A?aeiia?aeaeueiee ca aeione A.?. Eeoaeiaiei

I?aeienaii aei ae?oeo 10.11.98. Oi?iao 60o90/16.

Iai?? ionaoiee. Oiiai. ae?oe. a?eoo?a 1,00.

Oe?aae 100 i?ei. Caiiaeaiiy ?375.

Iaae?oeiaaii o aeaeaaieoeoa? OAeOO,

325008, i.Oa?nii, Aa?eneaanueea oina, 24.

I?I?NOA?NOAI INA?OE OE?A?IE

OA?NIINUeEEE AeA?AEAAIEE OAOI?*IEE OI?AA?NEOAO

EEAAEEI ?AI? ?AAIIAE*

OAeE 519.816

IIAeAE? NENOAI I?AeO?EIEE I?EEIssOOss ??OAIUe

A OI?AAE?II? AE?IAIEOeOAII

IA INIIA? OAI??? IA*?OEEO IIIAEEI

05.13.06 — Aaoiiaoeciaai? nenoaie oi?aae?iiy

oa i?ia?aneai? ?ioi?iaoe?ei? oaoiieia??

AAOI?AOA?AO

aeena?oaoe?? ia caeiaoooy iaoeiaiai nooiaiy

eaiaeeaeaoa oaoi?/ieo iaoe

OA?NII — 1999

Aeena?oaoe??th ? ?oeiien.

?iaioo aeeiiaii ia eaoaae?? i?ia?aiiiai caaacia/aiiy AII Oa?niinueeiai
aea?aeaaiiai oaoi?/iiai oi?aa?neoaoo.

Iaoeiaee ea??aiee: aeieoi? oaoi?/ieo iaoe, i?ioani?, Oiaeaeia A?eoi?
?ai?iae/, OAeOO, caa?aeoth/ee eaoaae?ith i?ia?aiiiai caaacia/aiiy AII

Iaoeiaee eiinoeueoaio: eaiaeeaeao oaoi?/ieo iaoe, aeioeaio,
?iaaeuenueeee O?aioe Ai?eniae/, OAeOO, i?i?aeoi? c
iaa/aeueii-iaoiaee/ii? ?iaioe

Io?oe?ei? iiiiaioe:

Iaoeiaee ea??aiee: aeieoi? oaoi?/ieo iaoe, i?ioani?, Oiaeaeia A?eoi?
?ai?iae/, OAeOO, caa?aeoth/ee eaoaae?ith i?ia?aiiiai caaacia/aiiy AII

Iaoeiaee eiinoeueoaio: eaiaeeaeao oaoi?/ieo iaoe, aeioeaio,
?iaaeuenueeee O?aioe Ai?eniae/, OAeOO, i?i?aeoi? c
iaa/aeueii-iaoiaee/ii? ?iaioe

Io?oe?ei? iiiiaioe:

1. Aeieoi? oaoi?/ieo iaoe, i?ioani? Oa?iiiaa Iaoae?y Aaea???aia,
Oa?e?anueeee aoiai?oa?iee ?inoeooo «Ia?iaeia Oe?a?inueea Aeaaeai?y»,
i?i?aeoi? c iaoeiai-aeine?aeii? ?iaioe

2. Aeieoi? oaoi?/ieo iaoe, i?ioani? Eieioei Aieiaeeie? Naiaiiae/,
Iaeanueeee ?inoeooo nooiiooieo a?enuee I?iiai?iie Oe?a?ie, i?ioani?
eaoaae?e a?enueeiai? e?aa?iaoeee oa ?ioi?iaoeee

I?ia?aeia onoaiiaa:

Oa?e?anueeee aea?aeaaiee oaoi?/iee oi?aa?neoao ?aae?iaeaeo?ii?ee

Caoeno a?aeaoaeaoueny “ ” 1999 ?. i aiaeei?
ia can?aeaii? niaoe?ae?ciaaii? a/aii? ?aaee E67.052.01 o Oa?niinueeiio
aea?aeaaiiio oaoi?/iiio oi?aa?neoao? ca aae?anith: Oe?a?ia, 325008, i.
Oa?nii, Aa?eneaanueea oina, 24, ei?i.3, aoae. 320.

C aeena?oaoe??th iiaeia iciaeiieoeny a a?ae?ioaoe? Oa?niinueeiai
aea?aeaaiiai oaoi?/iiai oi?aa?neoaoo ca aae?anith: Oe?a?ia, 325008,
i.Oa?nii, Aa?eneaanueea oina, 24.

Aaoi?aoa?ao ?ic?neaiee “ ” 1999?.

A/aiee nae?aoa?

niaoe?ae?ciaaii? a/aii? ?aaee
Eino?i A.I.

1

CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE

Aeooaeuei?noue oaie. Aeey no/aniiai ??aiy ?icaeoeo nenoai oi?aae?iiy
i?aei?e?inoaaie oa?aeoa?iei ? oa, ui a?eueo?noue caaea/ oi?aae?iiy oa
ieaioaaiiy ae??oo?oueny a oiiaao iaaecia/aiino?, iaoi/iino? e
iaaeinoaoiino? ?ioi?iaoe?? i?i i?ioeane e oiiae ooieoe?iioaaiiy
ae?iaieoeoaa, i?i aieea ciai?oiueiai na?aaeiaeua. I?e ieaioaaii?,
oi?aae?ii? e i?eeiyoo? ??oaiue iaiao?aeii a?aoiaoaaoe ia o?eueee
iaaecia/ai?noue oa?aeoa?enoee ae?iaie/eo nenoai, aea e iaaecia/ai?noue
aieeao ciai?oiueiai na?aaeiaeua, iaaeinoaoi?noue, iaoi/i?noue
?ioi?iaoe??, ?? aeeiai?/i?noue oa aaaaoi ?ioeo ia?aiao??a. Ana oea
noaiiaeoue aeaiaio iaaecia/aiino? o a?aeiioaii? aei ieaioaaiiy e
i?eeiyooy ??oaiue. I?e ?ic?iaoe? iiaeaeae oa aeai?eoi?a, ?ioi?iaoe?eieo
oaoiieia?e iaiao?aeii a?aoiaoaaoe an? oe? /eiieee e ?icaeyaeaoe ?iaioo
ae?iaie/eo nenoai a oiiaao iaaecia/aiino?.

?nio? aaeeeee ?ic?ea i?ae cia/ieie ianyaaie aeinooiii? ?ioi?iaoe??, ui
ae?iaey?oueny nenoaiaie oi?aae?iiy, e ?aaeueieie iiaeeeainoyie ii ?o
ni?eeiyooth oa ia?iaoe? i?e ieaioaaii? e o i?ioeanao i?eeiyooy ??oaiue a
oi?aae?ii? ae?iaieoeoaii. Oe? i?iaeaie noaaeyoue caaea/o ?ic?iaee iiaeo
iaoiae?a, iiaeaeae, aeai?eoi?a ? i?ia?ai aeey nenoai i?aeo?eiee
i?eeiyooy ??oaiue (NII?).

Ca’ycie ?iaioe c iaoeiaeie i?ia?aiaie, ieaiaie, oaiaie. Aeena?oaoe?ei?
aeine?aeaeaiiy i?iaiaeeeeny a?aeiia?aeii aei aea?aeaaieo
iaoeiai-oaoi?/ieo i?ia?ai 6.2.2 — Ia?niaeoeai? ?ioi?iaoe?ei? oaoiieia??
oa nenoaie; 6.2.1 — ?ioaeaeooae?caoe?y i?ioean?a i?eeiyooy ??oaiue, a
oaeiae ieai?a ii I?i?noa?noaai ina?oe, aeiiii?ee Oe?a?ie ii
Oa?niinueeiio aea?aeaaiiio oaoi?/iiio oi?aa?neoaoo.

Iaoa oa caaea/? aeine?aeaeaiiy. Iaoith aeaii? ?iaioe ? i?aeaeuaiiy
aoaeoeaiino? oa yeino? i?aeo?eiee i?eeiyooy ??oaiue a oi?aae?ii?
ae?iaie/eie nenoaiaie ca oiia iaaecia/aiino? oeyoii noai?aiiy
?ioaeaeooae?ciaaii? nenoaie i?aeo?eiee i?eeiyooy ??oaiue, ui caniiaaia
ia ?ic?iaoe? oa aeei?enoaii? iiaeaeae i?eeiyooy ??oaiue.

Iniiaiith caaea/ath aeine?aeaeaiiy ? ?ic?iaea nenoaie i?eeiyooy ??oaiue
a oi?aae?ii? ae?iaieoeoaii (NI?OA) aeey ?aae?caoe?? NII? o

18

A i?ioeanna ?aaeecaoeee ?acoeueoaoia enneaaeiaaiee ?ac?aaioai iaeao
i?eeeaaeiuo i?ia?aii, ?aaeecothuee ?ac?aaioaiiua iiaeaee e aeai?eoiu
i?eiyoey ?aoaiee a oi?aaeaiee i?iecaiaenoaii.

A ?aaioa i?eaaaeaiu iiaeaee, iaoiaeu, iaoaieciu e aeai?eoiu,
iicaieythuea iiauneoue yooaeoeaiinoue i?eiyoey ?aoaiee i?e oi?aaeaiee
i?iecaiaenoaaiiuie nenoaiaie, a /anoiinoe, i?e eaeaiaea?iii
ieaie?iaaiee. I?aeoe/aneia i?eiaiaiea ?acoeueoaou ?aaiou iaoee a aeaea
iaeaoia i?eeeaaeiuo i?ia?aii iiaenenoai iiaeaea?aeee i?eiyoey ?aoaiee.

