WWW.DISSERS.RU


...
    !

AHA AHHX .T. apao (aoyp), A.. y, A.B. Tpyo (Cam-emepyp) HEETE MHOECTBA B CEPTHOM OPOCE B cae peaaec aop aaa ax cepoo opoca, opac a x

eey eppea. p o ooeoe ee cepo oyaec e eeo oeceo oe, yae cee x oeeoc.

ee coa: cep, yepcaoe oeco, eeoe oeco, y paeoc, ceca epeea, cee o eeoc cepa.

oy XX coe oceco opac coac pe ao coa ocaoa. oy pee oopyoae oca oeo oceco pacpyyp (O) paoao oopao poe pecypc, a eo aecoe co coe o eeco. Opac oaaac a pa oaca, o coaao cepey ypoy aoao eoacoc a e cpa, o ocyapco Boopyee c, acoc, eo Toee apao aa execx ay, oe, aa ocyapceoo caeoo ocopoa aoyp.

Aao ao y aa execx ay, poeccop, ey ay copy Boeo-oceco aae e A.. Moacoo.

Aece Beao Tpyo cap peoaae Boeo-oceco aae e A.. Moacoo.

Cooo: 4M. 2004. 19.

Heemue oecma cnepmo onpoce oy pee ca aeo cee ac o ee yopoa. oe epep ayce ocecx aapao (A) c, ae pyx A oeoo a pooxoceoo aae o aec oocca yep cooeceo oopoococooc ooe cpa.

Bxo coaeoc ooe ae. a pe oea, a ae peaoaa oe oopa execoo coco oeo oceco pacpyyp, cyaa oopx ocyecec a peea aaex pecypco [1].

o oopo oaec ccea ocox ae, oe pooa ee coco aoo-o ppooo, coaoo .. oea [2]. Oao ocee o ae peec oee poa paoa oo o, a a ce ypaeec ace: oocoae oox pe e, apaex a peopaee eaopoo ee coco oea oopa, pecaee x a, pa pee. ooy aao oe o oopo O oaac ccea ocox a e, oe, pooa ee ypae x cocoe.

Bepee cce oopa pay cyaa O ooo opee x aecoe cocoe, cea paocpo oocpo poo eo ee, ca poa o oec epop, oo p peee o oooc x aee cyaa e aaoo peoa.

Cee pca oox pee aeo cee opeeec aeco pooa ee execoo coco oopyoa O a caapx peax cyaa, a p yco poee a e pax peoo-po aecx pao.

pee aa poopoa acoee pe pe ec ooe oeco apopoax eoo, ocoax a cacecx o-cacecx oex [3]. Tooc .T. apao, A.. myu, A.B. Tpyo ocoepoc oyaex poox oeo c cooa e ax eoo ac o eoc ae a opee apaepa poopyeoo e a o peo oee a ex o cpoe oeax o oea cacec oopox ae. C o o pe oopyoae O ec oeo eca co poopoa. a cooc oycoea, o-epx, y aoc aeo ac oopyoa, o-opx, ee oc ae ooo oopyoa, oopa ec cec e oocex ee, ecex x ocpy a ooe epo cyaa , pex, a oec o epeo opa, copy oopo, aec, pcy oo c epee oopa. B ax ycox eooo copa pepeeay opy opeex apaepo poopyeoo e , ceoaeo, pe pee a ocoe cacecx o-cacecx o ee oe pec ae opeoc.

O eecoopax oxoo oye poox oeo poecco, xapaepyxc ceeco yaoc, ec peee cepoo oea.

o cep oeae oa ccey oecx aeaecx eoo poeyp, apaex a oyee o ceaco opa, eoxoo pee ypa eecx aa [4]. p oye poox oeo ex ecoo coco O aece cepo cooac epco a, ocoo cyapy oe. o ooo pe aoa eo aoe eeapaeoe yace oecee eoaoc yopoa poe pecypca O.

cepoe oeae ocyecoc xoe cepoo o poca. B paccapaeo aae e oo opoca oc oy ee pooo opa o o apaepo, xapae pyx cocoe O, o a o cocoe peo x cyaa apyex peoo-poaecx pao.

Heemue oecma cnepmo onpoce B acoee pe pec ceye cepoo opoca [4]: cyccoe, eo oeo eepa e, aepoae eppoae. C e aeeo oe e epcoaa, cyapyeo O, o ocox oa oce, a ae epecax acao aoaa opa o cepo opa, p opaa opoca cepo cooao aepoae.

p opaa aepoa peycapaac eoxo oc pee yx aa: oyee yax o ecex oeo cepo pyoo cepo oe.

e cye cepo x oe cea cye, a a ee. B c c oo p poee cep oo opoca aae eo peyao cooa papaoa y . ae aeaecy eop eex oec [5].

