WWW.DISSERS.RU


...
    !

MATEMATECOE MOEPOBAHE .. Caee (Hoocuupc) BEPOTHOCTHA MOE CEPTHX OEHO B cae paccapaec apa epooco oe cepx oe o pep ee pee y

aaa. epa cepa oe a pax aopo a eaoae ooe oo Hoocpca. Bopa cepoe poopoae eoc oeca epop.

ee coa: eaoae ooe, eoc, cep a oea, oppoae, aa, epooc, cyaa epeea, pacpeeee, cpeee aee, aeaecoe oae.

Paccop pyy m cepo, oop pcoe oepa i = 1, , m. cep c oepo i oeae aoe j = 1, , n a x caa co x[i, j] 0. oeeoc i-o cepa o ee j-o caa oeaec co c[i, j] 0. poe oo, oa oeeoc i-o cepa o ao eae oe aec co s[i] 0. poco aco ye ooec cepo caa c pcoe oepa.

ae cepa oe oo peca ape X, a j- ece i-o coa oopo oeea oea x[i, j] i-o cepa j-o caa. Taoe pacopoae yoo, e oe Caee oop o-aeaecx ay, poeccop Hoocpcoo ocyapceoo yepcae. E-mail: savelev@math.nsc.ru.

Cooo: 4M. 2007. 24.

.. Caee oa co cepo oe ca caa. Oe oe eoc cepo o y ea paccapaex ca a oo peca ape C, a j- ece i-o co a oopo oeea oea c[i, j] 0 oeeoc i-o c epa o ee j-o caa. Ec cep o ee ao o caa cac oaoo oee (c[i, j] = c[j], 1 j n), o eco ap oo paccapa cpoy C, a j- ece oopo oeea oea c[j] oee oc cepa o ee j-o caa. Oe oe oe eoc cepo o ao eae oo peca cpo o S, a j- ece oopo oeea oea s[i] 0 oe oe eoc i-o cepa. Hyo ec oe cepe oe caa c yeo oeeoc cepo.

1.1. puep c amopau uu. B e .B. aoa [1] cceyec e pax aopo a oppoae ecoo caocoa oo. oce eoopo py po yepa aop oo cec cey o ee aopa c yco aa ce (1), oa (2), yua (3), ymypa (4), peuu (5). coy ae opoca, poeeoo cpe accx pyooee o Hoocpca, pa pepa 10 ae, oo copypoa ceyy aay o cepo oee. pya m = 10 cepo oeae e n = 5 yaax aopo. oeeoc aoo c epo opoce, oopoy oocc j- aop, oeaec o 5-ao ae caec oaoo cex cepo:

C = {4, 5, 3, 4, 3} (c[1] = 4, c[2] = 5, c[3] = 3, c[4] = 4, c[5] = 3).

peaaee oe opeo oeeoc cepo ocaoo poo. B aece aepa oo c a, o oeeoc cex cepo o ee aoo a oo opoca oao:

C = {1, 1, 1, 1, 1} (c[j] = 1, 1 j 5).

oe oe oeeoc i-o cepa o ao ea e coyec ca s[i] eo pao oe. B pepe ca cep Bepomocma oe cnepmx oeo o oax ocaec cpoo S = {12, 25, 26, 37, 16, 21, 10, 16, 5, 15}, a i- ece oopo oee ca s[i] cepa c oepo i = 1, 2, , 10.

Ta a oeeoc cepa e cea opeeec eo cae, o aece aepa oo ca, o oa oeeoc cepo oaoa, cooa cpoy S = {1, 1, 1, 1, 1, 1, 1, 1, 1, 1} (s[1] = 1, 1 i 5).

cep pe 10-ay ay {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

Bcaee oe pecac ape, a j- ece i-o coa oopo oee a x[i, j] oea j-o aopa i- cepo:

8 6 10 10 3 8 10 10 10 4 10 4 7 6 6 8 8 8 5.

X = 5 5 7 5 5 5 5 6 6 6 5 5 8 3 5 6 6 5 2 5 2 2 3 1 2 3 1.2. puep c npooo emuocmu. B cae .T. a paoa, .. ya, A.B. Tpycoa [2] peaaec eo aaa ax cepoo opoca, opac a eey eppea ax, ocaec pep pee oo eoa pooy execoo coco oea peyae peaaeoo oeca epop. B o pepe pacca paec pya cepo = 2 eoe, oopa oeae m e a execoe cocoe oea peyaa oe opeeeoo oea pao, paaeoe poeax ee eoc: 75, 50, 25, 0, 25, 50, 75. ypoe ace ae ca opo oepa 1, 2, 3, 4, 5, 6, 7.