Eeth/aaua neiaa: oi?aaeaiea, iaii?aaeaeaiiinoue, ia/aoeinoue, nenoaia
iiaeaea?aeee i?eiyoey ?aoaiee, iiiaie?eoa?eaeueiinoue, eeoei,
i?eieiathuaa ?aoaiea, nenoaia i?iecaiaenoaa.

SUMMARY

Kybalko I.I. Models of decision support systems in production management
based of theories of indistinct sets. — Manuscript.

A thesis on competition of the candidate degree in technical sciences on
a speciality 05.13.06 — automated control systems and progressive
information technologies. Kherson State Technical University, Kherson,
1998.

The mathematical models, algorithms and programs for efficiency and
quality rise of the decision making support in industrial systems in
conditions of uncertainty are offered and developed. The basis of the
decision support system is models of a bag type that extended by using a
theory of indistinct sets and a relaxation mechanism.

The operation production features in conditions of uncertainty are
investigated, the major factors applications reducing efficiency of
existing decision making support models are defined.

The model of a bag-relaxational type for decision making support is
developed. The known models and algorithms of problem solving of the
given class are advanced already.

The methods of an efficiency and quality evaluation of DSS constructed
based on SDMPM are represented.

Keywords: controlling, uncertainty, illegibility, decision support
system, multicriteriation, the person which adopt the decision, system
of production.

3

o/aiai-iaoiaee/iiai e i?aai?caoe?eii-iaoiaee/iiai oa?aeoa?o a
Oa?niinueeiio aea?aeaaiiio oaoi?/iiio oi?aa?neoao?.

Oai?aoe/i? oa i?aeoe/i? ?acoeueoaoe aeena?oaoe?eii? ?iaioe
aeei?enoiaoaaeeny oaeiae i?e aeeiiaii? ia eaoaae?? i?ia?aiiiai
caaacia/aiiy AII Oa?niinueeiai aea?aeaaiiai oaoi?/iiai oi?aa?neoaoo
?yaeo ainiaeiaia??ieo iaoeiai-aeine?aeieo ?ia?o (?a?no?aoe?ei? iiia?e
36/92, 39/92).

Iaoeia? iieiaeaiiy, aeniiaee oa ?aeiiaiaeaoe?? aeena?oaoe?eii? ?iaioe
aeei?enoai? a iaa/aeueiiio i?ioean? i?e i?aeaioiaoe? ?yaeo eo?n?a aeey
nooaeaio?a niaoe?aeueiino? 7.080403 «I?ia?aiia caaacia/aiiy
aaoiiaoeciaaieo nenoai».

Iniaenoee aianie caeiaoaa/a. An? iieiaeaiiy, ui aeiinyoueny ia caoeno,
iaeaaeaoue iniaenoi aaoi?o. C ?ia?o, aeeiiaieo o ni?aaaoi?noa?, ia
caoeno aeianaii o?eueee iaoa??ae, ui iaeaaeeoue aaoi?o.

Ai?iaaoe?y ?acoeueoao?a aeena?oaoe??. Iniiai? ?acoeueoaoe
aeena?oaoe?eii? ?iaioe aeiiia?aeaeeny e iaaiai?thaaeeny ia II
iaoe?iiaeuei?e iaoeia?e eiioa?aioe?? «?ioi?iaoeea: oai??y, oaoiieia?y,
oaoi?ea — ?OOO-95», Iaeana, 1995; i?aeia?iaei?e eiioa?aioe?? «Nicaeaiea,
eioaa?aoeey, eniieueciaaiea eioi?iaoeeiiiuo ?ano?nia eiiiaaoeeiiiiai
?acaeoey», Ee?a, 1997; IV i?aeia?iaei?e iaoeiai-i?aeoe/i?e eiioa?aioe??
«Eioi?iaoeeiiiua ?ano?nu: nicaeaiea, eioaa?aoeey e eniieueciaaiea»,
Aooa, 1997; ia nai?ia?ao iaoeiai? ?aaee AI Oe?a?ie c i?iaeai
«E?aa?iaoeea», «I?eeeaaei? i?iaeaie ?ioi?iaoeee», Oa?nii, 1995-1998??.;
i?aeia?iaei?e eiioa?aioe?? ii iaoaiaoe/iiio iiaeaethaaiith «Iaoaiaoe/i?
iiaeae? oa no/ani? ?ioi?iaoe?ei? oaoiieia?? «, Ee?a, 1998.

Ioae?eaoe??. ?acoeueoaoe aeeiiaii? ?iaioe a?aeia?aaeai? o 12 ae?oeiaaieo
i?aoeyo.

No?oeoo?a e ianya ?iaioe. ?iaioa neeaaea?oueny c anooio, /ioe?ueio
?icae?e?a, aeniiaeo, ia?ae?eo e?oa?aoo?e c 221 iaeiaioaaiiy oa
aeiaeaoe?a. Iniiaiee ci?no ?iaioe aeeeaaeaii ia 151 noi??ioe?, ?iaioa
i?noeoue 20 ?enoie?a oa 3 oaaeeoe?.

INIIAIEE CI?NO ?IAIOE

O anooi? iaa?oioiaaia aeooaeuei?noue oaie e iaiao?aei?noue ?ic?iaee
iiaeaeae nenoai i?aeo?eiee i?eeiyooy ??oaiue a oi?aae?ii? ae?iaieoeoaii
a oiiaao iaaecia/aiino?, iieacai? iaoeiaa iiaecia oa i?aeoe/ia
oe?ii?noue ?iaioe, aeeeaaeai? iniiai? io?eiai? ?acoeueoaoe.

16

//Eioi?iaoeeiiiua ?ano?nu: oaoiieiaee, eiiioieeaoeee. — Oa?nii. — 1997.
— N.81-85.

11. Eeaaeei E.E., Neaei?oe A.A. ?ac?aaioea iiaeaeae ?theca/iiai oeia
aeey iiaeaea?aeee i?eiyoey ?aoaiee //Eioi?iaoeeiiiua ?ano?nu: nicaeaiea,
eioaa?aoeey e eniieueciaaiea / Na. aeieeaaeia IV iaaeaeoia?iaeiie
iao/ii-i?aeoe/aneie eiioa?aioeee. — Aooa, 1997. — N.105-108.

12. Eeaaeei E.E. Eniieueciaaiea eioi?iaoeeiiiuo oaoiieiaee i?e
?ac?aaioea YN //Nai?iee Iaaeaeoia?. eiio. «Nicaeaiea, eioaa?aoeey,
eniieueciaaiea eioi?iaoeeiiiuo ?ano?nia eiiiaaoeeiiiiai ?acaeoey». —
Eeaa. — 1997. — N.78.

AIIOAOe?ss

Eeaaeei ?.?. Iiaeae? nenoai i?aeo?eiee i?eeiyooy ??oaiue a oi?aae?ii?
ae?iaieoeoaii ia iniia? oai??? ia/?oeeo iiiaeei. — ?oeiien.

Aeena?oaoe?y ia caeiaoooy a/aiiai nooiaiy eaiaeeaeaoa oaoi?/ieo iaoe ca
oaoii 05.13.06 — aaoiiaoeciaai? nenoaie oi?aae?iiy ? i?ia?aneai?
?ioi?iaoe?ei? oaoiieia??. Oa?niinueeee aea?aeaaiee oaoi?/iee
oi?aa?neoao, Oa?nii, 1998.

Cai?iiiiiaai? e ?ic?iaeai? iaoaiaoe/i? iiaeae?, iaoiaee oa aeai?eoie
aeey i?aeaeuaiiy aoaeoeaiino? oa yeino? i?aeo?eiee i?eeiyooy ??oaiue o
ae?iaie/eo nenoaiao ca oiia iaaecia/aiino? oeyoii noai?aiiy nenoaie
i?aeo?eiee i?eeiyooy ??oaiue ia iniia? iiaeaeae ?theca/iiai oeio
?icoe?aieo iaoaiaoe/iei aia?aoii oai??? ia/?oeeo iiiaeei.

Aeine?aeaeaii iniaeeaino? ooieoe?iioaaiiy ae?iaieoeoaa a oiiaao
iaaecia/aiino?, aecia/ai? iniiai? /eiieee, ui cieaeothoue aoaeoeai?noue
canoinoaaiiy ?nioth/eo iiaeaeae i?aeo?eiee i?eeiyooy ??oaiue.

?ic?iaeaii iiaeaeue ?theca/ii-?aeaenaoe?eiiai oeio aeey i?aeo?eiee
i?eeiyooy ??oaiue, o ye?e aeei?enoai? e oaeineiiaeai? aaea a?aeii?
iiaeae? e aeai?eoie ??oaiiy caaea/ aeaiiai eeano. Iiaeaii iaoiaee
ioe?iee aoaeoeaiino? oa yeino? NII?, iiaoaeiaaii? ia iniia? NI?OA.

Eeth/ia? neiaa: oi?aae?iiy, iaaecia/ai?noue, ia/?oe?noue, nenoaia
i?aeo?eiee i?eeiyooy ??oaiue, aaaaoie?eoa??ei?noue, iniaa, ui i?eeia?
??oaiiy, nenoaia ae?iaieoeoaa.