Moocee pep pee o eop pax cepax ay ex oaa ee ooopoc. Oao oeecex coooecx cceoax, ecop a a yaoc poe coea aecex oecex eoo aaa coax eoeo [2], pep pee eex oec pae pe. Ha ece o [3], cppy oooc ocpoe coopa a ocoe eeo opa. B ao cae paccapaec ee oo apaee pee eex oec: oyee cep o opa opae eex oec aa ax aepoa py cepo, ex pay cee oeeoc cceyeo peeo oac.

B peaaeo cepy aee aoy opocy cac cooece oeco apao oeo, pecax coo aecee cye, xapaepye cee paeoc .T. apao, A.. myu, A.B. Tpyo eoopoo eeoo coca yaeoo oea. peoo, o eoxoo c: a nouem a mexuecoe cocmo ue eomopoo oema noeue onpeeeoo oea pe omo-npouamuecux paom. p oee a o opoc oo ae apa a: nouumc aumeo, nouumc eaumeo, e ueumc, nocumc eaumeo, no cumc aumeo. Tpaoa o aumeo nou umc, a e a pyx o, coepaxc peaaex oeax, y aoo cepa co p o eea. ooy cep oe e oo pa pa, o eo e, oe, o opepoa eo oeceo. Cooec c o eo opeoe co cepy cxooec pyo, a a o e oaae oo opae o cocax yaeoo oea , ec o o ceae, o oe oyea pya oa. B c c cepy peaaec a opa oeceo eppea oeo: o oe a e oy, a ecoo oecex oeo, cooecyx eo oa paoo oea. opepo cepo ooe apa oeo ac aey. Hapep, paccapae o cyae oeco oox oeo oe e {75%, 50%, 25%, 0, 25%, 50%, 75%}. Ta, ec cep cae, o cee eoc a 25, 50 75 poeo ec ae, o o oe pa oe 75%, 50%, 25% (a oaae cee eoc). poe oo, o o e pco ao ao oee cee yepeoc o, o eo oa ye e eco. oo o oe c epa poecc aa cee yepeoc aee, oo p o epao-coy ay Xappoa, xapaepy y cee paeoc ax-o coc [5].

pae ae, cooecy copypoaoy e opocy, ee , pecae a. 1.

epe ae poc pao ee aoe cey eo coepa.

Heemue oecma cnepmo onpoce Bepeme nepo cmoe ma. 1 apuam omema, coom emcmyu Baey eu. Becume coomemcmyy cmpoy cmeneu yepeocmu mo, mo apuamy oym coom emcmoam ouecmee aeu ueeu emuocmu u npecmaeoo maue oecma.

Taua OPMA, PEAAEMA PECOHEHT Boo e ae e e oaa e e oc, %, o ope oy Bap a coo e c oa Baey o e y o e a 75 50 25 0 25 50 o c a e o o c e a e o He e c oc c e a e o oc c a e o Cmene yepeocmu uepemc ucoo ae uana oe 01;

0 auea cmene yepeocmu, 1 auoa.

Ecu B ucnmaeme ampyeu onpeeeuu cmeneu ye peocmu, mo ocnoymec ao, npueeo ma. 2.

o ea oacoc aa cepy apao oea, ey oe peocaea oooc xoa a pee peaaeoo oeca oeo. Ta, ec cep o ae cee eoc oae ee cee oee e a 100%, o o oe oo peaaeoe aee oeco cooecy ooeco, apep, {150%, 125%, 100%}.

.T. apao, A.. myu, A.B. Tpyo Taua BEPAHO-COBA AA XAPPHTOHA C e e yepe oc cooe ae e Oe coa 0,801, Bcoa 0,640, Cpe 0,370, H a 0,200, Oe a 0,00, aaea eoa opoca peec a ocopoe a oyp, e, a ye oeaoc e, aece cepo cy a epcoa, cyapy O. oa ac oo ep coaa ec yca Boeo-oceco aae e A.. Moacoo, e opoc pee eex o ec yac ye c 70-x . pooo ea. ooy a, po oe opoc, cep paoapa a oe oo e y cepo e ae apye eoxooc pecae cox oeo ae 01. Ec e oe cepo eao c o eop eex oec, o oee peoeo ec poea aa 0100. B o cy ae p aae peyao opoca eoxoo ye epe o o a ae 01.

