좫탅쾢뛔뻶닟뗄펰쿬쫇컞램에뚨뗄ꆣ평폚뻶닟헟뛔럧쿕뗄첬뛈쎻폐쏷쿔뗄쟣쿲,맊뛔탅쾢뗄ힷ쟳튲늻듦퓚쟣쿲탔ꆣ뚨샭6ꆡ뛔뇭1쯹쪾뗄뻶닟컊쳢,룹뻝ퟮ킡ퟮ듳뫳믚횵램퓲뻶닟,벴폃몯쫽f(ai)=max(maxxkj-xij)jk=maxsij뷸탐뻶닟,짨닺짺ퟮ폅뻶닟횵33f(ai)=minf(ai)뗄ힴ첬캪Ηj,퓲뛔폚ힴ첬Ηj늻랢짺뗄췪좫탅쾢,ji탅쾢믱뗃뫳뗄ퟮ폅뻶닟횵늻폅폚탅쾢믱뗃잰뗄ퟮ폅뻶닟횵,웤쯼쟩뿶뗄췪좫탅쾢뛔뻶닟뗄펰쿬늻쓜좷뚨ꆣꆡꆡ(횤싔)평폚ퟮ킡ퟮ듳뫳믚횵램퓲뗄뻶닟횵폫럧쿕컞맘,맊쯤좻뻶닟좡뗄쫇ퟮ킡횵,떫뻶닟헟죔좻퇡뛱탅쾢,헢쮵쏷뫳믚횵폫럧쿕뗄맘쾵쫇랴뇈뗄,벴쎰럧쿕뗄뻶닟헟늻틗뫳믚,뛸틗뫳믚뗄뻶닟헟늻풸틢쎰럧쿕ꆣꆡ횻뛔튻룶ힴ첬뷸탐췪좫탅쾢믱뗃퓚쪵볊뻶닟훐뮹믡폶떽헢훖쟩뿶,벴뻶닟헟뿉틔뛔튻룶좷뚨뗄ힴ첬믱뗃웤췪좫탅쾢,죧뛔폚ힴ첬Ηj,뿉틔춨맽횧뢶돉놾횪뗀pj=1뮹쫇pj=0,컒쏇돆헢훖탅쾢믱뗃캪떥ힴ첬췪좫탅쾢믱뗃ꆣ헢훖샽ퟓ퓚쪵볊훐쫇뫜뎣볻뗄,샽죧쫐뎡ힴ첬(=(Η1,ꆭ,Ηn)폐n훖뿉쓜,퓚튻룶쳘뚨뗄뛌웚쓚,볙짨쫐뎡ힴ첬횻폐튻훖뿉쓜,벴쪹뻶닟헟뿉틔춨맽뗷닩쇋뷢쓄튻룶ힴ첬랢짺,떫폐쪱쎻뇘튪,쯼횻탨횪뗀뛔웤짺닺ퟮ폐펰쿬뗄ힴ첬Ηi쫇럱랢짺벴뿉(헢쪱쯻뗄탅쾢돉놾믲탭뗍튻킩)ꆣ뛔폚떥ힴ첬췪좫탅쾢믱뗃,웤럖컶풭샭폫짏쏦쿠춬,떫캪쇋퓚늻춬ힴ첬탅쾢볤뷸탐뇈뷏,컒쏇뿉틔ퟷ튻룶뫏샭뗄볙짨:떱pj=1쪱,늻춬ힴ첬Ηj뗄췪좫탅쾢컞닮뇰ꆣ헢튻볙짨뗄몬틥쫇쯹폐뗄좷뚨탔뻶닟뛔폚뻶닟헟쫇컞닮뇰뗄ꆣ샻폃헢튻볙짨,컒쏇횻탨퇐뺿떱pj=0쪱탅쾢뛔폚뻶닟뗄펰쿬,쿞폚욪럹늻퓙룸돶떥ힴ첬췪좫탅쾢믱뗃퓚늻춬뻶닟ힼ퓲쿂뛔뻶닟뗄펰쿬,웤뷡맻폫짏쏦뗄샠쯆,쿂쏦룸돶튻룶떥ힴ첬탅쾢믱뗃뗄샽ퟓꆣꋙퟓ뿕볤뗄췪좫탅쾢늻냼삨p=(0,...,0),벴룃ퟓ뿕볤쓚죎뫎튻룶ힴ첬뚼늻랢짺늻쫇웤췪좫탅쾢ꆣ' 1994-2009 China Academic Journal Electronic Publishing House. All rights reserved.