5

ia/?oeino?, iaiiaiioe, oiio iaiao?aeii aeei?enoiaoaaoe nenoaio, ui
a?aoiao? an? noi?iie iaaecia/aiino? ?ioi?iaoe?? a i?ioean? i?eeiyooy
??oaiue.

Cai?iiiiiaaii eiioeaioe?th nenoaie i?eeiyooy ??oaiue a oi?aae?ii?
ae?iaieoeoaii (NI?OA). NII? ? ooieoe?iiaeueiei aeieii, ui
aaciina?aaeiuei ?aae?co? aca?iiae?th c II?, a NI?OA, a?aeiia?aeii aei
cai?iiiiiaaii? eiioeaioe??, ? aeiiii?aeiei eiiiiiaioii, ui
neeaaea?oueny c cania?a iiaeaethaaiiy i?eeiyooy ??oaiue, oa eiio?ieth?
i?ioean ooieoe?iioaaiiy NII?. Ia?aia no?oeoo?a aeicaiey? NI?OA ae?iaeoe
oa cai?iiiioaaoe II? aeae?eueea aeueoa?iaoeaieo ??oaiue e aeacaoe ia
iaea?eueo iioeiaeueia (c ?? oi/ee ci?o) ??oaiiy. Oaeei /eiii, NI?OA ?
nenoaiith, ui caaacia/o? i?aeo?eieo i?eeiyooy ??oaiue.

Aeei?enoaiiy eiioeaioe?? NI?OA i?e ?ic?iaoe? cania?a oi?aae?iiy
ae?iaie/eie i?ioeanaie aeicaiey? i?aeaeueoe iieacieee yeino? e
aoaeoeaiino? NII? ca ?aooiie aeei?enoaiiy iiaeae?
?theca/ii-?aeaenaoe?eiiai oeio c canoinoaaiiyi aia?aoo ia/?oeeo iiiaeei.

Aecia/aii, ui i?ioeaaeo?e iiooeo ??oaiue NI?OA iiaeii? a?aoiaoaaoe
iaoi/i?noue oa iaiiaiioo ?ioi?iaoe??, iia’ycaii? c i?ioeanaie
oi?aae?iiy, ui iio?aao? iayaiino? a nenoai? cania?a iiaeaethaaiiy
ia/?oei? oa iaoi/ii? ?ioi?iaoe??, ui iiaeooue aooe noai?ai? c
aeei?enoaiiyi iaoaiaoe/iiai aia?aoa oai??? ia/?oeeo iiiaeei ? oai???
i?eeiyooy ??oaiue. Aeey i?aai?caoe?? ooieoe?iioaaiiy nenoaie iaiao?aeia
oaeiae iayai?noue iaoai?ci?a naiiiaa/aiiy ia iniia? aiae?co oa eiio?ieth
i?eeiyoeo ??oaiue, ui iiaeooue aooe ?aae?ciaai? ca aeiiiiiaith ?nioth/eo
iaoiae?a ooo/iiai ?ioaeaeoo.

O ae?oaiio ?icae?e? aeeeaaeai? ?acoeueoaoe aeine?aeaeaiue, iia’ycaieo ?c
ae??oaiiyi iinoaaeaii? caaea/? — ?ic?iaeith iiaeaeae nenoai i?aeo?eiee
i?eeiyooy ??oaiue a oi?aae?ii? ae?iaieoeoaii ia iniia? oai??? ia/?oeeo
iiiaeei, aeei?enoiaoaaieo o NII? aeey iie?ioaiiy aoaeoeaiino? oa yeino?
oi?aae?iiy ae?iaie/eie nenoaiaie.

?ic?iaeaii iiaeae? ?theca/ii-?aeaenaoe?eiiai oeio, iaoai?cie
aeei?enoaiiy iiaeaeae a oiiaao iaaecia/aiino? oa oi?ioaaiiy iiaeaeae
ia/?oeiai aeai?o aeueoa?iaoea. ?ic?iaeaii aeai?eoie ?ica’ycaiiy
iinoaaeaieo caaea/. Iaaaaeaii caaaeuei? i?eioeeie ?ioa?aaeueii?
a?eoiaoeee, ui aeei?enoiao?oueny aeey i?ia?aiii? ?aae?caoe?? ?ic?iaeaii?
iiaeae? ?theca/ii-?aeaenaoe?eiiai oeio.

14

?theca/iiai oeio ca oiiae ?? ?icoe?aiiy iaoaiaoe/iei aia?aoii, yeee
aeicaiey? a?aoiaoaaoe aeeiai?eo i?ioeano oi?aae?iiy, iaaecia/ai?noue oa
noia?a/eea?noue ?ioi?iaoe??.

3. I?iaaaeaiee aiae?c a?aeiieo iiaeaeae iieacaa iaeii?eaeaoi?noue ?o
aeey ?ica’ycaiiy caaea/ oi?aae?iiy o ae?iaie/eo nenoaiao. O yeino?
iniiae nenoaie cai?iiiiiaaia aeei?enoaiiy oai??? ia/?oeeo iiiaeei, ui
iaaea? iiaeeeaino? aeey iieno ?ioi?iaoe?? i?i ia’?eoe, ?o aeanoeainoae,
a?aeiioaiue oa ca’yce?a o i?inoi?? i?eeiyooy ??oaiue, aeey iieno
iaiaaeaiue, a oaeiae aeicaiey? a?aoiaoaaoe iaaecia/ai?noue oa
noia?a/eea?noue.

4. ?ic?iaeaii iaoiaeeeo oi?iae?caoe?? caaea/ i?eeiyooy ??oaiue a
oi?aae?ii? ae?iaieoeoaii, a iniiao yei? iieeaaeaii caaaeueiee i?aeo?ae
aei i?aaenoaaeaiiy ?ioi?iaoe?? i?i i?ioeane oi?aae?iiy, caniiaaiee ia
aeei?enoaii? ?ioi?iaoe?eii? iiaeae? i?inoi?o i?eeiyooy ??oaiue, e
iaoaiaoe/iee aia?ao ia/?oeeo iiiaeei. Iieacaii, ui aeei?enoaiiy aeaiiai
aia?aoa aeicaiey? aeaeea?aoeaii i?aaenoaaeoe ?ioi?iaoe?th, iaiao?aeio
aeey ?ica’ycaiiy iinoaaeaieo caaea/.

5. ?ic?iaeaii iiaeaeue ?theca/ii-?aeaenaoe?eiiai oeio aeey i?eeiyooy
??oaiue, yea caniiaaia ia ?theca/i?e iiaeae? e ? oaeith, ui ia?aaeaa/a?
iayai?noue ia/?oeeo ioe?iie aeaiaio?a ? ia/?oeiai ii?yaeeo aeaiaio?a o
?thecaeo. Io?eiaia iiaeaeue aeicaiey? caaacia/eoe aoaeoeaia oi?aae?iiy
ae?iaie/eie i?ioeanaie, i?enei?th? i?eeiyooy ??oaiue e aea?
iaa?oiooaaiiy aeai?o iaee?auiai ??oaiiy c ?yaeo aeueoa?iaoeaieo.

6. C iaoith i?aeaeuaiiy aoaeoeaiino? e ciaioaiiy iia??oiino? ?ica’ycaiiy
caaea/? cai?iiiiiaaiee noaiioeiaeueiee ?aeaenaoe?eiee aeai?eoi,
iiaoaeiaaiee ia ia/?oeiio iaca’yciiio a?ia?a?ao? ia?aaaa aeey ni?iuaiiy
aeaeo oe?eueiai? ooieoe??, ui iaenei?co?oueny.

7. Cai?iiiiiaaii iaoiaee ioe?iee yeino? e aoaeoeaiino? NII? ca
aeiiiiiaith ?yaeo ia/?oeeo iieaciee?a, cai?iiiiiaai? iaoiaee cai?o e
aiae?co aeaieo aeey i?iaaaeaiiy oaei? ioe?iee. Ii??aiyeueia ioe?iea
yeino? NII?, ?ic?iaeaieo ?c canoinoaaiiyi NI?OA ? c aeei?enoaiiyi
o?aaeeoe?eieo i?aeoiae?a iieacaea, ui canoinoaaiiy NI?OA aeicaiey?
iie?ioeoe ye?noue oa aoaeoeai?noue NII? a oi?aae?ii? ae?iaieoeoaii. Ia
ii/aoeiaiio aoai? ooieoe?iioaaiiy NI?OA i?ia?a? a aoaeoeaiino?
o?aaeeoe?eiei NII?, ine?eueee iio??aai aeayeee /an ia iaa/aiiy oa
naiiiaa/aiiy.