Oe pac epaa x = [0,1]. oeeoc a oo cepo o aoy paccapaex 7 ypoe ee eoc peoaaec oaoo opao caec, o C = {1, 1, 1, 1, 1, 1, 1} (c[j] = 1, 1 j 7).

.. Caee Oa oeeoc 1-o 2-o cepo cec cae [2] o opeeeo eoe paaec cpoo S = {0, 3, 1} (s[1] = 0,3, s[2] = 1).

Bcaee cepa oe pecac ape X, a j- ece i- cpo oopo oeeo co x[i, j] oea j-o aopa i- cepo:

0 0,1 0,4 1 0,4 0,1 X = 0 0 0 0 0,2 0,6 1.

B o oe pacpeee oocex oeo oe eoc cepo oe cepe oe paccapae x caa opeec a cpee ae ax cepa yax oeo.

peoaac ec: co m cepo x oe pa i;

co n caa x oepa j;

apa X, a j- ece i o coa oopo oeea oea x[i, j] 0 i-o cepa j o caa;

apa C, a j- ece i-o coa oopo oeea oea c[i, j] 0 oeeoc i-o cepa o ee j-o caa;

cpoa S, a i- ece oopo oeea oe a s[i] 0 oe oeeoc i-o cepa o ao ea e. oepe, o ce paccapaee e peo aac ooe ( 0).

2.1. Pacnpeeeu. ae oey c[i, j] oeeoc i o cepa o ee j-o caa oppoao oeo n q[i, j] = c[i, j] c[i, k] (1 i m,1 j n).

k = peoaaec, o aeae cpoo ooee ( 0).

Cpoa Q[i] = {q[i, 1], q[i, 2], , q[i, n]} (1 i m) ocae pac peeee oeeoc i-o cepa o ea paccap Bepomocma oe cnepmx oeo n aex caa: q[i, j] 0, q[i, j] =1.

j = Ta opao, apa C aeec ape Q, a j- ece i-o coa oopo oeea eea oea q[i, j] oeeoc i-o cepa o ee j-o caa. Ec cep o ee aoo caa cac oaoo oee (q[i, j] = q[j], 1 j n), o eco ap oo paccapa cpoy Q, a j- ece oopo oeea e ea oea q[j] oeeoc cepo o ee j-o c aa. Ec oeeoc cex cepo o aoy paccapaeoy opocy oao, o oo opao c a, o c[j] = 1, q[j] = 1/n (1 j n). p ao paoepo ea eec oo aca ax cepa oe o. Coooee ey ocac pe.

Too a e ae acoy oey s[i] oe oe eoc i-o cepa o ao eae oppoao oe m o t[i] = s[i] / s[k]. ec ae peoaaec, o aea i= e cpoo ooee. Cpoa T = {t[1], t[2], , t[m]} oc ae pacpeeee oeo oe oeeoc cepo:

m t[i] 0, =1. Ec oa oeeoc paccapae t[i] j= o pye opoco y cex cepo oaoa, o oo op ao ca, o s[i] = 1, t[i] = 1/m (1 i m). p ao pao epo ea eec oo aca ox cep x oeo. opoe coooe ey ocac pe .

2.2. Cpeue aeu. Beey oey u[i, j] i-o cepa j-o caa, yay eo oeeoc cooecye yo oac, opee paeco u[i, j] = q[i, j]x[i, j] (1 i m, 1 j n).

.. Caee Beee yae oe pecac ap e U, a j- ece i-o coa oopo oeea oea u[i, j] i-o cepa j-o caa. Oy oey v[j] j-o caa, ay pyo cepo, ya oy o eeoc aoo x paccapaeo poo oac , opee a cpeee aee eex ya m x oeo cepo: V [ j] = [i]u[i, j] (1 j n).

t i= Cpoa V = {v[1], v[2], , v[n]} ocae oe cep e oe paccapaex caa a ee o ae. a aa opaa, ee pyo coepaeo eppepoa. ya oyee oe eeco opao oppoa epeec yepcay ay co ae opee [0,1]. o ececeo cea y co coa: c oo x oe cy c oo aca o oyeo oe. c pae cya ye peoaa cyy s acy v cpoo ooe (>0).

cpo V oyac cpo P = {p[1], p[2], , p[n]} R = {r[1], r[2], , r[n]}, n e p[ j] = v[ j] / s s = v[k],1 j n k = r[j] = v[j]/v (v = Max[v[k], 1 j n]).

n co, o 0 p[ j], r[ j] 1, p[ j] = 1.

j = Cpoa P ocae pacpeeee, caoe c oye o cep oea paccapaex ca a. co p[j] xapaepye o j-o caa coo yoc cex paccapaex caa. co r[j] o cae oocey aoc j-o caa. Cpo P R c pee ocaeo aa.

