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Інформаційна система для прогнозування нафтогазоносних покладів: Автореф. дис… канд. техн. наук / В.І. Шекета, Херсон. держ. техн. ун-т. — Херсон, 1

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

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

OAEAOA Aaneeue ?aaiiae/

OAeE 681. 3:622. 276

?IOI?IAOe?EIA NENOAIA AeEss I?IAIICOAAIIss IAOOIAACIIINIEO IIEEAAe?A

05.13.06 – Aaoiiaoeciaai? nenoaie oi?aae?iiy ?

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

AAOI?AOA?AO

aeena?oaoe?? ia caeiaoooy iaoeiaiai nooiaiy

eaiaeeaeaoa oaoi?/ieo iaoe

OA?NII – 1999

?iaioo aeeiiaii ia eaoaae?? i?eeeaaeii? iaoaiaoeee ?aaii-O?aie?anueeiai
aea?aeaaiiai oaoi?/iiai oi?aa?neoaoo iaooe ? aaco.

Iaoeiaee ea??aiee: eaiaeeaeao oaoi?/ieo iaoe, aeioeaio TH?/eoei
Aieiaeeie? Ieeiea?ae/, ?aaii-O?aie?anueeee aea?aeaaiee oaoi?/iee
oi?aa?neoao iaooe ? aaco, caa?aeoth/ee eaoaae?ith i?eeeaaeii? iaoaiaoeee

Io?oe?ei? iiiiaioe :

Aeieoi? o?ceei-iaoaiaoe/ieo iaoe, i?ioani? Oii/aiei A.I., Oa?niinueeee
aea?aeaaiee oaoi?/iee oi?aa?neoao, caa?aeoth/ee eaoaae?ith iaoaiaoe/iiai
iiaeaethaaiiy

Eaiaeeaeao oaoi?/ieo iaoe, aeioeaio E?ia ?.A., Oa?niinueeee aea?aeaaiee
aa?a?iee oi?aa?neoao, aeioeaio eaoaae?e aeiiii?/ii? e?aa?iaoeee

I?ia?aeia onoaiiaa :

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

Caoeno a?aeaoaeaoueny “17” aa?aniy 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 “14” eeiiy 1999?.

A/aiee nae?aoa?

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

CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE

Aeooaeuei?noue oaie. A aeaiee /an iaooiaaciaa aaeocue ia?
aaoiiaoeciaai? nenoaie ??cieo ??ai?a ? oei?a, a oaeiae ??ci? i?ia?aii?
eiiieaene aeey i?iaiico iaooiaaciiiniino?, iiooeo oa ?ica?aeee ?iaeiaeu
iaooe ? aaco, aea ianooaae oa aoaeoeai?noue canoinoaaiiy AII aeey
eiaeiiai ??aiy ??ci?. Oea iia’ycaia c oei, ui iaaeinoaoiuei
aeei?enoiaothoueny ?icaeiai? aace aeaieo ? a?aenooiy oeiiaa iaoiaeeea
iaaoooy ? iaeiie/aiiy ciaiue i?i iaooiaaciiini? iieeaaee oa
i?iaiicoaaiiy iaiao?aeiino? i?iaaaeaiiy iiooeiai-?ica?aeoaaeueieo ?ia?o
c aeei?enoaiiyi iiaeo ?ioi?iaoe?eieo oaoiieia?e .

Ai?iaaaeaeaiiy iiaeo ?ioi?iaoe?eieo oaoiieia?e a iaooiaacia?e ni?aa?
aea? iiaeeea?noue nooo?ai ci?ieoe aeiiii?ei-aeieia?/iee i?aeo?ae aei
iiooeiai-?ica?aeoaaeueieo ?ia?o ia iaooo ? aac . Ine?eueee iniiaieie
aeaea?aeaie ?ioi?iaoe?? i?e oaeeo iiooeiai-?ica?aeoaaeueieo ?iaioao ?
ao??iiy naa?aeeiaei, ye? aeiaaathoue cia/ieo eai?oaeueieo aeo?ao,
aaaeeeaei ? iaeiie/aiiy aac ciaiue, ui iiaeooue aooe aeei?enoai? i?e
i?iaiicoaaii? iaooiaaciiane/aieo iieeaae?a c aeei?enoaiiyi aenia?oieo
nenoai(AN).