7

ia?aaaa II? iiaea aooe iiaoaeiaaia a?ia?ia a?aeiioaiiy
ia?aaaae/aaeaeoaeino?, ui o caaaeueiiio aeiaaeeo ? /anoeiaei
eaac?ii?yaeeii. Oeae eaac?ii?yaeie iiaea aooe iiaeaiee o aeaeyae?
a?ia?a?aoa G=(V, U), aea U — iiiaeeia aeoa, ni?yiiaaieo a?ae a?eueo
e?aueo aei iaio e?aueo aeaiaio?a. Iaoae aoaeo a?ae aeeiiaiiy eiaeiiai
aeaiaioa iV oa?aeoa?eco?oueny aeayeei iaiaaaoeaiei /eneii ni; ai —
aaee/eia ?ano?no, iaiao?aeiiai aeey aeeiiaiiy aeaiaioa i; b — iaiaaeaiiy
ia ?ano?n; xi — ia/?oea aoeaaa ci?iia, ui aei??aith? 1, yeui aeaiaio i
aeeth/a?oueny a /enei a?ae?a?aieo, 0 — o i?ioeaiiio aeiaaeeo e ia?
ooieoe?? ?iciiae?eo iiaeeeainoae ia cia/aiiy a ae?aiacii? [0,1].
?icaeyiaii a oaeeo oiiaao caaea/o i?i oi?ioaaiiy eaeaiaea?iiai ieaio,
iinoaiiaea yei? ia? aeaeyae

iaenei?coaaoe wmetafile8? ?????????????
???????????yyy????.????1?????? ??????? a
???&??yyyy?????Ayyycyyya??‚?? ???&?
?MathType???????u@th??????i?e oiiaao wmetafile8? ??N???????????
???????????yyy????.????1?????? ???????
aA???&??yyyy?????Ayyycyyy???‚?? ???&?
?MathType???????u@th??????Ae??oaiiy aeaii? caaea/? ?noioii caeaaeeoue
a?ae aeaeo a?ia?a?aoa G. I?e a?aenooiino? ca’yceo i?ae aeaiaioaie ca
ia?aaaaith (on? iaii??aiyii?) caaea/a a?eueia a?ae iaiaaeaiue (G
aaniethoii iaca’yciee) e ? cae/aeiith caaea/ath i?i ?thecae.

sseui a?ia?a?ao ia?aaaa i?noeoue eiioo?e aai ? neeueii ca’yciei, caaea/a
iiaea ia iaoe aeiaeiiai i?eionoeiiai ??oaiiy. O oeueiio aeiaaeeo
aeo?aeia no?oeoo?a G iiaeiia aooe ia?aoai?aia aei iaei??? c a?aeiieo
no?oeoo? (C, NC, T, NT, R, S, S’,Z ,NZ ,P ,K — ?en. 1), aeey yeeo
a?aeiia?aeia caaea/a ia? ??oaiiy.

Aeey e?i?eiiai ii?yaeeo N caaea/a ae??oo?oueny i/aaeaeiei aeai?eoiii ?c
o?oaeii?noe?noth I (log n) iia?aoe?e. Aeey no?oeoo?e NC caaea/a iiaea
aooe ae??oaia -iaaeeaeaiei aeai?eoiii ?c o?oaeii?noe?noth O(nm/), aea m
— /enei eaioethaee?a. Aeey aeayeeo ie?aieo aeiaaee?a ?icoa?iaaieo
no?oeoo? (?c aeiaeaoeiaeie aeiiaaie aea?aaeaioiino? aai iaii??aiyiiino?
aeaiaio?a o i?ioa?eao) caaea/a iiaea aooe caaaeaia c? ciaioaiiyi
?ici??iino? aei aeiaaeeo iaca’yciiai a?ia?a?aoa.

Aeey no?oeoo? oeio T oa NT a?aeiiee -iaaeeaeaiee aeai?eoi ?c
o?oaeii?noe?noth I(n2/). O aeiaaeeo no?oeoo? oeio R ? aeioe?eueiei
iiia?aaei? ia?aoai?aiiy aei O oa S. Caaaeueiee aeiaaeie S
ii noo?

12

A?aecia/aii, ui ?ic?iaeaia iiaeaeue ? iaiiaiith, aea naiaioe/ii
ianoia?a/eeaith e aaeaeaaoiith i?aaenoaaeaiith ?ioi?iaoe?? a ?aieao
i?eeiyoi? iiaeae? i?eeiyooy ??oaiue.

Aeey i?aeoe/iiai aeei?enoaiiy cai?iiiiiaaii no?oeoo?o ?ioi?iaoe?eii?
iiaeae? i?inoi?o i?eeiyooy ??oaiue, aeae?eaii ?? ??ai?, aecia/aii
iaoiaee oi?iae?caoe?? caaea/ i?eeiyooy ??oaiue, ui i?iaiaeeoueny a
i’youe aoai?a:

1 aoai. Naiaioe/iee aiae?c ? iaiaaeaiiy i?inoi?o i?eeiyooy ??oaiue.

2 aoai. Oi?iae?caoe?y iiiyoue e a?aeiioaiue iaiaaeaiiai i?inoi?o
i?eeiyooy ??oaiue.

3 aoai. Iiaoaeiaa ocaaaeueiaiiai iieno ia’?eo?a iaiaaeaiiai i?inoi?o
i?eeiyooy ??oaiue.

4 aoai. Iiaoaeiaa oi?iaeueieo oai??e iaeano? i?eeiyooy ??oaiue.

5 aoai. Caiiaiaiiy ?ioi?iaoe?eiiai i?inoi?o.

Iiaecia cai?iiiiiaaii? iaoiaeeee iieyaa? a oiio, ui cai?iiiiiaaia
aeei?enoaiiy a?aeiieo ? ia?aa??aieo i?aeoeeith iaoiae?a o iiaeae?
?theca/ii-?aeaenaoe?eiiai oeio aeey ?aae?caoe?? ie?aieo aoai?a i?ioeano
i?eeiyooy ??oaiiy a ae?iaie/eo nenoaiao ca oiia iaaecia/aiino? ia iniia?
ia/?oeeo iiiaeei, ui aeicaiey? ae??ooaaoe oe?iea eiei caaea/ ii
i?aeaeuaiith aoaeoeaiino? ae?yeueiino? i?aei?e?inoa ia no/aniiio aoai?
?icaeoeo.

O /aoaa?oiio ?icae?e? iaaaaeaii iaoiaee iia?aoeaiiai ieaioaaiiy,
noi?ioeueaaii aieiaio i?iaeaio iia?aoeaiiai ieaioaaiiy, iaoai?ci
aeei?enoaiiy ?ic?iaeaieo iiaeaeae aeey caaea/ iia?aoeaiiai ieaioaaiiy,
oa?aeoa?enoeeo ?ic?iaeaiiai ?ioa?aaeueiiai iaeaoo, ui aeei?enoiao?
?ic?iaeai? iiaeae?, iaoai?cie, aeai?eoie oa iaoiaee.

Cai?iiiiiaaii iaoiae ioe?iee yeino? e aoaeoeaiino? NII? ca aeiiiiiaith
ia/?oeeo iieaciee?a aaeaeaaoiino?, ?ioi?iaoeaiino? e aaeaioeaiino?. Oe?
iieacieee iaiiaeeeai aei??yoe e aecia/eoe e?euee?nii c iaaiith
oi/i?noth, ine?eueee aiie ? «ia/?oeeie», a ?oiy ioe?iea a?oioo?oueny ia
ia/?oeeo oaeoao. I?ioa, iiaeia aecia/eoe ocaaaeueiaiee iieaciee ia
iniia? aeayeiai iaai?o ie?aieo iieaciee?a, oaeeo ye: ?iaa??aio?noue aei
?icoyao (??); ?iaa??aio?noue aei cnoao (?n); o?ainiiiiaai?noue (o);
no?ee?noue «o iaeiio» (ni); iiceoeaia ?aaeoe?y (i?); caa??aaiiy
aeii?ioaaiiy (cae); naaiaioiaai?noue ii a?eiiiiiaioao (na); oiaoeiaa
iioeiaeuei?noue (oi); eieaeueia caaeainiaai?noue (ec);

9

O o?aoueiio ?icae?e? a?aecia/aii, ui ?nioth/? iiaeae? iaeii?eaeaoi? aeey
ae??oaiiy caaea/ i?eeiyooy ??oaiue a NI?OA aiane?aeie ?oiuei?
iaoi?aa?naeueiino?, a?aenooiino? oi?iaeueieo cania?a i?aaenoaaeaiiy
iaiiaiioe oa iaoi/iino? ?ioi?iaoe??. Iaa?oioiaaii aeioe?euei?noue
aeei?enoaiiy iiaeaeae ?theca/ii-?aeaenaoe?eiiai oeio ia iniia? aia?aoa
oai??? ia/?oeeo iiiaeei aeey i?aeo?eiee i?eeiyooy ??oaiue a oi?aae?ii?
ae?iaie/eie nenoaiaie.