Bepomocma oe cnepmx oeo Ec oeeoc cex cepo o aoy paccap aeoy opocy oao oaoa oa oeeoc ao pye opoco y cex cepo, o oo opao c a, o c[ j] =1 s[i] =1 q[ j] =1/ n t[i] =1/ m (1 i m;

1 j n).

B o cyae m m m 1 1 a[ j] = n v[ j] = n x[i, j] = x[i, j].

t[i]q[ j]x[i, j] = n m n m i=1 i=1 i= Cpoa A = {a[1], a[2], , a[n]} ocae cpee ape ece ax cepa oeo paccapaex ca a. cpee e ac o oeo aa cepo.

2.3. opoe cocma. Oe v[j], p[j], r[j] e op a xapaep, x e cea oo coepaeo ep pepoa. Ec cepe oe paa aoc y aex caa, o eecoopao paccapa op oe coca x oeo, pacoo caa o y a oeo:

W = {w[1], w[2], , w[n]}, e w[1] = v[j[1]] w[2] = v[j[2]]... w[n] = v[j[n]].

o yopoeo cpoe W oo coca cpoy J = {j[1], j[2], , j[n]} oepo caa, pacoaaxc o y a oyex oeo aoc x caa. Bc aa c pa oea pacoaac a cooecy x ecax pooo. Ta e cpoa oepo oyc p aee ce v[j[k]] ca p[j[k]] r[j[k]]. Bcaae c oepo j[1] o cepo oee ec aoee a, a caae c oepo j[n] aeee a. Cpo P R oo cpaa oocey aoc pax caa. Cpoa J ee pyx ac o peaae x opax peopaoa cxox oeo x[i, j], ax cepa. Ee oo ca aoee ae peyao cep. py coa, peya cep eecoo pao peca opoo ae, a e acoo.

.. Caee 2.4. Bucume aopum. Ta opao, o c cepe oe o peaaeo eoe yo cea ceyee.

1- a. aca:

1) co m peex cepo x oepa i;

2) co n paccapaex caa x oepa j;

3) apy X, a j- ece i-o coa oopo oeea oea x[i, j] 0 i-o cepa j-o caa;

4) apy C, a j- ece i-o coa oopo oeea oea c[i, j] 0 oeeoc i-o cepa o ee j-o caa;

5) cpoy S, a j- ece oopo oeea oea s[i] oe oeeoc i-o cepa o ao eae.

n m 2- a. Bc cy [i] = j], = o c[i, s[i] j=1 i= oe t [i] = s[i]/, q[i, j] = c[i, j] / [i] (1 i m,1 j n).

m 3- a. o opye v[ j] = t[i]q[i, j]x[i, j] (1 j n) i= c peaaey oy cepy oey v[j] j-o caa.

m 4- a. Bc e s = v[k], v = Max[v[k] > 0, r = 1 k n] ooe p[j] = v[j]/s, r[j] = v[j]/v (1 j n), xapae pye cooeceo o j-o caa cooyoc cex paccapaex caa oocey po j-o caa o a cep oea.

5- a. Bca caa ope ya x cepx oeo. (Bcaa c pa oea paco aac a cooecyx ecax pooo.) Bepomocma oe cnepmx oeo aeau. Ec cep o ee aoo caa cac oaoo oee (c[i, j] = c[j], 1 j n), o eco ap oo paccapa cpoy C, a j- ece oopo oeea oea c[j] oeeoc cepo o ee j-o caa. Ec oeeoc cex cepo o a oy yaeoy opocy oao, o oo opao c a, o (c[j] = 1, 1 j n).

Ec oa oeeoc paccapaeo pye o poco y cex cepo oaoa, o oo opao ca, o (s[i] = 1, 1 i m). Ec oeaec aoc aapy ex caa, o x pacooee ope ya oe o oaae pacooee o yee paaeo cep a caa aoc. ep caoc caae, oopoe o cepo oee caec aoee a, a oce caeec aeee a.

pe peoey oe pepa, oca yax 1.1 1.2.

