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Експертні методи і моделі керування процесом навчання операторів ергатичних систем: Автореф. дис… канд. техн. наук / Н.М. Шибицька, Київ. міжнар. ун

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11

I?i?noa?noai ina?oe Oe?a?ie

Ee?anueeee i?aeia?iaeiee oi?aa?neoao oeea?eueii? aa?aoe??

Oeaeoeueea Iaoae?y Ieeiea?aia

OAeE 658.336:007:681.3.06 (043.3)

aenia?oi? Iaoiaee ? iiaeae? ea?oaaiiy

i?ioeanii iaa/aiiy iia?aoi??a

a?aaoe/ieo nenoai

Niaoe?aeuei?noue 05.13.03 – “Nenoaie ? i?ioeane ea?oaaiiy

Aaoi?aoa?ao

aeena?oaoe?? ia caeiaoooy iaoeiaiai nooiaiy

eaiaeeaeaoa oaoi?/ieo iaoe

Ee?a 1999

Aeena?oaoe??th ? ?oeiien.

?iaioa aeeiiaia a Ee?anueeiio i?aeia?iaeiiio oi?aa?neoao? oeea?eueii?
aa?aoe??.

Iaoeiaee ea??aiee : aeieoi? oaoi?/ieo iaoe, i?ioani?

Eoaeeiaiei Aiaoie?e Aieiaeeie?iae/,

Ee?anueeee i?aeia?iaeiee oi?aa?neoao

oeea?eueii? aa?aoe??, caa?aeoaa/ eaoaae?e

oai?aoe/ii? aeaeo?ioaoi?ee.

Io?oe?ei? iiiiaioe : aeieoi? oaoi?/ieo iaoe, i?ioani?

Naiieeia A?eoi? Aeieo?iae/, ?inoeooo

i?iaeai iiaeaethaaiiy a aia?aaoeoe?

IAI Oe?a?ie, caa?aeoaa/ a?aeae?eii

?i?oaoe?eiiai iiaeaethaaiiy;

eaiaeeaeao oaoi?/ieo iaoe, aeioeaio

E?eo Aiae??e Aai?a?eiae/, Iaoe?iiaeueiee oaoi?/iee oi?aa?neoao Oe?a?ie
“EI?”,

aeioeaio eaoaae?e oaoi?/ii? e?aa?iaoeee.

I?ia?aeia onoaiiaa: ?inoeooo eini?/ieo aeine?aeaeaiue IAI Oe?a?ie

oa Iaoe?iiaeueiiai eini?/iiai aaaionoaa Oe?a?ie.

Caoeno a?aeaoaeaoueny “ 21__aeiaoiy 1999 ?ieo i 14-30 aiaeei? ia
can?aeaii? niaoe?ae?ciaaii? a/aii? ?aaee Ae.26.062.05 a Ee?anueeiio
i?aeia?iaeiiio oi?-aa?neoao? oeea?eueii? aa?aoe??.

A?aeceae ia ?aoa?ao, caa??ai? ia/aoeith onoaiiae, i?ineii iaaeneeaoe ca
aae?anith: 252058, Ee?a, i?. Einiiiaaoa Eiia?iaa, 1, a/aiiio nae?aoa?th.

C aeena?oaoe??th iiaeia iciaeiieoenue a a?ae?ioaoe? Ee?anueeiai
i?aeia?iaeiiai oi?aa?neoaoo oeea?eueii? aa?aoe??.

Aaoi?aoa?ao ?ic?neaiee “ 16 aa?aniy 1999 ?ieo.

A/aiee nae?aoa?

niaoe?ae?ciaaii? a/aii? ?aaee

eaiaeeaeao oaoi?/ieo iaoe A.A.Aaneaeiaa

Caaaeueia oa?aeoa?enoeea ?IAIOE

Aeooaeuei?noue oaie. sse?noue ooieoe?iioaaiiy ? aaciaea aenieoaoaoe??
no/anieo oaoi?/ieo nenoai, cie?aia ? iia?o?yieo ei?aae?a (IE), aenoaa?
aeiaeaoeia? aeiiae aei aoaeoeaiino? ? iaae?eiino? iia?aoi?nueei?
ae?yeueiino?. Ethaeeia – iia?aoi? iaae?eaia oi?eaeueiith cae?ai?noth
ocaaaeueithaaoe ?ioi?iaoe?th i?i ?iaioo oaoi?/ii? nenoaie, oi?ioaaoe
i?ia?aio ea?oaaiiy nenoaiith, i?eeiaoe ? aaia?oaaoe ?ioi?iaoe?ei?
neaiaee.

Iaaeiioe?iea ethaenueeiai oaeoi?a i?e ea?oaaii? neeaaeieie oaoi?/ieie
nenoaiaie ? i?e/eiith aei 40 – 50 % aaa??e ? eaoano?io, ye? aeieeathoue
i?e aei?iaiaoaaiiyo ?aeao ? e?oae?a. Cie?aia, ca 1997 ??e ca aeaieie
cania?a ia’?eoeaiiai eiio?ieth 28 aa?aeiiiai?e Oe?a?ie ca?a?no?iaaii
a?aeoeeaiiy a ?iaio? eiiieaeno “IE-ae?iaae-na?aaeiaeua”, c yeeo: 11% –
ii?ooaiiy i?aaee aenieoaoaoe?? IE; 35% – ii?ooaiiy /a?ac iiieeee
i?eiooaaiiy IE.

Noaiaea?oe ? ?aeiiaiaeiaaia i?aeoeea ?NAI uiaei caaacia/aiiy aaciaee
iieueio?a (SARPs) aeicaieythoue aeae?eeoe iniiai? iai?yie aaeineiiaeaiiy
i?ioan?eii? i?aeaioiaee iia?aoi??a: aaeineiiaeaiiy cania?a ? iaoiae?a
i?aae’yaeaiiy ?ioi?iaoe??; ?ic?iaeo ? ai?iaaaeaeaiiy ??cieo
i?ia?aiii-oaoi?/ieo cania?a iaa/aiiy iia?aoi??a; aaeineiiaeaiiy cania?a
? iaoiae?a eiio?ieth ciaiue; ai?iaaaeaeaiiy cania?a ?a?no?aoe?? ?
iaeiie/aiiy ?acoeueoao?a iaa/aiiy.

O?aaeeoe?ei? iaoiaee iaa/aiiy oi?ioaaeeny aeanyoe??//yie. Aea
?acoeueoaoe iaoeiaeo aeine?aeaeaiue, i?iaaaeaieo a iao?e e?a?i?
(A.I.Nae?eaeia, A.Ae.Naiieeia, A.I.Aeiaayei, A.ss.Naaaeue?a, ?.N.I?iia,
A.A.Iaaeia, A.I.Ca?aeianueeee) ? o aeayeeo caei?aeiiieo (?.Aioonaeaiea?,
E.?iaaieaii, AE.I?aaea, J.R.Anderson), na?ae/aoue i?i oa, ui ?nioth/?
iaoiaee ? caniae i?aai?caoe?? i?ioeano iaa/aiiy ia aeinoaoiuei
a?aeiia?aeathoue no/aniei aeiiaai, ye? i?aae’yaeythoueny aei
aoaeoeaiino? ? iaae?eiino? i?aeaioiaee iia?aoi??a a?aaoe/ieo nenoai.