Taoe aoee ae oop o o, o cep, pa oe: emuocm nocumc eaumeo, ee y ceyee:

copee ceo, eoc occ a 25%;

ooo, o oa occ a 50%, o yepa o oo c ecoo ee yepeoc (0,8);

eoc oe e ec, o yepeoc o ee e (0,3);

cee yepeoc o, o oe ee oaa e eoc py pye ae, paa 0.

Bocoyec opao eex oec oca peyao opoca, poeeoo o oeo eoe.

Heemue oecma cnepmo onpoce Taua PMEP AOHEHHOO CEPTOM PAMEHTA AHET Boo e ae e e oaa e e oc, %, o ope oy Bap a coo e c oa Baey o e y o e a 75 50 25 0 25 50 o c a e o o c e a e o He e c oc c 0 0 0 0,3 1,0 0,8 e a e o oc c a e o peoo, o opaaec K cepo aea coep P eex opoco. Toa aoy opocy oo oca cooece cecy epeey Li (i =1, P), ae i oopo c apa oeo Lij = ( j =1, J ), e Ji o eco apao oeo a i- opoc. peeo pe eoy e opocy (aoe eo i-) ee:

Li (ueeue emuocmu paom up) = {e muocm nouumc aumeo (Li1), nouumc eau meo (Li2), e ueumc (Li3), nocumc eaumeo (Li4), nocumc aumeo (Li5)}.

a ye o oeeo paee, aoe aee c eco epeeo ec ee ooy eo oca coyec eeoe oeco. o oeco aaec a i aoo (eo) oece Ui = {uis, s =1, S } ecex ce, oxaae, o e opaaopo opoca, ec oo aao oecex oeo ceco epeeo Li. peoo, o i-o opoca oo aao e:

.T. apao, A.. myu, A.B. Tpyo Ui = {ui1 = 75;

ui2 = 50;

ui3 = 25;

ui4 = 0;

ui5 = 25;

ui6 = 50;

ui7 = 75}.

cep oe cooca ay oey oo oeca c oece oaaee cee yepeoc o, o eo oa ye e eco. B aee, cooec c epooe, po eop eex oec, o o aae ye aa aee y paeoc i i ooaa L (uis ), e i =1, P, j =1, J, k =1, K, s =1, S. co k ij L (uis ) xapaepye cee yepeoc k-o cepa, k ij paeo aece oea a i- opoc j-e aee c eco epeeo, o, o oecea oea o epe i eo oe p aee us. y paeoc L (ui ), ui Ui, eeo aooo oeca Ui eeoy o k ij ecy Lij, o e k-o cepa, o cyae ye aaac eop-cpoo L (ui ) = [L (ui1);

L (ui2 );

...;

L (uiS )].

k k k k i ij ij ij ij Hapep, ec k- cep p oee a copypoa e opoc pa oe Li4 = emuocm nocumc e aumeo eppepoa eo a, a o ao a. 2, o L (ui ) = [0;

0;

0;

0,3;

1;

0,8;

0].

k i o oaae, o aee Li4 ceco epeeo Li opao oo peca e eeoo oeca:

Li4 = emuocm nocumc eaumeo = (uis ) /uis = 7 Li s= = 0/75 + 0/50 + 0/25 + 0,3/0 + 1/25 + 0,8/50 + 0/75.

B o pae co + 7 oaa oepa o ee.

yoca aeeo aaa peya opoca K c epo o aoy i-y opocy eecoopao cec a (c. a. 4). B eax a. 4 oee ae y paeoc L (uis ).

k ij Heemue oecma cnepmo onpoce Taua PETAT OPOCA K CEPTOB O i-y BOPOC, PECTABEHHE B HEETO METPE Boo e ae e e oaa e e oc Ui, % c ep a 75 50 25 0 25 50 1 0 0,1 0,4 1,0 0,4 0,1 2 0 0 0 0 0,2 0,6 1, k 0 0 0 0,3 1,0 0,8 K 0 0 0 0,2 0,7 1,0 Ec ypoe oeeoc cex cepo oao, o ooea eea oea oe oyea a epeceee eex oec, cooecyx oea cepo.

y paeoc, oeceo xapaepya y oey cooec c pao oe oepa e pecee eex oec [4], opeeec o opye:

k ( ) = min(k ( ), k ( ),..., k ( ),..., k ( )).

ui ui1 ui 2 uis uiS i Oao coppoa pyy cepo oaoo oe eoc paec eooo. B c c oae eoxooc opeee cee oeeoc cepo ee yea p oye ooeo oe.

p pee o aa oae opoc o ope ep oeeoc cepa. y epy oo oy ye .T. apao, A.. myu, A.B. Tpyo eocpecex cceaecx ae a aeco po oo cepo oce opao a ocoe cee o x poeccoao eeoc.

