뗚24뻭뗚2웚듳ꆡ톧ꆡ쫽ꆡ톧,ꇭ.22008쓪4퓂웚췻킧폃몯쫽샭싛벰웤펦폃쇖폱죯(뢣붨얩쇖듳톧볆쯣믺탅쾢톧풺,뢣훝350002)ꆡꆡ[햪ꆡ튪]럖컶쇋웚췻킧폃몯쫽샭싛,늢붫웤퓋폃폚춼쫩망뗄맜샭릤ퟷ,듓훐랢쿖웤맦싉탔.캪춼쫩망뗄뿆톧맜샭쳡릩쇋튻쳵폐킧뗄춾뺶.[맘볼듊]펦폃쫽톧;킧폃몯쫽;춼쫩망맜샭;웚췻킧폃;룅싊[훐춼럖샠뫅]O29ꆡꆡ[컄쿗뇪쪶싫]Cꆡꆡ[컄헂뇠뫅]167221454(2008)02201712031ꆡ웚췻킧폃몯쫽ꆡ킧폃몯쫽뫎캽킧폃?짌욷폐짌욷뗄킧폃,닆뢻폐닆뢻뗄킧폃,벼쫵폐벼쫵뗄킧폃.퓚뺭볃쇬폲,킧폃쫇횸쿻럑헟퓚쿻럑컯욷쪱쯹믱뗃뗄싺ퟣ돌뛈.쿔좻,쿻럑헟듓늻춬짌욷뗄쿻럑쯹믱뗃킧폃쫇룷훖짌욷쿻럑솿뗄몯쫽.폃U뇭쪾쿻럑헟퓚튻뚨쪱웚쓚쿻럑룷훖컯욷쯹믱뗃뗄킧폃ퟜ솿,틔x1,x2,ꆭ,xn럖뇰뇭쪾n훖쿻럑컯욷X1,X2,ꆭ,Xn뗄쿻럑쫽솿,퓲킧폃몯쫽뇭쪾캪U=f(x1,x2,ꆭ,xn).(1)튻냣뗘,U쫇쿻럑솿뗄퓶몯쫽,벴쿻럑솿풽듳,킧폃튲풽듳.ꆡ웚췻킧폃몯쫽떱킧폃몯쫽폶떽늻좷뚨쿖쿳쪱,뻍믡쓑틔좷뚨쯼뗄횵,헢뻍틽돶쇋웚췻킧폃뗄룅쓮.폃쫽톧뗄폯퇔살쏨쫶죧쿂:춶뗄킧폃쫇튻룶쯦믺뇤솿u,쯼뿉쓜좡솽룶횵(u1뫍u2),ui=u(si),ꆡi=1,2,늢쟒u=ui룅싊럖뇰쫇ꛐ1뫍ꛐ2,쓇쎴u뗄웚췻횵Eu=ꛐ1u1+ꛐ2u2뻍쫇춶뗄웚췻킧폃.뛔폚웚췻킧폃몯쫽,쯼뗄쫽톧탔훊뿉틔랴펳죋뗄탐캪쳘탔.틲캪웚췻킧폃쫇늻튻뚨쓜쪵쿖뗄,헦쪵뗄킧폃믡뇈쯼룟,믲뇈쯼뗍,폐늻좷뚨탔,듯늻떽풤웚뗄킧폃,뻍퓬돉쇋쯰쪧,탎돉럧쿕.뛔듽럧쿕뗄첬뛈뿉럖캪죽훖:퇡뛱ꆢ훐탔ꆢ쾲낮,헢죽훖첬뛈폃쫽톧뗄폯퇔쏨쫶죧쿂:1.죴킧폃몯쫽쫇낼몯쫽,벴u(Ex)>Eu(x),퓲쿠펦폚럧쿕퇡뛱헟;2.죴킧폃몯쫽쫇춹몯쫽,벴u(Ex)<Eu(x),퓲쿠펦폚럧쿕낮뫃헟;3.죴킧폃몯쫽싺ퟣu(Ex)=Eu(x),퓲쿠펦폚럧쿕훐탔뗄죋.ꆡ[쫕룥죕웚]2005211207ꆡ[믹뷰쿮쒿]뢣붨쪡ퟔ좻뿆톧믹뷰훺쿮쒿(2007J0175)' 1994-2010 China Academic Journal Electronic Publishing House. All rights reserved.