Iaea?eueo oa?aeoa?iei iaaeie?eii o?aaeeoe?eiiai i?ioeano iaa/aiiy ?
ianeaiee oa?aeoa? oniiai aeeeaaeaiiy ciaiue, ui ia aeicaiey?
cae?enithaaoe cai?ioiee ca’ycie a?ae iniae, yea iaa/a?oueny aei
aeeeaaea/a c iiaeeea?noth iiaeaeueoiai eiio?ieth oa ?iaa??aioiino?
ioe?iee yeino? canai?iiy aeaeea?iaaieo ciaiue. Ca aeaieie ineoieia?/ieo
aeine?aeaeaiue ethaeeia caiai’yoiao? 10 % i?i/eoaiiai, 20 % ii/ooiai ?
30 % iiaa/aiiai. Aeyaeaii, ui aeei?enoaiiy aoae?ia?coaeueieo cania?a
ciaioo? ia 40 % iaiao?aeiee /an iaa/aiiy ? ia 20 % ca?eueoo? ??aaiue
canai?ii? ?ioi?iaoe??.

I?aeaeuaiiy aoaeoeaiino? nenoai i?ioan?eii? i?aeaioiaee iia?aoi??a
cia/iith i??ith aecia/a?oueny ai?iaaaeaeaiiyi iiaeo ?ioi?iaoe?eieo
oaoiieia?e, ye? aeicaieythoue a ?aieao ?aeeii? nenoaie iioei?coaaoe
i?ioean iaa/aiiy ? caaacia/eoe aaciaeo ooieoe?iioaaiiy a?aaoe/ii?
nenoaie.

O ca’yceo c oeei aeooaeueiith iaoeiaith caaea/ath ? ?ic?iaea iiaeo
iaoiae?a aiae?co ? neioaco nenoai ea?oaaiiy i?ioeanii iaa/aiiy oaeei
/eiii, uia ca iaeneiaeueii ei?ioeee no?ie iaa/eoe iia?aoi?a caaeai?e
noi? ciaiue, oi?iue ? iaaee?a, iaiao?aeieo aeey aeeiiaiiy i?ioan?eii?
ae?yeueiino?.

?nioth/? iaoiaee ioe?ithaaiiy i?ioan?eii? i?aeaioiaee aeei?enoiaothoue
aeiionoei? a?aie/i? a?aeoeeaiiy cia/aiue /aniaeo ? oi/i?nieo
oa?aeoa?enoee ea?oaaeueieo ae?e iia?aoi?a aai ?iia??i?noue aeeiiaiiy
eiio?ieueiiai caaaeaiiy. Ine?eueee oe?eueiaa ooieoe?y iaa/aiiy iineoue
ia/?oeee oa?aeoa? ? eaae?o?eaoe?eia oa?aeoa?enoeea iia?aoi?a ia i?noeoue
eiie?aoieo ia?aiao??a ??aiy i?ioan?eii? i?aeaioiaee, aeooaeueiith iinoa?
caaea/a ?ic?iaee aenia?oieo iaoiae?a ioe?ithaaiiy i?ioeano iaa/aiiy.

Nenoaie ? i?ioeane ea?oaaiiy iaa/aiiyi iia?aoi??a oa?aeoa?ecothoueny
iaaecae/aeiith neeaaei?noth aioo??oi?o ? ciai?oi?o aca?iica’yce?a ? ?
neaai oi?iae?ciaaiith iaeanoth iaoeiaeo aeine?aeaeaiue. Iiaeae?
ea?oaaiiy i?ioeanii iaa/aiiy aoaeothoueny ia oi?iae?caoe?? iieno
ia’?eo?a ? neioac? no?oeoo?, ye? a?aeia?aaeathoue niaoeeo?eo
?ioi?iaoe?eii? aca?iiae?? iia?aoi?a ? oaoi?/ii? nenoaie. Ca?aene iaaoaa?
aeooaeueiino? caaea/a iiaeaethaaiiy ae?yeueiino? iia?aoi?a a nenoai?
iaa/aiiy, yea iieyaa? a e?euee?niiio ioe?ithaaii? ooieoe?e iai’yo? ?
aeyaeaii? iaoaiaoe/ieo caeaaeiinoae, ye? anoaiiaeththoue aca?iica’ycie
i?ae oa?aeoa?enoeeaie ?ioi?iaoe??, ui iaaeoiaeeoue, oaeaee?noth ??
caiai’yoiaoaaiiy ? o?eaae?noth caa??aaiiy.

Ca’ycie ?iaioe c iaoeiaeie i?ia?aiaie, ieaiaie, oaiaie. Aeena?oaoe?eia
aeine?aeaeaiiy ? /anoeiith ieaiiaeo ?ia?o: aea?aeathaeaeaoii?
iaoeiai-aeine?aeii? ?iaioe (IAe?) 293-AA93: “?ic?iaea ? aeine?aeaeaiiy
eiii’thoa?ii? oaoiieia?? a aeeaeaeoe/ieo nenoaiao iaa/aiiy oaeoeueoaoo
aa?aoe?eiiai iaeaaeiaiiy” ca 1993-1995 ??.; aea?aeathaeaeaoii? IAe?
704-AA96:“Aeine?aeaeaiiy iiaeeeainoae noai?aiiy nenoai ea?oaaiiy e?oae?a
c aeei?enoaiiyi iaoiaeo iae?i?eiiai ioe?ithaaiiy ?ooo
aaaaoiia?aiao?e/ieo ia’?eo?a ca 1996-1998 ??.

Iaoa ? caaea/? aeine?aeaeaiiy: ia iniia? aeine?aeaeaiiy ?nioth/eo
iaoiae? i?aai?caoe?? i?ioeano iaa/aiiy i?aeaeueoe aoaeoeai?noue
i?ioan?eii? i?aeaioiaee iia?aoi??a ? caaacia/eoe aaciaeo a?aaoe/ii?
nenoaie oaeeie ?ic?iaeaie: no?oeoo?ii? iiaeae? iiaeaiiy ? aeai?eoi?a
ea?oaaiiy aeeaeaeoe/ieie ciaiiyie; aenia?oieo iaoiae?a ioe?ithaaiiy ?
?aeaioeo?eaoe?? ia?aiao??a ia’?eoa ea?oaaiiy a nenoai? iaa/aiiy;
iiaeaeae canai?iiy ? caa?aaeaiiy ?ioi?iaoe?? a iai’yo? iia?aoi?a;
i?ia?aiii-oaoi?/ieo cania?a ea?oaaiiy i?ioeanii iaa/aiiy iia?aoi??a
a?aaoe/ieo nenoai.