Cai?iiiiiaaii ianooiio oaoiieia?th oi?ioaaiiy neeaaeo e iine?aeiaiino?
aoai?a i?ioeano i?eeiyooy ??oaiue ca oiia iaaecia/aiino?:

— iaea?aeaiiy ?ioi?iaoe?? i?i i?iaeaiio neooaoe?th a noai? ia’?eoa
ea?oaaiiy;

— iiia?aaei? oi?ioethaaiiy i?iaeaiii? neooaoe?? (iioi/iee ??
aiae?c, c’ynoaaiiy iniaeeainoae aeieeei? i?iaeaie, nooi?iue oa?i?iiaino?
e iaiao?aeiino? ?? ?ica’ycaiiy);

— aecia/aiiy oe?eae ?ica’ycaiiy i?iaeaie oa aea?? e?eoa???a
aoaeoeaiino?;

— aeyaeaiiy e oi?ioaaiiy iaiaaeoaaeueieo oiia;

— ?ic?iaea aeueoa?iaoea, aecia/aiiy iiaeeeaeo aa??aio?a ?ica’ycoaaiiy e
iiia?aaei?e ?o aiae?c c iaoith a?aeeeaeaiiy aeaeeii iaaoaeoeaieo;

— oi?ioethaaiiy iinoaiiaee caaea/?;

— ?ic?iaea eia?ei-iaoaiaoe/ii? iiaeae? caaea/?, yea aea? ciiao
ioe?ithaaoe aoaeoeai?noue eiaeii? aeueoa?iaoeae;

— aiae?c ? aea?? iaoiae?a ?ica’ycoaaiiy caaea/? oa ?ic?iaea aeai?eoio;

— ioe?ithaaiiy aeueoa?iaoea ? aecia/aiiy iaeaoaeoeai?oi?;

— i?eeiyooy ??oaiiy ea??aieeii ia i?aenoaa? aeina?aeo oa c o?aooaaiiyi
nioe?aeueiiai, ineoieia?/iiai, oaoiieia?/iiai oa ?ioeo aniaeo?a
ea?oaaiiy;

— ?aae?caoe?y e eiio?ieue i?eeiyoeo ??oaiue.

Iiaeaii oi?iaeueio iiaeaeue aaoiiaoeciaaiiai iiooeo ??oaiiy o aeaeyae?
ei?oaaeo

O = ,

aea O,DI,Z,Q oa e — iiiaeeie a?aeiia?aeii iiiaio?a /ano, i?eionoeieo
cia/aiue, oe?eae ea?oaaiiy, ca’yce?a i?ae ? oa O e caeiiii??iinoae
ae?yeueiino? ia’?eoa; ? oa W — ?ioi?iaoe?y i?i noai a?aeiia?aeii ia’?eoa
ea?oaaiiy e ciai?oiueiai na?aaeiaeua; DX — ae?eyiea i?eionoeieo
cia/aiue; V — iiaeeeaino? cania?a ia/enethaaeueii? nenoaie; P —
a?aeiiino? i?i nenoaio a?aeaeaaaiiy ia?aaaae II?; oe —
a?aeia?aaeaiiy, yea

10

oa?aeoa?eco? i?ioean iiooeo ??oaiiy.

Aeey ?aae?caoe?? a?aeia?aaeaiiy

oe : I X

cai?iiiiiaaii oaeo iine?aeiai?noue aoai?a i?ioeano i?eeiyooy ??oaiue:

1) oi?ioaaiiy i?iaeaiii? neooaoe?? S

oe1 = ;

2) eeaneo?eaoe?y neooaoe?e

oe2 = ,

aea K1, K2 oa ?1 — iiiaeeie a?aeiia?aeii eean?a neooaoe?e, i?aaee
eeaneo?eaoe?? e aenia?oieo ia?aaaa i?ae /an ioe?ithaaiiy neooaoe?e
(?1P);

3) aea?? no?aoaa?e iiooeo ??oaiue (oi?ioaaiiy caaea/)

oe3 = ,

aea R — ?ano?ne aeey e?ea?aeoaaiiy i?iaeaiii? neooaoe??; ?2 oa N —
iiiaeeie a?aeiia?aeii ia?aaaa i?ae /an aeai?o no?aoaa?e oa no?aoaa?e
iiooeo ea?oth/eo ??oaiue (ei?eaoaaiiy ae?iaie/eo ieai?a, cai?ia ?ano?n?a
oiui);

4) iiaoaeiaa iiaeae? iiooeo ??oaiiy

oe4 = ,

aea P3 oa M — iiiaeeie a?aeiia?aeii ia?aaaa II? i?ae /an iiaeaethaaiiy
oa oi?iaeueieo iiaeaeae;

5) eiino?othaaiiy i?ioeaaeo?e iiooeo ??oaiue

oe5 = ,

aea V, ?4 oa A — iiiaeeie a?aeiia?aeii iiaeeeainoae cania?a
ia/enethaaeueii? nenoaie (iiaeae?, aeai?eoie, iiaeoe?, caniae
ni?eeoaaiiy oiui), ia?aaaa II? i?ae /an eiino?othaaiiy i?ioeaaeo?e
iiooeo ??oaiue oa aeai?eoi?/ieo i?ioeaaeo? iiooeo ??oaiue;

6) oi?ioaaiiy aa??aioa ??oaiiy

oe6 = ,

aea F — iiiaeeia e?eoa???a ioe?iee ei?eniino? ??oaiiy;

7) aea?? ??oaiiy

oe7 = ,

aea ?6 — iiiaeeia ia?aaaa (iaoi?iaeueiiai oa?aeoa?o) i?ae /an aeai?o
??oaiiy; O* — e?aua ??oaiiy, ui eiai i?eeia? II? ia iniia? ioe?iie.

Cai?iiiiiaai? aoaie i?ioeano iiooeo ??oaiiy aeathoue ciiao noi?ioethaaoe
iinoaiiaeo caaea/? aaeaioaoe??, yea iieyaa? o aecia/aii? i?ioeaaeo?e
iiooeo A ea?oth/eo ae?e X a?aeiia?aeii aei noaio ia’?eoa ? oa

11

aieeao ciai?oiueiai na?aaeiaeua W. I?ioean iiooeo aeueoa?iaoea
neeaaea?oueny c o?ueio iniiaieo ooieoe?iiaeueieo aeie?a:

1) oi?ioaaiiy neooaoe?e S — i?ecia/aiee aeey aeyaeaiiy e iieno neooaoe??
S ia iniia? aiae?co ?ioi?iaoe?? i?i noai ia’?eoa ? oa ciai?oiueiai
na?aaeiaeua W e aeina?aeo II?; ooieoe?iioaaiiy oeueiai aeieo, yeee
i?noeoue aoaie oe1 oa oe2, aecia/aii oaeei a?aeia?aaeaiiyi:

o1 : I W ? S;

2) eiino?othaaiiy iiaeae? M — i?ecia/aiee aeey noai?aiiy iiaeaeae iiooeo
aeueoa?iaoea ??oaiue a?aeiia?aeii? iioi/ii? i?iaeaiii? neooaoe?? S;
ooieoe?iioaaiiy oeueiai aeieo, yeee i?noeoue aoaie oe3 oa oe4, iiaeaii
oaeei a?aeia?aaeaiiyi:

o2 : S C ? M;

3) iiooeo A — i?ecia/aiee aeey oi?ioaaiiy e aeai?o aeueoa?iaoeaieo ae?e
ia i?aenoaa? iiaeae? I, i?ioeaaeo?e iiooeo aeueoa?iaoea ??oaiiy A
oa nenoaie ia?aaaa II? ?; ooieoe?iioaaiiy oeueiai aeieo, yeee i?noeoue
aoaie oe5, oe6 oa oe7 aecia/aii oaeei a?aeia?aaeaiiyi:

o3 : M A ? X.

O caaaeueiiio aeae? aaeaioeaia iiaeaeue iiooeo aeueoa?iaoea ??oaiiy ia?
aeaeyae:

I S M X,

y1 y2 y3

aea y1, y2 oa y3 — ooieoe?? a?aeiia?aeii iieno neooaoe??, ia?aaaaeaiiy
eiai a oi?iae?ciaaio iiaeaeue oa aecia/aiiy i?ioeaaeo?e oi?ioaaiiy
??oaiiy.

Iaaaaeai? aoaie ooieoe?iioaaiiy iathoue caeaoi?noue aaeaiooaaoeny aei
aeieeei? neooaoe?? ca ?aooiie eiino?othaaiiy e ei?eaoaaiiy aeaiaio?a
i?ioeano iiooeo aeueoa?iaoea ??oaiue (iiaeaeae, no?aoaa?e, aeai?eoi?a).

Aeeeaaeaii iniiai? iieiaeaiiy, iaoiaee, iiaeae? oa caniae iiaoaeiaai? ia
iniia? ?ic?iaeaii? iiaeae?. Aecia/aii no?oeoo?o iiaeae?, aaaaeaii
i?aaeea iiaoaeiae aeai?eoi?a ??oaiiy a aeai?e iiaeae?:

a) aii?yaeeoaaiiy ia’?eo?a (ii iac?inoaiith aai iaciaioaiith iaiao?aeieo
?ano?n?a);

a) a?aooaaiiy nooiaiy caiiaiaiiy ?thecae?a;

a) ?icaeaea aeo?aeii? iiiaeeie ia’?eo?a ia a?oie (aeecueeeo ia’?eo?a;
ia’?eo?a, ui neeaaeathoue aeaye? caaeai? eiio?ao?aoe??);

a) ?aeaenaoe?y aeo?aeii? caaea/?.

8

aiaeia?/iee G, aea c iaioith ?ici??i?noth, oiaoi S ? i/aaeaeiith
i?ii?aeiith iiaeaeeth. S’ yaey? niaith aeayeee “a?a?eae” e?i?eiiai
ii?yaeeo S e ?icoa?aaii? no?oeoo?e S. O?ae ??oaiiy a oeueiio aeiaaeeo
aeaeyaea? oae — nii/aoeo a?aeae?athoueny, iiee aeiioneathoue ?ano?ni?
iaiaaeaiiy, caiiaeaiiy aa?oi?o iaeiiaeaiaioieo i?ioa?e?a; yeui iayaiee
?ano?n ia ae/a?iaiee, oi caaea/a noaaeoueny aeey caeeoeo ?ano?no e
?icoa?iaaii? i?aeno?oeoo?e, ui caeeoeeany.