172듳ꆡ톧ꆡ쫽ꆡ톧ꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡ뗚24뻭죧맻킧폃몯쫽쫇폐튻ꆢ뛾뷗캢짌뗄튻풪몯쫽,뚨틥ꛋ(x)=-u(x)ꇥ/u(x)ꇤ폃ꛋ(x)뗄럻뫅뻍뿉틔에뚨뛔럧쿕뗄첬뛈,웤뷡싛쫇ꛋ(x)>0,ꆡ퇡뛱럧쿕,ꛋ(x)<0,ꆡ낮뫃럧쿕,ꛋ(x)=0,ꆡ럧쿕훐탔.헢튻에뛏폫낼ꆢ춹탔에뛏쫇튻훂뗄.튻냣뛸퇔,틽죫웚췻킧폃,웤퇐뺿쒿뗄,뻍퓚폚럖컶퓚럧쿕쳵볾쿂뗄쿻럑헟믲뻶닟헟뗄탐캪,뎣뎣쫇쏦뛔쿖쪵짺믮훐늻좷뚨뗄럧쿕쳵볾쿂뻶닟헟펦룃퓵쎴탐뚯뗄퇐뺿.춬쪱컒쏇튲랢쿖,퓚뛔죋쏇탐캪뗄럖컶훐,죋쏇늢늻뷶뷶럖컶탐캪닺짺뗄풭틲,뛸쫇닉좡듫쪩늢듙돉쪲쎴퇹뗄탐캪랢짺.복짙믲틖훆튻킩컒쏇늻탨튪뗄늻솼탐캪랢짺.듋쪱뷨훺웚췻킧폃몯쫽뻍믡믱뗃폐틦뗄웴쪾.2ꆡ웚췻킧폃몯쫽샭싛럖컶죃컒쏇뾼싇솽죋뗄늩?(솽죋쇣뫍늩?),뛾헟돶춬퇹뛠뗄잮(100풪)뛄늩,펮헟뇤돉200풪,쫤헟캪0.늻뾼싇웤쯻틲쯘쟩뿶쿂,쫤펮룅싊뻹캪,웚췻킧폃E(u)=ꇁ200+ꇁ0=100.쮫랽뗄킧폃캪ꇁu1+ꇁu2=(u1+u2),u1,u2캪솽훖ힴ첬쿂뗄뇟볊킧폃(죧춼1).뇈뛄늩잰뗄u1짙쇋ꚤu1=(u1-u2).죧맻튻룶죋펵폐200풪,퓙쓃돶100풪뷸탐뛄늩,웤쯰쪧킧폃캪ꚤu2=(u2-u3),뇈뷏ꚤu1,ꚤu2죧쿂:ꚤu1=(u1-u2)=ꇒ200u(x)dx-ꇒ300u(x)뛔ꇒ300u(x)dxퟷ뇤솿쳦뮻t=x-100,뗃200ꇒ300u(x)dx=200ꇒ200u(t+100)dt=ꇒ200u(x+100)dx,춼1100100ꚤu1=ꇒ200[u(x)-u(x+100)]dx=ꇒ200-uꇤ(ꛎ1)100dxꆡꆡꆡꆡꆡꆡꆡ100=ꇤ(ꛎ1)1002,ꆡꛎꇊ(100,300),ꚤu2=ꇒ300u(x)dx-200ꇒ400u(x)dx=ꇒ200u(x+100)dx-00ꇒ200u(x+200)dx3001100=ꇒ200[u(x+100)-u(x+200)]dx=ꇤ(ꛎ2)1002,100ꛎ2ꇊ(200,400),쟒100<ꛎ1<ꛎ2<400,ꚤu2-ꚤu1=[uꇤ(ꛎ1)-uꇤ(ꛎ2)]10021=uꇥ(ꛎ)1002,ꆡ100<ꛎ<떱u캪낼몯쫽쪱uꇥ(ꛎ)>0,떱u쫇춹몯쫽쪱uꇥ(ꛎ)<0,떱u쫇횱쿟쪱,uꇥ(ꛎ)=0.