Iinoaaeaia iaoa aeinyaa?oueny ae??oaiiyi oaeeo iaoeiaeo caaea/:
aeine?aeaeaiiy aeeaeaeoe/ieo i?eioeei?a i?aai?caoe?? nenoaie ? i?ioeano
ea?oaaiiy iaa/aiiyi a ?ioi?iaoe?eiiio na?aaeiaeu?; aiae?c ?nioth/eo
iiaeaeae iiaeaiiy ciaiue, iaoiae?a ioe?ithaaiiy ? ea?oaaiiy ciaiiyie a
i?ioean? iaa/aiiy; ?ic?iaea iiiaeeiii? iiaeae? iaoeiaiai ci?noo
iaa/aiiy, iaoiaeeee aenia?oiiai ioe?ithaaiiy ciaiue ? oi?iue iia?aoi?a,
iaiao?aeieo aeey aeeiiaiiy i?ioan?eii? ae?yeueiino?; iiaeaeae ea?oaaiiy
?ioi?iaoe?eieie iioieaie aeeaeaeoe/ieo ciaiue ia iniia? cai?iiiiiaaieo
aeai?eoi?a i?eeiyooy ??oaiiy; iaoiaeeee ?aeaioeo?eaoe?? oa aiae?co
ia?aiao??a ia’?eoa ea?oaaiiy; iiaeae? canai?iiy ? caa?aaeaiiy ciaiue a
aeiaai/ani?e iai’yo? iia?aoi?a; i?ia?aiia ?aae?caoe?y nenoaie ea?oaaiiy
i?ioeanii iaa/aiiy iia?aoi?a a na?aaeiaeu? ia?niiaeueiiai eiii’thoa?a.

Iaoeiaa iiaecia iaea?aeaieo ?acoeueoao?a iieyaa? a ianooiiiio:

– i?iaiae?ciaaii i?ia?aiii-oaoi?/i? caniae ? iaoiaee aeoea?caoe??
iaoeiaiai ci?noo iaa/aiiy, cai?iiiiiaaii ???a?o?/io iiaeaeue
aeaeea?aoeaiiai iiaeaiiy aeeaeaeoe/ieo ciaiue, yea a?oioo?oueny ia
ia’?eoii-i???ioiaai?e iaoiaeieia?? i?iaeooaaiiy;

– noi?ioeueiaai? ?ioi?iaoe?ei? i?eioeeie ea?oaaiiy aeeaeaeoe/ieie
ciaiiyie a eiii’thoa?i?e nenoai? iaa/aiiy (ENI);

– ?ic?iaeaii oai?aoeei-iiiaeeiio iiaeaeue no?oeoo?e aeeaeaeoe/ieo ciaiue
? iaa?oioiaaii iaiao?aei? oa aeinoaoi? oiiae neioaco i?i?iaeueii?
no?oeoo?e ciaiue aeey ea?oaaiiy i?ioeanii iaa/aiiy; ae?aeiioe/iee iaoiae
aiae?co no?oeoo?e aeeaeaeoe/ieo ciaiue a ?iciiae?eaieo nenoaiao;

– ?ic?iaeaii aaeaioeai? aeai?eoie ea?oaaiiy ?ioi?iaoe?eieie iioieaie;
iaoiaeeeo aenia?oiiai ioe?ithaaiiy ciaiue ? oi?iue iia?aoi?a,
iaiao?aeieo aeey aeeiiaiiy i?ioan?eii? ae?yeueiino?; iaoiaeeeo
aecia/aiiy ooieoe?e iaeaaeiino? ciaiue iia?aoi?a ciaiiyi nenoaie
iaa/aiiy ? aeeiai?/i? oeaee ioe?ithaaiiy; iaoiaeeeo ?aeaioeo?eaoe??
ia’?eoa ea?oaaiiy a i?ioean? iaa/aiiy; iaoaiaoe/io iiaeaeue canai?iiy ?
caa?aaeaiiy ciaiue a iai’yo? iia?aoi?a; i?iaiae?ciaaii ?ioi?iaoe?ei?
i?ioeane a nenoai? iaa/aiiy ia iniia? noaeeo /ano ? ia?aiao??a
?ioi?iaoe?eii? iiaeae?.

I?aeoe/ia cia/aiiy iaea?aeaieo ?acoeueoao?a. ?ic?iaeai? i?eioeeie,
iaoiaee, iiaeae? ea?oaaiiy i?ioeanii iaa/aiiy, a oaeiae aeai?eoi?/ia ?
?ioi?iaoe?eia caaacia/aiiy iieeaaeaii a iniiao i?ia?aiii? ?aae?caoe??
eiii’thoa?ii? nenoaie i?ioan?eii? i?aeaioiaee iia?aoi??a. A ?iaio?
iaa?oioiaaia iaiao?aei?noue ai?iaaaeaeaiiy ia aoai? ia?aaeo?aiaaea?ii?
i?aeaioiaee aenia?oieo iaoiae?a ? iiaeaeae ea?oaaiiy c iaoith
i?aeaeuaiiy aoaeoeaiino? i?ioeano iaa/aiiy iia?aoi??a a?aaoe/ieo nenoai.
I?iaaaeai? aenia?eiaioaeuei? aeine?aeaeaiiy i?aeoaa?aeeee iieiaeaiiy,
ye? aeiinyoueny ia caoeno.

?aae?caoe?y ?acoeueoao?a. ?ic?iaeai? aenia?oi? iaoiaee ? iiaeae?
ea?oaaiiy i?ioeanii iaa/aiiy iieeaaeaii a iniiao ?aeiiaiaeaoe?e i?e
aeeiiaii? athaeaeaoieo IAe? 293-AA93 oa IAe? 704-AA96.

?acoeueoaoe aeine?aeaeaiue aoee aeei?enoai?: i?e ?ic?iaoe?
aeai?eoi?/iiai, ?ioi?iaoe?eiiai ? i?ia?aiiiai caaacia/aiiy eiii’thoa?ieo
nenoai iaa/aiiy ? eiio?ieth ciaiue a eieaeuei?e ia/enethaaeuei?e ia?aae?
ca niaoe?aeueiinoyie oaeoeueoao?a aa?aoe?eiiai iaeaaeiaiiy, aaoiiaoeee ?
ia/enethaaeueii? oaoi?ee EIOOeA; a i?ioean? i?aeaioiaee iia?aoi??a
ea?oaaiiy aa?aoe?eieie nenoaiaie a Aea?aeaai?e eueioi?e aeaaeai??
Oe?a?ie; a ?ic?iaoe? iaoeiai? oaie Oeaio?aeueiiai iaoeiai-aeine?aeiiai
?inoeoooo ca?ieieo nee Oe?a?ie; a nenoai? iaa/aiiy a I?aeia?iaeiiio
iaoeiai-iaa/aeueiiio oeaio?? ?ioi?iaoe?eieo oaoiieia?e ? nenoai IAI ? II
Oe?a?ie.