Aaaeeeaee ie?aiee aeiaaeie aiae?ciaaii? caaea/? aeieea? i?e ni=1,
i=wmetafile8? ???????????????
???????????yyy????.????1?????? ???????
? ???&??yyyy?????Ayyyyyy`???? ???&? ?MathType??@?
???u?????????»????-?????[?@????[?E???uAth??????

?en. 1. Aca?iica’ycie aaciaeo no?oeoo? ia?aaaa.

Iiaeaeue ? aeinoaoiuei neeaaeiith e i?aeo?ae aei ??oaiiy iiaea
a?oiooaaoeny ia aeayeiio iacia/iiio ii?ooaii? iaiaaeaiue. Iiaeia
?icaeyaeaoe e aeaye? ii?ooaiiy iaiaaeaiue ae?oai? oiiae a aeai?e
iinoaiiaoe?.

O yeino? iia??oiino? (ioe?iee nooiaiy ii?ooaiiy iaiaaeaiiy) iiaeia
aeei?enoiaoaaoe /enei ia? ia’?eo?a (/enei aeoa, /enei aeaaaeaieo aeoa),
ui ii?ooothoue a?aoiao oiiao.

13

iaea?aeaiiy e?euee?nieo ioe?iie aaaeeeaino? no?ao (ian); iiae?ai?noue
??ciiiai?oieo iioeiaeueieo oii?yaeeiaaieo ?icaeaie (io?); ioe?iea yeino?
ai?ieneiaoe?? (ya); no?ee?noue aei cai?oaiiy oa ?icai?oaiiy (nc?);
no?ee?noue aei noyaoaaiiy no?ao (nnn); ianoia?a/eea?noue a?oiiai?
ia?aaaae (iai).

Ioe?iea aaeaeaaoiino? NII? aeey caaeaii? i?aaeiaoii? iaeano? aecia/aia
ye ooieoe?y:

wmetafile8? ??O???????????
???????????yyy????.????1?????? ??????? ` 

???&??yyyy?????Ayyy?yyy`

???? ???&? ?MathType??p?
???u?????????»????-?????F?y???0+???0+???y???F
?o???0@

???0@

???o???u y?????? a ioe?iea ?ioi?iaoeaiino?, ye ooieoe?y:

wmetafile8? ??w???????????
???????????yyy????.????1?????? ???????
`@???&??yyyy?????Ayyy?yyy????? ???&? ?MathType??p?
???u?????????»????-?????F?????0@???0@???????F
?????0i???0i???????u y??????Ioe?iea aaeaioeaiino?
NII? iiaea aooe aecia/aia ye ooieoe?y:

wmetafile8? ??9???????????
???????????yyy????.????1?????? ???????
`?’???&??yyyy?????Ayyycyyy@’???? ???&? ?MathType??p?
???u?????????»????-?????^?l???8$???8$???l???^
?e&???82’???82’???e&???u y??????Aiae?c aoaeoeaiino?
aeei?enoaiiy NI?OA aeey ??oaiiy caaea/ i?aeo?eiee i?eeiyooy ??oaiue, o
ii??aiyii? c ?nioth/eie i?aeoiaeaie, iieacaa iie?ioaiiy yeino? NII? ii
iieacieeao aaeaeaaoiino? a 1,1 ?aco, ?ioi?iaoeaiino? a 1,1-1,2 ?aco,
aaeaioeaiino? a 1,2 ?aco.

Canoinoaaiiy NI?OA aeicaiey? ciaioeoe /an iiooeo i?eeiyoiiai ??oaiiy e
a?aeiia?aeii ciaioeoe caaaeueiee /an ae??oaiiy caaea/?. NI?OA iiaea aooe
canoiniaaia a ?yae? ??ciiiai?oieo caaea/ oi?aae?iiy ae?iaie/eie
nenoaiaie.

O aeniiaeao noi?ioeueiaai? aeaiaee oa ?aeiiaiaeaoe??, io?eiai? a
?acoeueoao? i?iaaaeaieo o aeena?oaoe?ei?e ?iaio? aeine?aeaeaiue.

AENIIAEE

A ?acoeueoao? aeeiiaiiy aeine?aeaeaiue io?eiai? oae? oai?aoe/i? e
i?aeoe/i? ?acoeueoaoe.

1. I?iaaaeaiee aiae?c ?nioth/iai ??aiy ?icaeoeo cania?a i?aeo?eiee
i?eeiyooy ??oaiue e noaio ?ia?o a iaeano? ?o ?ioaeaeooae?caoe?? iieacaa,
ui i?aeaeuaiiy aoaeoeaiino? oa yeino? NII? iiaeeeaa oeyoii
oaeineiiaethaaiiy ?nioth/eo ? ?ic?iaee iiaeo cania?a i?aeo?eiee
i?eeiyooy ??oaiue ia iniia? iiaeaeae ?theca/ii-?aeaenaoe?eiiai oeio.
Aeyaeai? iniaeeaino? ia?iaethaaii? ?ioi?iaoe?? aeicaieeee aecia/eoe
i?aeoiaee aei ?? oi?iae?caoe??.

2. ?ic?iaeaii eiioeaioe?th NI?OA, o ?aieao eio?i? iiaeeeaa noai?aiiy
ia?niaeoeaieo cania?a i?aeo?eiee i?eeiyooy ??oaiue. O yeino? oi?iaeueii?
iniiae aeey iiaoaeiae NI?OA aa?oi aea?aoe iiaeaeue

6

X = xij = (x1ij; x2ij) | x1ij; x2ij [0,1], j = wmetafile8?
??O???????????? ???????????yyy????.????1??????
???????   ???&??yyyy?????Ayyy°yyya????? ???&?
?MathType??P? ???u?????????»????-?????X?@????X?I???u
y??????A iinoaiiaeao on?o caaea/ a?aoiaothoueny ianooii? iaiaaeaiiy:

wmetafile8? ??>???????????
???????????yyy????.????1?????? ???????
?@???&??yyyy?????Ayyy1/2yyy???1/2?? ???&?
?MathType??a????u@th??????Oi?iaeueia iinoaiiaea aaaaoiaa??aioii?
caaea/? i?i ?thecae i?e aiae?ciaai?e ?ioai?aoaoe?? ia? aeaeyae

iaenei?coaaoe Y(X) = wmetafile8? ??v???????????
???????????yyy????.????1?????? ??????? ?a
???&??yyyy?????Ayyy?yyy  ????? ???&?
?MathType??a????u@th??????i?e oiiaao (a0) + wmetafile8?
??†??????????? ???????????yyy????.????1??????
??????? ?  ???&??yyyy?????Ayyy?yyy` ????? ???&?
?MathType??a????u@th??????Aeai?eoie ??oaiiy iaei?ino?oeo ie?aieo
aeiaaee?a caaea/? a?oioothoueny ia -iaaeeaeaiiio iie?iii?aeueiiio
(oaeaeeiio) aeai?eoi? aeey caaea/? i?i ?thecae (iaoiae ?ioa?aae?a). I?e
oeueiio ia?aaeaa/a?oueny oii?yaeeoaaiiy aeaiaio?a iiiaeeie aeueoa?iaoea
ii iac?inoaiith aaee/ei (ai) aai (ai) + +(ai). Ioe?iee oeeo aeai?eoi?a
aiaeia?/i? ioe?ieai aeai?eoio ?icaeaee ia ?ioa?aaee — O(m2/).
?ica’ycaiiy aeiiii?aeieo caaea/ caniiaaia ia -iaaeeaeaiiio
iie?iii?aeueiiio (oaeaeeiio) aeai?eoi? aeey «ae?aaeiiai?» caaea/? i?i
?thecae c ioe?ieaie o?oaeii?noeino? oa iai’yo?, a?aeiia?aeii

Owmetafile8? ??Aeey ae??oaiiy caaea/? aeei?enoiao?oueny (,
)-iaaeeaeaiee iie?iii?aeueiee (oaeaeeee) aeai?eoi ?c ?aeaenaoe??th c
ioe?ieaie o?oaeii?noeino? oa iai’yo?, a?aeiia?aeii:

Owmetafile8? ??O aeiaaeeo, eiee G yaey? niaith ia/?oeee a?ia?a?ao
ia?oiai ?iaeo, aeai?eoi a?oioo?oueny ia iine?aeiai?e iinoaiiaoe? e
ae??oaii? aeey o?aaiaio?a G iaei?ino?oeo ? aeiiii?aeieo caaea/.

Cai?iiiiiaaii iiaeaeue ?theca/ii-?aeaenaoe?eiiai oeio aeey caaea/?
i?eeiyooy ??oaiue oaeiai aeaeo.

? iaa?? aeaiaio?a V=1, …, i, …, n, eiaeai ?c yeeo oa?aeoa?eco?oueny
iiiaeeiith iaiao?aeieo aeey aeeiiaiiy ?ano?n?a. Ia iiiaeei? aaeoi?ieo
ioe?iie aeaiaio?a ca e?eoa??yie yeino?, ia iniia?

15

NIENIE IIOAE?EIAAIEO I?AOeUe

1. Eeaaeei E.E., ?aaeaaineay E.I. Iino?iaiea e naiii?aaiecaoeey iiaeaeae
a eiiaeie?iaaiiuo eioaeeaeooaeueiuo nenoaiao //Aanoiee OAOO. — 1997. —
?2. — N.122-125.