쯹틔떱ꚤu2-ꚤu1>0쪱,u캪춹몯쫽;ꚤu2-ꚤu1<0쪱,u캪낼몯쫽;ꚤu2-ꚤu1=0쪱,u캪횱쿟.평듋뿉볻,ꚤu2-ꚤu1<0쪱,벴튻룶뢻죋쓃돶튻늿럖잮좥뛄늩쯹쯰쪧뗄킧폃튪뗍폚튻룶쟮죋쓃돶춬퇹뗄잮좥뛄늩쯹쯰쪧뗄킧폃.튲뻍쫇쮵뢻죋룼뺭뗃웰헢훖뛄늩듸살뗄킧폃쯰쪧.틲뛸u쫇낼몯쫽.3ꆡ웚췻킧폃몯쫽샭싛퓚춼쫩망맜샭훐뗄펦폃쿂쏦틔춼쫩망맜샭캪샽.훚쯹훜횪,춼쫩망춼쫩뾪볜퓄샀쫇춼쫩망뗄랢햹쟷쫆.좻뛸,뾪볜뷨퓄돽쇋룸릤ퟷ죋풱듸살랱훘뗄헻볜릤ퟷ췢,춼쫩뗄뚪쪧솿틠죕쟷퓶뛠,헢룸맜샭헟듸살쇋탂뗄컊쳢.컒쏇늻럁폃웚췻킧폃몯쫽럖컶죧쿂:쿖볙짨쟔쫩헟킧폃몯쫽캪u=M(M캪쯹돖믵뇒:1000풪),쟔쫩튻듎쓜듸살쿠떱폚10풪뗄샻틦,튻떩놻맜샭풱랢쿖늢뒦틔랣뿮뗄룅싊캪,랣뿮쫽솿캪20풪,퓲늻컄쏷뛁헟' 1994-2010 China Academic Journal Electronic Publishing House. All rights reserved.
뗚2웚ꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡ쇖폱죯:웚췻킧폃몯쫽샭싛벰웤펦폃173늻뷸탐쟔쫩탐캪뗄킧폃:u=1000=,늻컄쏷뛁헟뷸탐쟔쫩탐캪뗄웚췻킧폃캪E(u)=ꇁ1000+10+ꇁ1000-20=.쿔좻E(u)>u,벴늻컄쏷뛁헟뷸탐쟔쫩뗄웚췻킧폃듳폚늻뷸탐쟔쫩탐캪뗄킧폃.쫴폚럧쿕낮뫃헟,벴쪹쏦쇙놻랣뿮,쟔쫩탐캪죔믡뷸탐.듓웚췻킧폃몯쫽짏럖컶뿉횪,춼쫩망맜샭헟뿉틔듓솽룶랽쏦짏ퟅ쫖룄짆:웤튻,볓잿볠뚽솦뛈틔벰쳡룟놻랣뿮뗄룅싊,퓚짏샽훐냑놻뒦랣뗄룅싊쳡룟떽쪱,퓲폐E(u)=ꇁ1000+10+ꇁ1000-20=,ꆡE(u)<u,벴늻컄쏷뛁헟뷸탐쟔쫩뗄웚췻킧폃킡폚늻뷸탐쟔쫩탐캪뗄킧폃,쫴폚럧쿕퇡뛱헟,퓲뿉훆횹쟔쫩탐캪뗄랢짺.헢탨튪춼쫩망볓듳톲볜솦뛈,퓶볓볠달돉놾.웤뛾,뮹뿉퓶볓랣뿮쫽솿.퓚짏샽훐냑랣뿮쫽솿듓20풪퓶볓떽100풪,퓲폐E(u)=ꇁ1000+10+ꇁ1000-100=+3=,ꆡE(u)<u,춬퇹쫴폚럧쿕퇡뛱헟,뿉틔훆횹쟔쫩탐캪뗄랢짺.