Iniaenoee aianie caeiaoaa/a. Iai?yie aeine?aeaeaiue, ?aea? ? iaoiaee
?ic?iaeyeenue aaoi?ii naiino?eii.

Ai?iaaoe?y ?acoeueoao?a aeena?oaoe??. Iniiai? iieiaeaiiy aeena?oaoe?eii?
?iaioe aeiiia?aeaeenue, iaaiai?thaaeenue ? ioae?eoaaeenue ia oaeeo
iaoeiai-iaoiaee/ieo eiioa?aioe?yo (IIE) ? nai?ia?ao: IIE “I?iaeaie oa
ia?niaeoeae oi?aae?iiy ye?noth i?aeaioiaee niaoe?ae?no?a”, 1993 ?.;
ca?oi?e iaoeiai-oaoi?/i?e eiioa?aioe?? (IOE) EIOOeA ca 1993 ?.;
iaoeiai-i?aeoe/iiio nai?ia?? c i?iaeai canoinoaaiiy eiii’thoa?ieo
iaa/aeueieo nenoai, 1994 ?.; ca?oi?e IOE iaoeiaeo eieaeoea?a
oi?aa?neoaoo ca 1994 ?.; i?aeia?iaei?e IOE “Aaeiieea-95”; ca?oi?e IOE
EIOOeA ca 1995 ?.; IIE “I?iaeaie aaaaoinooiaiaai? i?aeaioiaee aaeaeaa??a
oa oao?aoe?a c iai?yio: “Aa?aoe?y oa einiiiaaoeea”, 1995 ?.; IOE
“I?iaeaiu niaa?oainoaiaaiey nenoai ay?iiaaeaaoeeiiiiai ianeoaeeaaiey e
oi?aaeaiey iiaeaeaeiuie iauaeoaie” “Ay?iiaaeaaoeey-96”; i?aeia?iaei?e
IOE “Iaania/aiea aaciianiinoe iieaoia a iiauo yeiiiie/aneeo oneiaeyo”,
1997 ?.; XVII ca?oi?e IOE EIOOeA ca 1996 ?.; ca?oi?e IOE EIOOeA ca 1997
?.; i?aeia?iaei?e IOE “I?iaeaiu ?acaeoey ay?iiaaeaaoeeiiiiai
ianeoaeeaaiey e aaeiieee aicaeooiuo noaeia” “Ay?iiaaeaaoeey e
aaeiieea-98”.

Ioae?eaoe??. Iaoeia? ? i?aeoe/i? ?acoeueoaoe iioae?eiaai? a 23
ae?oeiaaieo ?iaioao: 6 noaoae a iaoeiaeo aeo?iaeao ? ca??ieeao iaoeiaeo
?ia?o (4 – iioae?eiaaii aaoi?ii iniaenoi), o?e iaa/aeueii-iaoiaee/ieo
aeaeaiiy, 14 – a iaoa??aeao ? oacenao eiioa?aioe?e.

No?oeoo?a ? ianya aeena?oaoe??. Aeena?oaoe?eia ?iaioa neeaaea?oueny c?
anooio, i’yoe ?icae?e?a, aeniiaeo, o?ueio aeiaeaoe?a, aeo?a
ai?iaaaeaeaiiy, nieneo aeei?enoaieo aeaea?ae c 161 iaeiaioaaiue ?
i?noeoue 236 noi??iie, c yeeo 183 noi??iie iniiaiiai oaenoo, 11
oaaeeoeue, 63 ?enoie?a.

Ci?no ?iaioe

O anooi? aeeeaaeaii nooue ? noaiiaeua iaoeiai? i?iaeaie oa iaa?oioiaaii
aeooaeuei?noue ?ic?iaee iaoiae?a, aeai?eoi?a ? iiaeaeae ea?oaaiiy
i?ioeanii iaa/aiiy iia?aoi??a a?aaoe/ieo nenoai; noi?iiaaii oe?e?,
caaea/?, iaoeiao ? i?aeoe/io iiaecio ?iaioe.

A ia?oiio ?icae?e? c?iaeaii aiae?c i?ia?aiii-oaoi?/ieo cania?a
o?aiaaea??a ? no/anieo eiioeaioe?e i?aai?caoe?? i?ioeano iaa/aiiy
iia?aoi??a. ?icaeyiooi i?eioeeie oi?ioaaiiy ? iaoiaeeeo ea?oaaiiy
iaoeiaei ci?noii iaa/aiiy, a iniiao yeeo caeeaaeaii ae?yeuei?niee
i?aeo?ae aei iaaoooy ciaiue. Aeoeaioiaaii oaaao ia i?iaeaiiiio i?eioeei?
ea?oaaiiy ciaiiyie a i?ioean? iaa/aiiy.

Caaea/a aeoea?caoe?? ?ioi?iaoe?eiiai na?aaeiaeua iaa/aiiy ? ae?iaeaiiy
iioeiaeueieo ea?oaaeueieo ae?e ae??oo?oueny ia iniia? eiai?oeaieo
iaoai?ci?a ea?oaaiiy aeeaeaeoe/ieie ciaiiyie: eiii?eyoe??,
i?ioeaaeo?ae?caoe??, eiiiiceoe??, eii?aeeiaoe??, ocaaaeueiaiiy,
?icae?eaiiy, iineeaiiy.

Ia iniia? aiae?co aeeaeaeoe/iiai ? eiai?oeaiiai i?aeoiae?a aei i?iaeaie
iaa/aiiy noi?ioeueiaaii ?ioi?iaoe?ei? i?eioeeie ea?oaaiiy aeeaeaeoe/ieie
ciaiiyie: a?aeiia?aeiino? oe?eae iaa/aiiy nenoai? ciaiue ? oi?iue
iia?aoi?nueei? ae?yeueiino?; no?oeoo?oaaiiy iaoeiaiai ci?noo aei
iaiiae?eueieo aeaiaio?a ciaiue (?ioi?iaoe?eieo ia’?eo?a) a iaaeao
aeenoeeie?ie c iaoith aeyaeaiiy i?aeaeenoeeie?ia?ieo ca’yce?a ?
ea?oaaiiy aeeaeaeoe/ieie ciaiiyie; ooieoe?iiaeueiiai aca?iica’yceo
ciaiue ?c nenoaiith oi?iue; ca’yciino? ? iiaiioe aeeaeaeoe/ieo ciaiue,
iaiao?aeieo aeey oi?ioaaiiy nenoaie oi?iue aeeiioaaoe i?ioan?eio
ae?yeuei?noue.