24쾵춳릤돌샭싛폫쪵볹1998쓪12퓂4ꆡ떥ힴ첬췪좫탅쾢믱뗃뗄샽ퟓ뻶닟컊쳢죧뇭3쯹쪾ꆣ뇭3룸돶쇋뻶닟컊쳢뗄튻룶쿈퇩훷맛룅싊,늢쟳돶쇋늻춬랽낸뗄웚췻쫕틦,웤훐a0쫇췪좫탅쾢믱뗃탐캪,뇭훐쫽뻝룹뻝탅쾢믱뗃탐캪돉놾C=10볆쯣ꆣ뇭4쫇뛔뇭3뗄ힴ첬Η1뷸탐뗄탅쾢믱뗃탐캪뫍뻶닟컊쳢컞탅쾢믱뗃탐캪뗄튻룶뇈뷏,ힴ첬뿕볤뗄쿈퇩룅싊P캪캴횪,쇐돶쇋4훖뻶닟ힼ퓲쿂뗄뻶닟뷡맻벰탅쾢믱뗃뫳뗄ퟮ폅뻶닟횵뗄뇤뮯ꆣ뇭3ꆡ쪵샽뻶닟뻘헳뇭4ꆡ떥ힴ첬췪좫탅쾢믱뗃탐캪폫늻뷸탐탅쾢믱뗃탐캪뗄뇈뷏(Η1Η2Η3PΗ=(0,p2,p3)P=(E(ai)뻶닟ힼ퓲1p1,p2,p3)캴횪PꇺPΗퟮ폅1Ap1===뻶닟뷡맻뻶닟횵뗄뇤뮯a0-1010108ퟮ듳ퟮ킡a3a2퓶듳a1-100209ퟮ듳ퟮ듳a1ꆡa3a1ꆡa3늻뇤a205128Laplacea3a2퓶듳ퟮ킡ퟮ듳뫳믚횵a2a2ꆡa3늻뇤ꆡꆡp1=1쪱,뻶닟랽낸캪a2,뻶닟뇤캪좷뚨탔,뻶닟뷡맻컞닮뇰ꆣ떱튻룶뻶닟컊쳢뗄뷡맻뿕볤틑횪뫳,뿉틔뛔탅쾢믱뗃럑폃뗄횵뫍쇩쏴뛈뷸탐럖컶ꆣ뛔폚샖맛쾵쫽ힼ퓲,뿉틔뻍늻춬뗄Κꇊ[0,1]뷸탐쳖싛,헢샯쿞폚욪럹캴쇐죫뇭훐ꆣ5ꆡ뷡싛놾컄퇐뺿쇋췪좫탅쾢믱뗃뗄쫂잰럖컶컊쳢,헫뛔늻좷뚨탔뻶닟럖컶룸돶쇋췪좫탅쾢뛔뻶닟뗄펰쿬,듓뛸뗃돶뻶닟헟믱뗃췪좫탅쾢뗄쳵볾,벴뻶닟헟퓚쪲쎴쟩뿶쿂닅믡뻶뚨믱뗃탅쾢;퓚쳖싛훐뿉틔뾴돶탅쾢폫럧쿕첬뛈뗄쓚퓚맘쾵;뛔폚떥ힴ첬탅쾢뗄믱뗃튲쫇튻룶폐틢틥뗄컊쳢ꆣ닎뾼컄쿗1ꆡ돂췵춢뇠훸1뻶닟럖컶1놱뺩:뿆톧돶냦짧,19872ꆡ뗔솢쇖,헅쟬뫩뇠훸1펦폃뻶닟럖컶1짏몣:춬볃듳톧돶냦짧,19943ꆡGregory,Geoffrey1DecisionAnalysis,PitmanPublishing,128LongAcreLondonWC2E9AN,ꆡ헅죰쟥1늻췪헻탅쾢쿂뻶닟럖컶뗄샭싛폫펦폃퇐뺿1놱몽맜샭톧풺늩쪿톧캻싛컄,19955ꆡ헅캬펭훸1늩?싛폫탅쾢뺭볃톧1짏몣:짏몣죽솪쫩뗪ꆢ짏몣죋쏱돶냦짧솪뫏돶냦,1996' 1994-2009 China Academic Journal Electronic Publishing House. All rights reserved.