3.1. Oea amopo uu. oca oe a e pepa 1.1 poo ce o yaa opya, oyae:

Q = {0,21, 0,26, 0,16, 0,21, 0,16} T = {0,07, 0,14, 0,14, 0,20, 0,09, 0,11, 0,05, 0,09, 0,03, 0,08} 1,68 1,26 2,11 2,11 0,63 1,68 2,11 2,11 2,11 2, 1,05 2,63 1,05 1,84 1,56 1,58 2,11 2,11 2,11 0, 0, U = 0,79 0,79 1,11 0,79 0,79 0,79 0,79 0,95 0, 1,26 1,26 1,05 1,05 1,68 0,63 1,05 1,26 1,26 1, 0,79 0,32 0,79 0,32 0,32 0,47 0,16 0,32 0,47 0, .. Caee V = {1,79, 1,65 0,86,1,14, 0,48} P = {0,30, 0,28, 0,15, 0,19, 0,08} R = {1, 0,92, 0,48, 0,64, 0,27} W = {1,79, 1,65, 1,14, 0,86, 0,48} J = {1, 2, 3, 4, 5} B cpoe V ee v[j] c oepo j ec oe cep o oeo j-o aopa. B cpoe P ee p[j] c oepo j xapaepye o j-o aopa cooyoc cex paccapaex aopo. B cpoe R ee r[j] c oe po j ocae ooceoe e j-o aopa. Cpoa J o aae, o o cep oea ooaee oepa aop pacoaac ope ya x cey opao: ce, oa, ymypa, yua, peuu. Oco oe e a eaoae ooe oo, o e cepo, oaae ce oa (58%). yypa, ya, pe oaa cooyoc eee e (42%). o pecaec paooo. oepe, o pe e oo o pepe pee peaaeo eo aaa peyao cepoo opoca. Meaoae ooe co co, x yee peye ceax yox coooecx cceoa. B acoc, y yoe aapyex pepe o ce, o, yyp, y , pe cee x a oppoae ecoo caocoa. Hyo o ae ya ay a coc paccapaex aopo, x aoe e.

pee cpae peya, oope oyac, ec peoo, o cep e oaoy yy oee oc o ce opoca oaoy oy oeeoc.

Q = {0,2, 0,2, 0,2, 0,2, 0,2} T = {0,1, 0,1, 0,1, 0,1, 0,1, 0,1, 0,1, 0,1, 0,1, 0,1} V = {1,70, 1,24, 1,06, 1,12, 0,62} Bepomocma oe cnepmx oeo P = {0,30, 0,22, 0,18, 0,20, 0,11} R = {1, 0,73, 0,62, 0,66, 0,36} W = {1,70, 1,24, 1,12, 1,06, 0,62} J = {1, 2, 3, 4, 5} Pacooee aopo o ocaoc pe. ec oo coooe ey : ce oeaec a ooceo oee e aop, a oe pc aec ooceo eee e (73% eco pex 92%). x oee e ocaec opy (52%). e e oa po cpoa cpex ao paccapa ex aopo A = {8,5, 6,2, 5,3, 5,6, 3,1}.

Aaoe peya oye py m = cepo. C yeo x aa pacpeeee ooc ee e aapyex aopo ocac cpoa P = {0,29, 0,28, 0,14, 0,18, 0,11} R = {1, 0,96, 0,46, 0,63, 0,34}.

oa aa cepo e yac, cpo e P = {0,29, 0,28, 0,14, 0,18, 0,11} R = {1, 0,77, 0,61, 0,62, 0,49}.

Pacooee aopo o ocaoc e e ca.

oyea oa cpoa cpex ao oepae o:

A = {8,51, 6,56, 5,20, 5,28, 4,18}.

3.2. poo emuocmu. oca oe a e pepa 1.2 poo ce o yaa opya, oyae:

Q = {1/7, 1/7, 1/7, 1/7, 1/7, 1/7, 1/7} T = {0,23, 0,77} .. Caee 0 0,14 0,57 0,143 0,057 0,014 U = 0 0 0 0 0,029 0,086 0, V = {0, 0,003, 0,013, 0,033, 0,035, 0,069, 0,110} P = {0, 0,012, 0,050, 0,125, 0,133, 0,263, 0,417} R = {0, 0,03, 0,12, 0,30, 0,32, 0,63, 1} W = {0,110, 0,069, 0,035, 0,033, 0,013, 0,003, 0} J = {7, 6, 5, 4, 3, 2, 1} B cpoe V ee v[j] c oepo j ec oe cep o oeo j-o ee ypo eoc. B cpoe P ee p[j] c oepo j xapaepye o j- oe coo yoc cex ax oeo. B cpoe R ee r[j] c oepo j ae ooee j- oe acao. Cpoa J oaae, o o cep oea ooaee oepa ypo ee eoc pacoaac ope ya e: 75%, 50%, 25%, 0, 25%, 50%, 75%.