Aeeeaaeaii iaoiaeeeo i?iaeooaaiiy ENI. ?ic?iaeaii ???a?o?/io iiaeaeue
no?oeoo?e aeeaeaeoe/ieo ciaiue a ENI, yea a?oioo?oueny ia iiaeoeueiiio
i?eioeei? ? aeicaiey?: oi?iaeueii anoaiiaethaaoe eia?/io ca’yci?noue
aeaiaio?a ciaiue; oniaaeeiaoaaoe ciaiiy c iiaeoe?a aa?oi?o ??ai?a;
iaiaaeeoe eean ?ioi?iaoe?eieo ia’?eo?a iiooeo; oi?ioaaoe iiaeoe?
ia’?eo?a ia iniia? iaoai?ci?a aeeo/aiiy iaaei??iino?
(i?ioeaaeo?ae?caoe?y), eiiiiceoe?? ? ocaaaeueiaiiy, ui aeicaiey?
iia?aoi?o ia?iaeyoe aeeaeaeoe/i? ciaiiy c aenieith aoaeoeai?noth.
Aiane?aeie cacia/aiiy iiiaeeie a?aeiioaiue i?ae iiaeoeyie iiaeia
iiaoaeoaaoe no?oeoo?o, yea a?aeiia?aea? ??ciei oe?eyi aeei?enoaiiy
ciaiue.

O ae?oaiio ?icae?e? ?ic?iaeaii iaoiaee ? aeai?eoie ea?oaaiiy
?ioi?iaoe?eieie iioieaie aeeaeaeoe/ieo ciaiue a nenoai? iaa/aiiy.

I?iaiae?ciaaii aeei?enoaiiy eia?/ii?, i?iaeoeoe?eii?, o?aeiiai? ?
ia’?eoii-i???ioiaaii? iiaeaeae aeey iiaeaiiy ciaiue a ENI. Iaoeiai
iaa?oioiao?oueny ia?niaeoeai?noue ia’?eoii-i???ioiaaii? iaoiaeieia??
iiaeaiiy ciaiue a nenoaiao iaa/aiiy. Aaaaeaii iiiyooy ?ioi?iaoe?eiiai
ia’?eoa (?I) ye aeaiaioa?ii? nieneiai? iaeeieoe? ciaiue. C onueiai
??ciiiai?ooy a?aeiioaiue ?I aeae?eaii a?aeiioaiiy, ye? aeanoea? aacai
aeeaeaeoe/ieo ciaiue.

Iaoeiaee ci?no iaa/aiiy cia?aaeaii o aeaeyae? niaoe?aeueii? iiiaeeie,
yea caaeiaieueiy? aeeaeaeoe/i? i?eioeeie ? oi?iaeueii ia’?aeio? aeaiaioe
iiiaeeie O aeaieo a aeayeo no?oeoo?o.

Aecia/aiiy. No?oeoo?ith I aeeaeaeoe/ieo ciaiue iacaaii a?ia?ia
a?aeiioaiiy I Xx Q ? oaea, ui aeey aoaeue-yeeo ia? ia’?eo?a xi , xj
aeaea?oiaiai aeiaooeo Xx aeaiaio?a iiiaeeie X ni?aaaaeeeai:

Hxi, xji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, xjj = , Hxi, xji , Hxi, xjj Q.

Oea icia/a?, ui aeaiaioo iiiaeeie Q a?aeiioaiue aca?iii iaeiicia/ii
a?aeiia?aea? o?eueee iaeei aeaiaio aeaea?oiaiai aeiaooeo Xx.

Aeiaaaeaii oai?aio i?i oi?iaeuei? e?eoa??? ?nioaaiiy aea?aaa ii/aoeiai?
no?oeoo?e ye i?aeiiiaeeie iiiaeeiii? iiaeae?, yea a?aeiia?aea?
aeeaeaeoe/iei i?eioeeiai iiaiioe ? ca’yciino? ciaiue, iaiao?aeieo aeey
oi?ioaaiiy nenoaie oi?iue aeeiioaaoe i?ioan?eio ae?yeuei?noue.

Oai?aia. Aea?aaii D a?ia?iiai a?aeiioaiiy I ? aeania i?aeiiiaeeia D
H aeaiaio?a, /enei yeeo iiaeiii aooe ia iaeeieoeth iaioa, i?ae a O,
ca?aaoeny c I ia iiiaeei? O ? caaeiaieueiyoe oiiao ca’yciino? aeaiaio?a
a D.

Aeiiaa ?ioi?iaoe?eii? ca’yciino? aeaiaio?a a D ? ca?a D c I ia iiiaeei?
O aea?aaeaioia a?aenooiino? oeeee?a i?e oi?ioaaii? ?ioi?iaoe?eieo
iioie?a.

?ic?iaeaii aaeaioeaiee aeai?eoi ea?oaaiiy ?ioi?iaoe?eiei iioieii ia
iniia? noae-nieneiaeo iiaeaeae, yeee aeicaiey? aiane?aeie aaia?aoe??
iiaeeeaeo no?aoaa?e iaa/aiiy ?iaeea?aeoae?coaaoe i?ioean iaa/aiiy
iia?aoi?a.

Aeai?eoi oi?ioaaiiy ?ioi?iaoe?eiiai iioieo V i?noeoue i?ioeaaeo?e:

1. Ia iiiaeei? O aenia?oii caaeaieo ?I oi?io?ii aeaea?oiaee aeiaooie ?
aeeo/a?ii ia?e (xi , xj), aeey yeeo i j. Aeae? i?ae ia?ith (xi , xj)
?icoi??ii aeaiaeaiaioio iiiaeeio xi , xj Oo . Noi?iiaaia iiiaeeia Oo ?
aaciaith aeey ia/?oei? iiaeiiiaeeie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 Oo, yeo
caaeiaieueiy? ooieoe?y iaeaaeiino?:
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(xi , xj ) =
picscalex100010009000003a40200000200170000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c024005c0281200000026060f001a00ffffffff00001000
0000c0ffffffbcffffff80280000fc0400000b00000026060f000c004d61746854797065
0000200110000000fb0280fe0000000000009001000000020002001053796d626f6c0002
040000002d01000008000000320a6e043a0001000000ef0008000000320ade043a000100
0000ee0008000000320a22023a0001000000ef0008000000320a42033a0001000000ed00
08000000320aa6013a0001000000ec0010000000fb0240fe000000000000900100000002
0002001053796d626f6c0002040000002d01010004000000f001000008000000320a4504
b71b01000000ce0008000000320aa501181d01000000ce0017000000fb0240fe00000000
00009001000000cc0402001054696d6573204e657720526f6d616e2043797200cc790400
00002d01000004000000f00101000c000000320a4504e42009000000e7ede0e9e4e5edee
2e0008000000320a45047b2001000000200008000000320a4504c21e02000000ede50800
0000320a4504601e01000000200008000000320a45047f1b01000000200008000000320a
4504d2190100000020000c000000320a4504aa100a000000e2b3e4edeef8e5ededff0800
0000320a4504d10f02000000202008000000320a4504720b01000000200009000000320a
4504cb0803000000e4ebff0008000000320a4504f2070200000020200a000000320a4504
ff02060000002020ffeaf9ee08000000320a4504cb0102000000302c08000000320a4504
00010200000020200c000000320aa5012a2009000000e7ede0e9e4e5edee2c0008000000
320aa501c11f01000000200008000000320aa501e01c01000000200008000000320aa501
c31a0200000020200c000000320aa5019b110a000000e2b3e4edeef8e5ededff08000000
320aa501c21002000000202008000000320aa501fa0b02000000202009000000320aa501
530903000000e4ebff0008000000320aa5017a080200000020200a000000320aa5018703
060000002020ffeaf9ee08000000320aa501530202000000312c08000000320aa501b901
02000000202017000000fb0240fe0000000000009001010000cc0402001054696d657320
4e657720526f6d616e2043797200cc79040000002d01010004000000f001000008000000
320a4504101d01000000510008000000320a4504341a01000000710009000000320a4504
490d030000002c20780008000000320a4504e20b01000000780008000000320aa501711e
01000000510008000000320aa501951b01000000710009000000320aa5013a0e03000000
2c20780008000000320aa501da0c01000000780017000000fb02e0fe0000000000009001
010000cc0402001054696d6573204e657720526f6d616e2043797200cc79040000002d01
000004000000f001010008000000320a91040e1b01000000690008000000320af1016f1c
01000000690008000000320af101c20d01000000b30017000000fb02c0fe000000000000
9001010000cc0402001054696d6573204e657720526f6d616e2043797200cc7904000000
2d01010004000000f001000008000000320a9104520f010000006a0008000000320a9104
c80c01000000690008000000320af1014310010000006a000a00000026060f000a00ffff
ffff01000000000010000000fb021000070000000000bc02000000cc0102022253797374
656d00cc040000002d01000004000000f001010003000000000000000000

2. Noi?iiaaiee iio?e V vi = q i (xi , xj) iiaeiai ca?aaoeny c
ii/aoeiaith nenoaiith aeeaeaeoe/ieo ciaiue ia aenia?oii caaeai?e O
iiiaeei? ?I:
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(xi , xj ) i = X; aeey N aeaiaio?a vi V, aea i = 1, N.

Ca?a noi?iiaaii? iiiaeeie V c ii/aoeiaith nenoaiith ciaiue ia iiiaeei? O
ia?aaeaa/a? iae?e aeeaeaeoe/iiai e?eoa??th iiaiioe ciaiue. Aeae?
iio??aii aaanoe i?ioeaaeo?o ia?aa??ee iiiaeeie V ia ?ioi?iaoe?eio
ca’yci?noue c iaoith aeyaeaiiy a?aeiioaiiy aea?aaeaioiino? (iiae?aiino?)
aeey aeaiaio?a iiiaeeie O.

3. Aeey aenia?oii caaeaiiai aeaea?aea xi a iiiaeei? O ia?aa??y?oueny
a?aeiioaiiy q i Q iaeei xi aei iaeiiai xj ? iaeei xi aei i?aeiiiaeeie
Oi O c aeaiaioaie, aeey yeeo caaeaia a?ia?ia a?aeiioaiiy q i Q. I?e
oeueiio i?aeiiiaeeia Oi O aecia/a? ??aaiue ???a?o?? iiaeaiiy ciaiue aeey
caaeaiiai xi. Aeae? i?ioeaaeo?a iiaoi?th?oueny aeey aeaea?ae c iiiaeei
Oi ? ia?aa??ythoueny a?ia?i? a?aeiioaiiy q i Q c i?aeiiiaeeiith O Oi c
iaoith oi?ioaaiiy Xj O Oi. I?ioeaaeo?a aaaaea?oueny aeeiiaiith, yeui q
i Q aecia/aia ia iiiaeei? O.

Cai?iiiiiaaiee aaeaioeaiee aeai?eoi aeicaiey? aaia?oaaoe ?I ia ??cieo
??aiyo neeaaeiino? aeeaeaeoe/ieo ciaiue (?en.1). Cae?eniaii aiae?c
e?eoa???a, ye? coiiaeththoue neeaaei?noue iaoa??aeo, yeee aea/a?oueny.
?ioi?iaoe?eio neeaaei?noue cai?iiiiiaaii aecia/aoe ca aeiiiiiaith
eiao?oe??ioa iane/aiino?: ki = I/ I , aea I = I’ + I – caaaeueia
e?euee?noue ?I; I’, I – e?euee?noue aaea a?aeiieo ? iiaeo iiiyoue. Ianya
ne?a na?aaeiueiai ?I: Nn? = N / I , aea N – caaaeueia e?euee?noue ne?a.

Cai?iiiiiaaii ae?aeiioe/iee niin?a aiae?co aeeaeaeoe/ieo ciaiue, ye?
aeicaieythoue aoaeoaaoe aeai?eoie oi?ioaaiiy eean?a aea?aaeaioieo
no?oeoo? c ?icia?aeaeaiiyi ia/enethaaeueiiai i?ioeano. Noi?ioeueiaaii
i?aaeea ia’?aeiaiiy i?aeno?oeoo? c iaoith oi?ioaaiiy iiaii? no?oeoo?e
aeeaeaeoe/ieo ciaiue. ?icaeyiooi oi?iaeuei? i?aaeea ?iciiae?eo no?oeoo?e
I ia /anoeie I1, I2 I ? i?aaeea ia’?aeiaiiy D1 H1, D2 H2 i?aeiiiaeei
D1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 D2 c iaoith oi?ioaaiiy no?oeoo?e D. I?e iiae?e? iaiao?aeii
aeio?eioaaoenue oiiae: I1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 I2 = ?, aea ? – ca’ycia i?aeiiiaeeia.

Oaa?aeaeaiiy 1. sseui i?aeiiiaeeia aeaiaio?a iioieo ? Di , Dj ?
caaaeueiith aeey oeeo i?aeno?oeoo?, oi a ?acoeueoao? ia’?aeiaiy Di
picscalex100010009000003890000000200120000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c022002a0011200000026060f001a00ffffffff00001000
0000c0ffffffbeffffff60010000de0100000b00000026060f000c004d61746854797065
0000400011000000fb0240fe000000000000900100000002040200104d54204578747261
0002040000002d01000008000000320aa00132000100000055000a00000026060f000a00
ffffffff01000000000010000000fb021000070000000000bc02000000cc010202225379
7374656d00cc040000002d01010004000000f00100000300000000000000806148000000
0000 Dj io?eia?ii iiaio no?oeoo?o D.