2. Eeaaeei ?.?. Aeei?enoaiiy iiaeaeae ?theca/ii-?aeaenaoe?eiiai oeio
aeey caaea/? eaeaiaea?iiai ieaioaaiiy a ae?iaie/eo nenoaiao //Aanoiee
OAOO. — 1998. — ?2(4). — N.123-125.

3. Eeaaeei E.E. Iiaeaee ia/aoeiai auai?a a nenoaiao iiaeaea?aeee
i?eiyoey ?aoaiee //Iaoaiaoe/aneea iiaeaee e nia?aiaiiua eioi?iaoeeiiiua
oaoiieiaee: Na. iao/. o?. — Eeaa: Einoeooo iaoaiaoeee IAI Oe?aeiu. —
1998. — N.59-61.

4. Eeaaeei E.E. Iaeioi?ua iniaaiiinoe i?ioeanna i?eiyoey ?aoaiee
//Aaoiiaoeea, aaoiiaoecaoeey, yeaeo?ioaoie/aneea eiiieaenu e nenoaiu. —
1998. — ?2. — N.156-158.

5. Eeaaeei E.E. I?aaiecaoeey nenoaiu iiaeaea?aeee ?aoaiee a n?aaea
eioaa?e?iaaiiuo aaoiiaoece?iaaiiuo i?iecaiaenoa oaenoeeueiie
i?iiuoeaiiinoe //I?iaeaiu eaaeie e oaenoeeueiie i?iiuoeaiiinoe Oe?aeiu.
— 1998. — ? 1. — N.208-211.

6. Eeaaeei E.E. Oa?aeoa?enoeee e i?eioeeiu iino?iaiey oi?aaeai/aneeo
yenia?oiuo nenoai i?eiaieoaeueii e oaenoeeueiie i?iiuoeaiiinoe
//I?iaeaiu eaaeie e oaenoeeueiie i?iiuoeaiiinoe Oe?aeiu. — 1998. — ? 1.
— N.212-214.

7. Eeaaeei E.E. Iiauoaiea yooaeoeaiinoe iienea ?aoaiey i?e ?ac?aaioea
YN, iniiaaiiuo ia ciaieyo //?ioi?iaoeea: oai??y, oaoiieia?y, oaoi?ea —
?OOO-95. — Iaeanna. — 1995. — N.68.

8. Eeaaeei E.E., Neaei?oe A.A. Naiiiao/aiea nenoai iiaeaea?aeee i?eiyoey
?aoaiee //Eioi?iaoeeiiiua ?ano?nu: oaoiieiaee, eiiioieeaoeee. — Oa?nii.
— 1997. — N.69-71.

9. Eeaaeei E.E., Aaiue A.I., Neaei?oe A.A. Eioaeeaeooaeecaoeey ia?aaioee
eioi?iaoeeiiiuo iioieia a nenoaiao iiaeaea?aeee i?eiyoey ?aoaiee
//Eioi?iaoeeiiiua ?ano?nu: oaoiieiaee, eiiioieeaoeee. — Oa?nii. — 1997.
— N.75-77.

10. Eeaaeei E.E., Aaiue A.I., Oi?iaeecaoeey i?aaenoaaeaiey eioi?iaoeee a
nenoaiao iiaeaea?aeee i?eiyoey ?aoaiee

4

O ia?oiio ?icae?e? i?iaaaeaiee aiae?c ?nioth/iai ??aiy ?ia?o a iaeano?
eiii’thoa?ecaoe?? oi?aae?iiy ae?iaieoeoaii ? i?eeiyooy ??oaiue a oiiaao
iaaecia/aiino?, ?icaeyiooi ia’?eo aeine?aeaeaiue e noai aiae?ciaaieo
caaea/, aeeiiaii nenoaiiee aiae?c ??aiy eiii’thoa?ecaoe?? caaea/
oi?aae?iiy ae?iaieoeoaii a oiiaao iaaecia/aiino?, iaa?oioiaaia
aeooaeuei?noue i?iaaaeaieo aeine?aeaeaiue, iieacaia iaiao?aei?noue
?ic?iaee iiaeaeae nenoai i?aeo?eiee i?eeiyooy ??oaiue a oi?aae?ii?
ae?iaie/eie nenoaiaie.

Aeey no/aniiai aoaio aeiiii?ee oa?aeoa?ii oa, ui a?eueo?noue i?iaeai
oi?aae?iiy ae?iaieoeoaii ae??oothoueny a oiiaao iaaecia/aiino? iioi/ieo
? ia?niaeoeaieo caaea/, oiia ooieoe?iioaaiiy oa aieeao iaaeieeoiueiai
na?aaeiaeua. Aeaea?aeaie iaaecia/aiino? ? a?aenooi?noue,
aeaoa?i?iiaai?noue oa i?ieea?noue ?ioi?iaoe?? i?i i??i?eoaoi?noue
neooaoe?e i?e aiae?c? oiia ooieoe?iioaaiiy, i?e aeai??
aaaaoie?eoa??eiiai ??oaiiy, iaocaiaeaeai?noue, i?ieea?noue oa
noia?a/eea?noue caaaeaiue oa iiaeeeaeo ?ano?n?a, a?aeoeeaiiy aeo?aeieo
onoaiiaie a?ae ?aaeueii ?nioth/eo oiia, neaaei? oi?iae?caoe?? i?ioean?a
? o.i. Cacia/ai? aeaee iaaecia/aiinoae aiinyoue aeaiaio iaaecia/aiino? a
i?ioean oi?aae?iiy oa i?eeiyooy ??oaiue.

Iiaeaii aiae?c iaoiae?a iiaeaethaaiiy e iioei?caoe?? oi?aae?iiy
ae?iaieoeoaii. A?eueo?noue caaea/ iiaoaeiae iiaeaeae iaeaaeaoue aei
eeano iaei?aeoii iinoaaeaieo caaea/. I?iaiae?ciaaii iniiai? oeie
iiaeaeae ? ia iniia? aiae?co noi?ioeueiaaia iaoa, iinoaaeai? caaea/?
aeine?aeaeaiiy, aecia/ai? iaae? aeine?aeaeaiiy.

Ine?eueee i?ioean oi?aae?iiy ae?iaieoeoaii neaaei oi?iae?ciaaiee e ia
i?aeaea?oueny ai??i?i?e aeai?eoi?caoe??, i?aeaeueoe iieacieee yeino?
NII? iiaeia oeyoii aeei?enoaiiy i?aeoiae?a, a iniia? yeeo eaaeaoue
iaoaiaoe/i? iiaeae?, caniiaai? ia aia?ao? oai??? ia/?oeeo iiiaeei.
Caaea/? aeine?aeaeaiiy iaiaaeothoueny iioei?caoe??th no?oeoo?e NII? ?
?ic?iaeith iiaeae? i?aeo?eiee i?eeiyooy ??oaiue.

Ia iniia? i?iaaaeaiiai aiae?co noi?ioeueiaaii aeiiae uiaei iaoaiaoe/iiai
caaacia/aiiy NII?. Aecia/aii, ui a iaea?eueo?e i??? i?aae’yaeaiei
aeiiaai caaeiaieueiy? aa?enoe/iee i?aeo?ae, canoiniaoaaiee i?e
iiaoaeia? iiaeaeae ?theca/iiai oeio, ca oiiae eiai
?icoe?aiiy oi?iaeueiei aia?aoii, ui aeicaiey? a?aoiaoaaoe
iaaecia/ai?noue oa iaoi/i?noue ?ioi?iaoe?? o i?inoi?? i?eeiyooy ??oaiue.
Iaaecia/ai?noue ?ioi?iaoe?? ia? oa?aeoa? ye aeiaaeeiaino?,
oae ?

17

AIIIOAOeEss

Eeaaeei E.E. Iiaeaee nenoai iiaeaea?aeee i?eiyoey ?aoaiee a oi?aaeaiee
i?iecaiaenoaii ia iniiaa oai?ee ia/aoeeo iiiaeanoa. — ?oeiienue.

Aeenna?oaoeey ia nieneaiea o/aiie noaiaie eaiaeeaeaoa oaoie/aneeo iaoe
ii niaoeeaeueiinoe 05.13.06 — aaoiiaoece?iaaiiua nenoaiu oi?aaeaiey e
i?ia?anneaiua eioi?iaoeeiiiua oaoiieiaee. Oa?niineee ainoaea?noaaiiue
oaoie/aneee oieaa?neoao, Oa?nii, 1998.

Aeenna?oaoeey iinayuaia aii?ino ?ac?aaioee iiaeaeae i?eiyoey ?aoaiee i?e
oi?aaeaiee i?iecaiaenoaii a oneiaeyo iaii?aaeaeaiiinoe n eniieueciaaieai
oai?ee ia/aoeeo iiiaeanoa. Iieacaia oeaeaniia?aciinoue ?aoaiey
iinoaaeaiiie caaea/e n iiiiuueth nouanoaothueo iiaeaeae ?theca/iiai
oeia, iooai eo oniaa?oainoaiaaiey: aaaaeaiey iaoaiaoe/aneiai aiia?aoa
oai?ee ia/aoeeo iiiaeanoa e i?eiaiaiey iaoaiecia ?aeaenaoeee. Iainiiaaia
iioeiaeueiinoue aeaiiiai iiaeoiaea n oi/ee c?aiey iiauoaiey iauae
yooaeoeaiinoe ooieoeeiie?iaaiey NII?.