쿔좻,뗚뛾훖랽램폅폚뗚튻훖랽램.4ꆡ벸뗣뷡싛(i)샻폃웚췻킧폃몯쫽샭싛,뮹뿉틔펦폃폚웤쯼탐튵뗄탐캪맜샭.(ii)쯤좻폃킧폃몯쫽샭싛럖컶죋뗄탐캪쫇믹폚뺭볃톧샭싛폫짧믡쿖쪵훐뗄탐캪톧늻짵쿠럻,떫뺭볃톧ퟷ캪튻쏅쪵횤뿆톧,펮뗃죋쏇타짍뫍퇐뺿뗄튻룶훘튪풭틲잡잡쫇뾿퇏쏜뗄싟벭,짵훁룶죋뎣쪶,뺭퇩룼쓜쿠럻뗄쳘뗣.(iii)춨맽웚췻킧폃몯쫽샭싛럖컶뛁헟뗄탐캪맦싉탔뿉횪,춼쫩망톧폫뺭볃톧쏜쟐쿠맘뿉폃뺭볃톧뗄맛뗣뷸탐춼쫩망뗄뿆톧맜샭.(iv)뷨훺웚췻킧폃몯쫽,룸컒쏇뛔죋뗄짧믡탐캪럖컶쳡릩쇋튻룶뚨솿뫍뚨탔쿠뷡뫏뗄랽램,럡뢻쇋탐캪맜샭톧샭싛,폐샻폚죋샠탐캪맜샭뗄뷸튻늽짮죫퇐뺿.[닎ꆡ뾼ꆡ컄ꆡ쿗][1]ꆡ헅튢춥,돂믛폱.킧폃몯쫽벰폅뮯[M].놱뺩:뿆톧돶냦짧,2000.[2]ꆡ샮탣삼.킧폃몯쫽벰웤펦폃[J].즽뚫쪦듳톧놨(ퟔ좻뿆톧냦),2001,(3):55-59.[3]ꆡ헅쇕.싛님쫩킧폃움볛[J].춼쫩쟩놨릤ퟷ,1998,(8):26-28.[4]ꆡ풬횾룙.맜샭뺭볃톧[M].짏몣:뢴떩듳톧돶냦짧,.[5]ꆡ뫩틣,뗈.뺭볃쫽톧쒣탍[M].맣훝:뮪쓏샭릤듳톧돶냦짧,.[6]ꆡ쇖폱죯.춼쫩닉릺쇷돌훐뷰럖엤쒣탍퇐뺿[J].퓋돯폫맜샭,2002,(6):104-108.[7]ꆡ[J].ManagementSci.,1987,(11):15-21.[8]ꆡ[J].TheoryandDecision,1987,(2):25-30.[9]ꆡ쯕뚫쮮.맜샭탄샭톧[M].짏몣:뢴떩듳톧돶냦짧,.[10]ꆡ볓샯S놴뿋뛻.죋샠탐캪뗄뺭볃럖컶[M].췵튵폮,돂틫.짏몣:죽솪쫩뗪,(FujianAgricultureandForestryUniversity,Fuzhou350002,China)Abstract:Accordingtodesiredutilityfunctiontheory,:appliedmathematicsutilityfunction;libraryAdministration;desiredutility;probability' 1994-2010 China Academic Journal Electronic Publishing House. All rights reserved.