Oaa?aeaeaiiy 2. sseui ia?aoei Di , Dj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 P aei??aith? ionoi, oi ia’?aeiaiiy Di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 Dj ia ? no?oeoo?ith D.

Oaa?aeaeaiiy 3. sseui ia?aoei Di , Dj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 P aei??aith? aeayeei i?aeiiiaeeiai Bi , Bj e Bi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 Bj ?, oi ia’?aeiaiy Di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 Dj ia ? iiaiith no?oeoo?ith D.

I?iaaaeai? aeine?aeaeaiiy aoaeoeaiino? cai?iiiiiaaiiai aeai?eoio
aaia?aoe?? aea?aaeaioieo i?aeno?oeoo? (A.1) ii??aiyii c iaea?eueo
a?aeiieie (A.2) aeicaieeee aeyaeoe cia/io caeaaei?noue ?inoo aeo?ao
iaoeiiiai /ano a?ae no?oeoo?ii? neeaaeiino? aac aeaieo, yea
aecia/a?oueny /eneii eean?a no?oeoo?e aeeaeaeoe/ieo ciaiue (?en.2).
Cai?iiiiiaai? iiiaeeii? iiaeae? no?oeoo?e ? ae?aeiioe/iee niin?a
iiaeaiiy aeeaeaeoe/ieo ciaiue aeicaieeee iiaoaeoaaoe aoaeoeai? aeai?eoie
ea?oaaiiy ?ioi?iaoe?eieie iioieaie, ye? aea?aeii a?ae??ciythoueny ca
aeo?aoaie iaoeiiiai /ano a?ae ?nioth/eo, ui aeiaiaeeoue i?aeoe/io
aeioe?euei?noue cai?iiiiiaaiiai i?aeoiaeo aei ?ic?iaee aeai?eoi?a
ea?oaaiiy aacaie aeaieo ?ioi?iaoe?eieo nenoai.

O o?aoueiio ?icae?e? i?iaiae?ciaaii iaoiaee ae?aaiinoeee i?ioeano
iaa/aiiy ? iaoeiai iaa?oioiaaii no?oeoo?iee i?aeo?ae aei oanoiaiai
eiio?ieth ciaiue c iaoith aecia/aiiy a?aeiioaiue ciaiue ? oi?iue a
nenoai? iaa/aiiy. C?iaeaii aiae?c ?ioi?iaoe?eieo iiaeaeae iia?aoi?a,
yeee iaa/a?oueny: ??cieoeaai?, ia?oo?aaoe?eii?, iaa?eaeii? ? aeiaaaeaii
aeioe?euei?noue ?oiueiai canoinoaaiiy.

Oi?iaeueii i?ioean iaa/aiiy iia?aoi?a iiaeia iieacaoe ye ae??oaiiy
iioei?caoe?eii? aaaaoie?ieiai? caaea/? oi?ioaaiiy ciaiue ? oi?iue ia
eiaeiiio e?ieo iaa/aiiy. No?oeoo?o iiaeae? i?ioeano ia?iaee ciaiue
aoaeaii ioioiaeithaaoe c aano?aeoiei a?aoii S o aeaeyae? aeayeiai
a?aeiioaiiy ia iiiaeei? aeaiaio?a ciaiue xi X ? oei?a a?ia?ieo
a?aeiioaiue vi V. E?ioeaaa iaoa Z (?en.3) iaa/aiiy oi?io?oueny,
aeoiaey/e c aeiia eaae?o?eaoe?eii? oa?aeoa?enoeee niaoe?ae?noa ? ?
i?aei-iiaeeiith aaciai? iiiaeeie ciaiue X, aea aeey xZ caaeaia ooieoe?y
iaeaaeiino? z(x).

Aeinyaiaiiy iaoe Z aecia/a?oueny aeinyaiaiiyi i?aeoe?eae Tj O. Iiiaeeia
O oi?io? eean oe?eae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 Tj = Z, ? aeae? aei oi?ioaaiiy iaa/ath/eo ae?e ? no?oeoo?oaaiiy
ciaiue ia aeaiaioe x1, … , xk , ye? ia iio?aaothoue iiaeaeueoiai
iiae?eo (ieaei?e ??aaiue), i?e oeueiio xi T , T X .

Cacia/eii, ui ciaiiy (oi?iiy) Y iia?aoi?a ? ia/?oea i?aeiiiaeeia
iiiaeeie X c aeayeith ooieoe??th iaeaaeiino? y (x), yea oa?aeoa?eco?
nooi?iue canai?iiy aeaiaioa xi iiiaeeie ciaiue X, xi X. Ia/?oea
i?aeiiiaeeia Y iiiaeeie X yaey? niaith iiiaeeio ia?: Y = (x /Y(x)), xi
X, Y(x) [0 …1]. Aeey caaeaiiai aeaiaioa t ciaiue aa?oiueiai ??aiy
aenia?oii caaeaii no?oeoo?o ciaiue o aeaeyae? ooieoe?? v = G (xi , t ),
aea i = 1, k. Oey ooieoe?y aeey eiaeii? ia?e (xi , t) aeaiaio?a ciaiue
??cieo ??ai?a o?eno? o?eueee iaeia a?aeiioaiiy (i?aaeie – iauaaeie) c
iiiaeeie V. Iiiaeeio V a?aeiioaiue i?ae aeaiaioaie ciaiue xi ,t aeaio
non?aei?o ??ai?a cia?aaeaii aaaiaeie eiao?oe??ioaie V (x), ye? caaeai?
aenia?oii ia aoai? no?oeoo?oaaiiy ciaiue ? iiaoaeiae aea?aaa oe?eae
(oi?iue).

Ioe?ieii aianie aeaiaio?a ciaiue xi ieaeiueiai ??aiy o oi?ioaaiiy
iaeeieoe? ciaiue Oj aa?oiueiai ??aiy. Aeey i?eaaaeaiiy aei ii?iaeueiiai
aeaeyaeo OjX ? oi?ioaaiiy ?aeeiiai aaceno iaiao?aeii aeeiiaoe ia?ao?ae
aei a?aeiinieo aaaiaeo eiao?oe??io?a: (xi) = V (xi)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 (xi), i = 1, n, i?e oeueiio aeio?eio?oueny oiiaa: (xi)= 1, i = 1,
k , aea k – /enei ?ioeeaeaioe?e. Oiae? iiiaeeia Y ciaiue iia?aoi?a Y = =
(xi / y (xi)) , aea y (xi) = [0 ; 1] – nooi?iue iaeaaeiino? aeaiaioa
ciaiue xi X nenoaie i?aeiiiaeei? Y.