A oiaea oai?aoe/aneeo enneaaeiaaiee i?aaeeiaeaiu e ?ac?aaioaiu
iaoaiaoe/aneea iiaeaee, aeai?eoiu e i?ia?aiiu aeey iiauoaiey
yooaeoeaiinoe e ea/anoaa iiaeaea?aeee i?eiyoey ?aoaiee a
i?iecaiaenoaaiiuo nenoaiao a oneiaeyo iaii?aaeaeaiiinoe iooai nicaeaiey
nenoaiu iiaeaea?aeee i?eiyoey ?aoaiee ia iniiaa iiaeaeae ?theca/iiai
oeia ?anoe?aiiuo iaoaiaoe/aneei aiia?aoii oai?ee ia/aoeeo iiiaeanoa.

Oai?aoe/aneea ?acoeueoaou ?aaiou i?iaa?aiu e iiaeoaa?aeaeaiu
i?aeoe/aneei aiaae?aieai ia i?iecaiaenoaaiiuo i?aaei?eyoeyo.

A ?aaioa enneaaeiaaiu iniaaiiinoe ooieoeeiie?iaaiey i?iecaiaenoaa a
oneiaeyo iaii?aaeaeaiiinoe, ii?aaeaeaiu iniiaiua oaeoi?u nieaeathuea
yooaeoeaiinoue i?eiaiaiey nouanoaothueo iiaeaeae iiaeaea?aeee i?eiyoey
?aoaiee.

?ac?aaioaia iiaeaeue ?theca/ii-?aeaenaoeeiiiiai oeia aeey iiaeaea?aeee
i?eiyoey ?aoaiee, a eioi?ie eniieueciaaiu e oniaa?oainoaiaaiu oaea
ecaanoiua iiaeaee e aeai?eoiu ?aoaiey caaea/ aeaiiiai eeanna.

I?aaenoaaeaiu iaoiaeu ioeaiee yooaeoeaiinoe e ea/anoaa NII?, iino?iaiiie
ia iniiaa nenoaiu i?eiyoey ?aoaiee a oi?aaeaiee i?iecaiaenoaii (NI?OI).

2

nenoaiao oi?aae?iiy ae?iaieoeoaii ia iniia? iiaeaeae i?eeiyooy ??oaiue
?c aeei?enoaiiyi iaoaiaoe/iiai aia?aoa ia/?oeeo iiiaeei.

?ica’ycaiiy iinoaaeaii? caaea/? iio?aao? ae??oaiiy oaeeo ieoaiue:

ii??aiyeueiee aiae?c ?nioth/eo iiaeaeae, iaoiae?a oa aeai?eoi?a;

?ic?iaea iiaeaeae oa iioeiaeueieo aeai?eoi?a i?ioeano i?eeiyooy ??oaiue;

oi?iae?caoe?y iaoaiaoe/ii? iiaeae? i?ioeano i?eeiyooy ??oaiue;

neioac iioeiaeueii? no?oeoo?e NII?;

ioe?iea aoaeoeaiino? ?ic?iaeaieo iiaeaeae oa aeai?eoi?a ia iniia?
NI?OA.

Iaoiaee aeine?aeaeaiiy. Aeey ?ica’ycaiiy iinoaaeaieo caaea/
aeei?enoiaoaaeeny iaoiaee oai??? i?eeiyooy ??oaiue, oai??? eiia??iinoae,
oai??? ia/?oeeo iiiaeei, oai??? iioeiaeueiiai oi?aae?iiy, eiia?iaoi?i?
iiaeae? ai?ieneiaoe?? ?ioi?iaoe??.

Iaoeiaa iiaecia io?eiaieo ?acoeueoao?a ?iaioe iieyaa? a oiio, ui
cai?iiiiiaaii aeei?enoaiiy a?aeiieo ? ia?aa??aieo i?aeoeeith iaoiae?a o
iiaeae? ?theca/ii-?aeaenaoe?eiiai oeio aeey ?aae?caoe?? ie?aieo aoai?a
i?ioeano i?eeiyooy ??oaiiy o ae?iaie/eo nenoaiao a oiiaao iaaecia/aiino?
ia iniia? ia/?oeeo iiiaeei, ui aeicaiey? ae??ooaaoe oe?iea eiei caaea/
ii i?aeaeuaiith aoaeoeaiino? ae?yeueiino? i?aei?e?inoa ia no/aniiio
aoai? ?icaeoeo.

I?aeoe/ia cia/aiiy ?acoeueoao?a ?iaioe iieyaa? a iiaeeeaino?
iia?aoeaiiai aianaiiy ci?i o i?ioean i?eeiyooy ??oaiue, o iiaeeeaino?
iiaoaeiae iiaeae? ?theca/ii-?aeaenaoe?eiiai oeio aeey i?eeiyooy ??oaiiy
ia iniia? oai??? ia/?oeeo iiiaeei, o iiaeeeaino? ciaioaiiy
o?oaeii?noeino? i?ioeano oi?iae?caoe?? caaea/ ia aeayeeo aoaiao, ?
aecia/a?oueny iiaeeea?noth aeei?enoaiiy ?acoeueoao?a aeine?aeaeaiue i?e
aaeineiiaeaii? ?nioth/eo ? ?ic?iaoe? ia?niaeoeaieo cania?a NII? ia
iniia? NI?OA aeey i?aeaeuaiiy iieaciee?a ?oiuei? aoaeoeaiino? oa
yeino?. ?ic?iaeai? iiaeae?, iaoiaee e aeai?eoie aeicaieythoue
ae??oeoe ?yae i?iaeaiieo caaea/ a oi?aae?ii? ae?iaieoeoaii. Aeei?enoaiiy
iaoeiaeo iieiaeaiue, ?aeiiaiaeaoe?e, iiaeaeae aeicaiey? cia/ii
i?enei?eoe i?ioean i?eeiyooy ??oaiue oa nei?ioeoe /an noai?aiiy NII?.

?aae?caoe?y ?acoeueoao?a ?iaioe. ?acoeueoaoe ?iaioe ai?iaaaeaeai? ia
?yae? i?aei?e?inoa: ae?iaie/iio ia’?aeiaii? «Oa?niinueeee eiiaaeiiaee
caaiae ?i. Iao?ianueeiai»; ae?iaie/iio ia’?aeiaii? «Aaaiaiyii-iaia?iaee
eiia?iao»; ?aaeaini? «Aeaei?aoeai? eoeueoo?e»; i?e i?aeaioiaoe? ?yaeo
A?I

Aeena?oaoe??th ? ?oeiien.

?iaioo aeeiiaii ia eaoaae?? i?ia?aiiiai caaacia/aiiy AII Oa?niinueeiai
aea?aeaaiiai oaoi?/iiai oi?aa?neoaoo.

Iaoeiaee ea??aiee: aeieoi? oaoi?/ieo iaoe, i?ioani?, Oiaeaeia A?eoi?
?ai?iae/, OAeOO, caa?aeoth/ee eaoaae?ith i?ia?aiiiai caaacia/aiiy AII

Iaoeiaee eiinoeueoaio: eaiaeeaeao oaoi?/ieo iaoe, aeioeaio,
?iaaeuenueeee O?aioe Ai?eniae/, OAeOO, i?i?aeoi? c
iaa/aeueii-iaoiaee/ii? ?iaioe

Io?oe?ei? iiiiaioe:

1. Aeieoi? oaoi?/ieo iaoe, i?ioani? Oa?iiiaa Iaoae?y Aaea???aia,
Oa?e?anueeee aoiai?oa?iee ?inoeooo «Ia?iaeia Oe?a?inueea Aeaaeai?y»,
i?i?aeoi? c iaoeiai-aeine?aeii? ?iaioe

2. Aeieoi? oaoi?/ieo iaoe, i?ioani? Eieioei Aieiaeeie? Naiaiiae/,
Iaeanueeee ?inoeooo nooiiooieo a?enuee I?iiai?iie Oe?a?ie, i?ioani?
eaoaae?e a?enueeiai? e?aa?iaoeee oa ?ioi?iaoeee

I?ia?aeia onoaiiaa:

Oa?e?anueeee aea?aeaaiee oaoi?/iee oi?aa?neoao ?aae?iaeaeo?ii?ee

Caoeno a?aeaoaeaoueny “ ” 1999 ?. i aiaeei?
ia can?aeaii? niaoe?ae?ciaaii? a/aii? ?aaee E67.052.01 o Oa?niinueeiio
aea?aeaaiiio oaoi?/iiio oi?aa?neoao? ca aae?anith: Oe?a?ia, 325008, i.
Oa?nii, Aa?eneaanueea oina, 24, ei?i.3, aoae. 320.

C aeena?oaoe??th iiaeia iciaeiieoeny a a?ae?ioaoe? Oa?niinueeiai
aea?aeaaiiai oaoi?/iiai oi?aa?neoaoo ca aae?anith: Oe?a?ia, 325008,
i.Oa?nii, Aa?eneaanueea oina, 24.

Aaoi?aoa?ao ?ic?neaiee “ ” 1999?.

A/aiee nae?aoa?

niaoe?ae?ciaaii? a/aii? ?aaee
Eino?i A.I.

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