B epo cyae aece ep oeeoc cepo oo epy eoope y o aeaecoo oa oy ooe pooo cepo k o cx peaa poopyex apaepo ucm aeaecoo o a apaa oo ooe [6]. Haoee yoo aaa epy oeeoc k-o cepa oppoa o eo a M[ ucm - k ] M[(ucm - k )2 ] k = k =.

K K - k )2 ] M[(ucm M[ ucm - k ] k =1 k = Tao oxo oe cooa oo p eo paoe c ocoo pyo cepo, xoe oopo cpy c aae e ooe.

p cooa ocex eoo poecce cep oo opoca eoxoo xapaepc poeccoa o eeoc cepo, o oopx ac eo oee oc. Moeco x xapaepc a opao opee ec cepo eeoc cepo. Oao o cex cyax ey oocc ae xapaepc, a aaea ooc ca pao cepa.

e aax xapaepc cpyeap cepoo opoca eoxoo cooecyee o eco ooex opoco D = {Dn, n =1, N}.

p o aoy opocy Dn cooecye oeco o n n eo Bn = {Bm, m =1, M }. p oppoa oeca oe o a ooee opoc eoxoo ya, o o e o pecae ae opa.

Paccop aop peopaoa oeo cepo a ooee opoc oecee oe x Heemue oecma cnepmo onpoce n oeeoc. oo aoy Bm-y apay oea a Dn- ooe opoc oca cooece ooe n M n oppoa oe n, p o =1. Bea m m m= oea n ac o oepa apaa oea a oo m e opoc cec cooec co cey paee:

m n n =, m =1, M. (1) m Mn m m= n Toa op k- cepo opeoo Bm-o apaa oea a Dn- ooe opoc ooao opeee eoo p oe oeca n, oop ooa a n. B m k eo oppoa oe oeeoc k-o cepa ac o cex oeo a ooee opoc c ec cooec co cey pao:

N n k n= k =. (2) N maxn m n= m Be ypo oeeoc cepa a eey o ecey epy k (ui ) peaaec peaoa ye o e oepa paa. Maeaec paae ee o oeceo ep k (ui ) peayec ye oee ee cee, cooecyy oey oeeoc cep a k 1:

k ~ k (ui ) = k (ui ), i =1, P. (3) B peyae opoca oeca cex cepo = {k, k =1, K} aoo i-o (i =1, P) opoca ae ee K eex o .T. apao, A.. myu, A.B. Tpyo ~ ecex ep k (ui ), yax cee oeeoc opaaex cepo. Toa eeoe oeco, xapaep yee ooeoe ee py opaaex cepo p oee a i- opoc ae, oo opee a epeceee eex e cepo, eee y paeoc ~ ~ (ui ) = min {k (ui )}, k =1, K, i =1, P. (4) i k oye ooaoo oeceoo peyaa opo ca eoxoo yaa a ope ee aooo oeca Ui. Oo pa o ee ui, oop ee acay cee paeoc oyeoy ooeoy eeoy oecy e cepo py:

~ ui* = arg max (ui ),ui Ui. (5) ui i peoo, o e cepo py yx eo e, opepyc a peeoe a. 2 oeco oeo x eppea, a oe a copypoa aae ca opoc e ceyx eex oec (cpo 1 2 a. 4):

L1= 0/75 + 0,1/50 + 0,4/25 + 1,0/0 + 1,0/25 + 0,4/50 + 0/75;

L2= 0/75 + 0/50 + 0/25 + 0/0 + 0,2/25 + 0,6/50 + 1,0/75.

Ta a pepe paccapaec oo o opoc, o peex opyax aee ec i oye.

y paeoc, xapaepye eeoc o eo cepo, cooeceo pa:

1(u) =[0;

0,1;

0,4;

1,0;

0,4;

0,1;

0], 2 (u) = [0;

0;

0;

0;

0,2;

0,6;

1,0], u U.

opeee cee oeeoc cepo aa a ooex opoca: D1= ay oocm B auaeme? D2= Coo em B paomaeme upe?.

epoo opoca peaac ceye apa oeo:

Heemue oecma cnepmo onpoce B1= ueep, B1 = cmapu ueep, B1 = aau 1 2 omeeu, B1 = aau omea, a opoo B1 = e ee nmu em, = om nmu o ecmu em, B3 = ce ec B mu em.