Aeey ioe?iee nooiaiy a?aeiia?aeiino? ciaiue Y iio??aiei ciaiiyi T
nenoaie ia caaeaiiio ??ai? aeaeea?oaaiiy ciaiue nei?enoa?iiny ooieoe??th
oniaaeeoaaiiy iioiiie-iauaaeie. Ia/eneaiiy ooieoe?? oniaaeeoaaiiy T
aeicaiey? ioe?ieoe aianie ie?aiiai aeaiaioa xi ciaiue – iioiie?a o
oi?ioaaiiy aeaiaioa tj ciaiue – iauaaeea ? yaey? niaith caeaaei?noue:

Y (t) = Y (x) * (x) , Y (t) = Y(x) *V (xi)/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 (xi), aea i=1, n.

Caaeai? a?aeiioaiiy ia iiiaeei? aeaiaio?a ciaiue – iioiie?a
aeicaieythoue ia/eneeoe cia/aiiy ooieoe?? iaeaaeiino? Y (t j) ? ioe?ieoe
nooi?iue canai?iiy ciaiue iia?aoi?ii ia ?ic?aooieiaiio ??ai? – iauaaeeo:

Y (t j) =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 (Y (xi) * V (xi) /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 V (xi)).

Oaeei /eiii, cae?enieaoe iaaeaaia?/i? aei??thaaiiy ia ieaeiueiio ??ai?
no?oeoo?e ciaiue iiaeia aeeiiaoe iie?ieiaa cai?oaiiy aeaiaio?a ciaiue ?
c a?aooaaiiyi oe?eueiai? ooieoe?? ioe?ieoe aeinyaiaiiy e?ioeaai? iaoe
iaa/aiiy.

Aeey ia?aoiaeo aei eeane/ieo ioe?iie ciaiue o e?iaa?noe/ieo oa?i?iao
?ic-?iaeaii aeeiai?/i? oeaee ioe?ithaaiiy. Nei?enoa?iiny e?iaa?noe/iith
ci?iiith (“Ioe?iea”, Term, Q), aea Term = “iacaaeia?eueii”,
“caaeia?eueii”, “aeia?a”, “a?aei?iii”, Q – aaciaa iiiaeeia ioe?iie
ciaiue ii /eneia?e oeae? Q=[0…1]. Ia/?oea i?aeiiiaeeia iiiaeeie Q
yaey? niaith iiiaeeio ia?: =(A (q)/q), q i Q, A (q) [0…1]. A
?acoeueoao? aenia?oiiai iieooaaiiy oi?io?oueny iao?eoey aenia?oieo
ioe?iie c aeaiaioaie m i j, ye? a?aeia?aaeathoue cia/ou?noue aeaiaioa q
i ii??aiyii c aeaiaioii q j aeey aecia/aiiy e?iaa?noe/iiai iiiyooy, yea
iieno?oueny ia/?oeith iiiaeeiith .

Cia/aiiy ooieoe?? iaeaaeiino? A iiaeia iiaeaoe o aeaeyae? aii??e/iiai
aaeoi?a h c aeaiaioaie: h i =A (q i), i=1, 2, … , n ; iiia?i?
ii??aiyiiy – iao?eoeath I a?aeiioaiue c aeaiaioaie m i j = h i / h j.
Aeey aecia/aiiy j-ai aeaiaioa aaeoi?a h ciaoiaeeii noio aeaiaio?a a
eiaeiiio j-io noiaioe? iao?eoe? I, c a?aooaaiiyi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 i = 1 , m i i = 1, noia aeaiaio?a i-ai noiaioey: kj =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 i j =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(h i / h j) =(1 /h j)*
*picscalex63010009000003880000000200120000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02600220031200000026060f001a00ffffffff00001000
0000c0ffffffbeffffffe00200001e0200000b00000026060f000c004d61746854797065
0000600010000000fb02c0fd0000000000009001000000020002001053796d626f6c0002
040000002d01000008000000320ae901370001000000e5000a00000026060f000a00ffff
ffff01000000000010000000fb021000070000000000bc02000000cc0102022253797374
656d00cc040000002d01010004000000f001000003000000000000000000806148000000
0000h i = 1 / h j , oiae? aaeoi? h j = 1 / kj (?en.4).

A ?iaio? aeeeaaeaii iaoiae oi?ioaaiiy a?aeiioaiiy ?iaeea?aeoaeueii?
ia?aaaae ciaiue iia?aoi?a ia iiiaeei? aoaeiiieo ciaiue nenoaie, yeee
aeicaiey? aeeiiaoe ?ioaa?iaaio ioe?ieo ciaiue. Ia/?oea a?ia?ia
a?aeiioaiiy R aecia/a?oueny ye noeoii?noue ia? (x, y) aeaiaio?a ciaiue
iia?aoi?a ? ciaiue nenoaie, ui oa?aeoa?ecothoueny ooieoe??th iaeaaeiino?
R (x, y), yea eiaei?e ia?? (x, y) noaaeoue o a?aeiia?aei?noue nooi?iue
iaeaaeiino? a?aeiioaiith R. I?aenoieiaa a?aeiioaiiy R ia iiiaeei?
aeaiaio?a ciaiue iia?aoi?a aecia/a? a?aeiioaiiy ia?aaaae ?
ia/eneth?oueny x, u X ca oi?ioeith:

R(y, u)=V F S (y, z) F -1 (x, u)= MAX[ MIN( F S (y, z), F -1 (x,
u))].

A ?iaio? aeine?aeaeaii e?eoa??? oanoiaiai eiio?ieth (ia’?eoeai?noue,
iaae?ei?noue, aae?aei?noue, oi/i?noue iaoiaeo iaaeaaia?/ieo
aei??thaaiue), ye? ?aae?ciaai? iaoiaeeeaie: I.1 – nenoaia aeeiio?
“aei?noea ii??aiyiiy a?aeiia?ae? c aoaeiiii; I.2 – i?iiiio?oueny aea??
aa??aio?a a?aeiia?aeae, aiaethth/e aei aoaeoo “i?ciaaaiiy c ioe?ieith ca
aeaiaaeueiith oeaeith; I.3 – i?ney ii??aiyiiy a?aeiia?ae? c aoaeiiii
nenoaia i?iiiio? iiaeeea? aa??aioe a?aeiia?aeae c ioe?ithaaiiyi ca
?aiaiaith oeaeith; I.4 – nenoaia aeeiio? aenia?oia ioe?ithaaiiy c
a?aooaaiiyi a?aeiinieo aaa caieoaiue ? a?aeiia?aeae ca ia/?oeith oeaeith
[0,1].

Aeine?aeaeai? iniiai? ia?aiao?e, ye? aecia/athoue aae?aei?noue iaoiaeo
iaaeaaia?/ieo aei???a: neeaaei?noue, ?iciiae?eueia caeaoi?noue,
ii?iaeueiee caeii ?iciiae?eaiiy (?en.5). Aea??ea ?iciiae?eaia ca
ii?iaeueiei caeiiii ? oano aaaaea?oueny aae?aeiei, yeui |As|

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