p o epe 2 oe ece e oe cooy oc o 68%. Ha ocae 5 oeo pxoc 32%. Ha oee epo pecaec yeee eoc a 75%. C oe yepeoc a ocoa oyex cep x oeo oo poopoa yeee eoc a 50% 75%.

aeaue. B cae [2] aece cepo oe ya aec 50%. o peya oyaec p oaaeo ea cooa aco oe. Boeee cee t[1] = 0,3 oeo x[1, j] epoo cepa ae cpoy eo eex oeo {0,05, 0,76, 1, 0,76, 0,5, 0}. ae, o p ao ea yeee oeeoc cepa ee yee eo oeo. Boeee cee t[2] = 1 oeo x[2, j] opoo cepa e ee x: {0, 0, 0, 0, 0, 2, 0, 6, 1}. B pa x cpoax a ao ece ay oey, oy ae cpoy yo {0, 0, 0, 0, 0, 0,2, 0,5, 0}. Macaa Bepomocma oe cnepmx oeo x ax oeo poopye oee eoc a 50%.

3.3. Mameamuecoe ouaue. peya oya ec, ec cooa epooce eo. ee eop epooce oe e .B. eeo A.. Xa [3].

Paccop opeeey a oece = {1, 2, 3, 4, 5, 6, 7} oe po cyay epeey co ae: [1] = 75, [2] = 50, [3] = 25, [4] = 0, [5] = 25, [6] = 50, [7] = 75.

Pacpeeee cyao epeeo opee, co y yaoe eae peyao, oppy a e cepa oe yaae oe oeeoc c epo. Hoppoae o opye p[i, j] = x[i, j] / x[i, k] r = (1 i 2, 1 j 7) pepaae 1- 2- cpo X[1] X[2] a p X, ax cepa oeo, cooeceo cpo P1 = {0, 0,05, 0,2, 0,5, 0,2, 0,05, 0} P2 = {0, 0, 0, 0, 0,11, 0,33, 0,056} o ee p[1, j] cpo p1 a oppoay oey t[1] = 0,23 oeeoc 1-o cepa, a ee p[2, j] cpo p a oppoay oey t[2] = 1 oeeoc 2-o cepa. Ca a peya, o opye Pr [[ j]] = t [1] p[1, j] + t [2] p[2, j] (1 j 7) oyae pacpeeee Pr = {0, 0,011, 0,046, 0,115, 0,132, 0,268, 0,428} cyao epeeo. Ha j- ece cpoe Pr co epooc Pr[[ j]] oo, o cyaa epeea pe aee [ j]. Maeaecoe oae M cyao epeeo pao M = j] Pr[[ j]] = 47.

[ j= Moo oa, o peyae peaaex epop eoc occ a 47%. Opyee ae 50%. ae , o Pr =[ 50] = Pr [[6]] + Pr [[7]] = 0,268 + 0,428 0,7, .e. c oo epooc eoc occ a 50% .. Caee oe. oyea epooc 0,696 a yaao ye 3.2 oe 0,68 ee eoc a 50% 75%.

poe oo, Pr[ 0] = Pr[[4]] + Pr[[5]] + Pr[[6]]+ Pr[[7]] = = 0,115 + 0,132 + 0,268 + 0,428 0,94.

Ocoac a ao cepo oee oo c yepe oc yepa, o peyae peaaex epop eoc e oc. Bepooc oo, o oa o cc a 25% oe paa peo 83%. Ta o eo cepa ae ocec poo.

TEPATPA 1. ao .B. Meaoae ooe opocx oo.

Hoocpc: Bec HPCOO, 2006.

2. apao .T., myu .., Tpyo A.B. Heee oeca cepo opoce // Cooo: eooo, eo, aeaece oe. 2004. 19.

C. 142157.

3. eeo .B., Xuu A.. eeapoe eee eop epooce.

M.: Haya, 1982.




2011 www.dissers.ru -

, .
, , , , 1-2 .