Ha opoc cep oe cey opao: ep cep pa B1 = ueep B1 = eee nmu em, a opo cep B1 = aau omea B3 = ce ecmu em.

Oe a ooee opoc oo c oe oeeoc aoo cepo.

o opye (1) oeo a ep opoc ee: 1 =, 2 3 4 1 =, 1 =, 1 = ;

oeo a opo opoc 1 =, 2 3 10 10 10 2 2 =, 3 =. Hao, o epx ec oaae oep 6 opoca, a oep oea a eo. Ta a ep c ep a oa opoca pa oe, ee ep oep, o 1 2 1 = 1 =, 1 = 1 =. Bopo cep a ep opoc 1 10 pa eep oe, a a opo pe. ooy 1 = 1 = ;

2 2 = 3 =.

o opye (2) ce oe oeeoc cepo:

1 1 4 1 + 1 10 + 6 1 + 2 10 + 1 2 1 = = = 0,3 2 = = =1, 2 4 3 4 1 + 3 + 1 + 3 + 4 10 6 10 2 2 e 1 = max(1, 1, 1, 1 ), 3 = max(1, 2, 3 ).

4 1 2 3 4 .T. apao, A.. myu, A.B. Tpyo Ta a oe oeeoc opoo cepa pa e 1, o ~2 oppepoa eoxoo oo y (u) = 2 (u) paeoc eeoo oea epoo cepa. o op ye (3) axo:

~ 0, 1 (u) = 1 (u) = [0;

0,1;

0,4;

1,0;

0,4;

0,1;

0]0,3 = [0;

0,5;

0,6;

1,0;

0,6;

0,5;

0]1.

y paeoc, xapaepyy ooeoe ee cepo, opee o opye (4):

~ ~ ~ ~ ~ ~ ~ (u) = min( 1 (u), (u)) = [min( 1 (u1 ), (u1 ));

min( 1 (u2 ), (u2 ));

2 2 ~ ~ ~ ~ ~ ~ min( 1 (u3 ), (u3 ));

min( 1 (u4 ), (u4 ));

min( 1 (u5 ), (u5 ));

2 2 ~ ~ min( 1 (u6 ), (u6 ))] = [0;

0;

0;

0;

0,2;

0,5;

0].

Bocooac opyo (5), ae ooe pey a opoca cepo: acaoe aee y pa eoc (u) = 0,5 cooecye u5=50%. Ta opao, o peyaa opoca oo cea cey o: oee peoo-poaecx pao oo ye e oc pao oea a 50%.

Paee oeaoc, o paccope oxo oye aay cepx oeo peec a ocopoe aoyp poopoa pax cyaaox e pop a eee execoo coco oeo ae o oceco pacpyyp. Oao o oaae coo cee ooc , o aey e, oe pee pax oacx eeoc , acoc, cooo ecx cceoax.

TEPATPA 1. apu .B., cyno P.M., poxopou B.E, myu A.. oe ypae cocoe cox execx oeco a peea aox cpoo cyaa // opaoe exoo. 2000. 5. C. 712.

oee cee y paeoc, aao eop-cpoo, eoxoo oec y cee a ee eop-cpo.

Heemue oecma cnepmo onpoce 2. oo oo coap pyccoo a / - cecx cceoa PAH;

Coc. . pe. C.A. yeo. C.: Hop, 2000.

3. Ocmpeocu B.A., Cauo H.. Bepoocoe poopoae paoococooc eeo . M.: epoaoa, 1990.

4. Teop opa p pee. M.: Haya, 1982.

5. ae . oe ceco epeeo eo peee p pex pee. M.: Mp, 1976.

6. Tamapoa.. aecee eo cpyype eooo aaa ax // Cooo: eooo, eo, aeaece oe. 2002. 14.

C. 3352.

7. Myxamuoa O.P. ocpoee aa coopa a ocoe eeo o // Cooo: eooo, eo, aeaece oe. 2000. 12.

C. 154172.

8. Opocu C.A. poe p pee p eeo cxoo opa. M.: Haya, 1981.

9. uma .. paeece pee. M.: -o MOC, 1998.

10. In Jae Myung, Sridhar Ramamoorti, Andrew D. Bailey, Jr. Maximum Entropy Aggregation of Expert Predictions. Manag. Sci.,1996. 42. 10. C. 4655.




2011 www.dissers.ru -

, .
, , , , 1-2 .