Aenia?oi? nenoaie, ye nenoaie ooo/iiai ?ioaeaeoo, aeei?enoiaothoue
ciaiiy aenieieaae?o?eiaaieo niaoe?ae?no?a-aenia?o?a aeey ?ica’ycoaaiiiy
caaea/ a ii??aiyii aocueeeo i?iaeaiieo iaeanoyo. I?iaeaiia
ni?yiiaai?noue ? iiaeeea?noue ae??ooaaoe oe?ieee eean caaea/ c?iaeea
aenia?oi? nenoaie iacai?iieie a aaaaoueio aaeocyo i?iieneiaino? ? iaoee
. Nueiaiaei? ia ia?oee ieai aeoiaeyoue i?iaeaie, iia’ycai? c i?aeoe/iith
?aae?caoe??th AN a aaeeeeo ? neeaaeieo i?iaeaiieo iaeanoyo .

Iniiaiith ia?aoeiaeith ia oeyoo noai?aiiy ? iioe?aiiy aenia?oieo nenoai
? i?iaeaia iaaoooy ? i?aaenoaaeaiiy ciaiue . Cia/ia e?euee?noue
?ioi?iaoe??, ?? neaaea no?oeoo?iaai?noue, o?oaeiiu? aenia?oa i?e ni?ia?
iiynieoe iine?aeiai?noue nai?o i??eoaaiue ii i?eeiyooth iaaiiai ??oaiiy
i?ecaiaeyoue aei oiai, ui i?ioean ia?aaea/? ciaiue a?ae aenia?oa aei
nenoaie cae?enith?oueny c aaeeeeie o?oaeiiuaie, iaoiaeii “ni?ia, iiieeie
? aei?aaeaiue” . ?nioth/? iaoiaeeee ii ?iaio? c aenia?oii ? aeaeaei
iaiiaieie . Neaaeei i?noeai ? ?o iacaeaoi?noue eiio?iethaaoe i?ioean
i?eeiyooy ??oaiue aenia?oii ? i?aeo?eiee a aenia?oa iino?eiiai ?ioa?ano
aei i?ioeano ia?aaea/? ciaiue . A ?acoeueoao? i?ioean ia?aaea/? ciaiue
ia?aoai?th?oueny a aaniethii iaoe?eaaa ? iiiioiiia caiyooy aeey
aenia?oa, a i?ioean oi?ioaaiiy aace ciaiue ?icoy-ao?oueny a /an?. C
ae?oaiai aieo, i?e i?aaenoaaeaii? aaea iaaooeo ciaiue aeieeathoue
o?oaeiiu? o aeai?? i?aaeeueiiai niiniao i?aaenoaaeaiiy ? a?aeiia?aeieo
?ino?o-iaioaeueieo cania?a. A neeaaeieo i?iaeaiieo iaeanoyo /anoi
aeieea? iio?aaa a eiia?iiaaiiio canoinoaaii? aaea ?nioth/eo niinia?a
i?aaenoaaeaiiy, a oaeiae o ai?iaaaeaeaii? iiaeo niaoeeo?/ieo i?eeii?a .

?, ia?aoo?, ua a?eueo neeaaeiith i?iaeaiith ? i?ioean eia?/iiai
aeniiaeo. Aocueeei i?noeai oe??? i?iaeaie ? iaiao?aei?noue cae?enithaaoe
i?ioean eia?/iiai aeniiaeo a oiiaao iaiiaii? ? iaoi/ii? ?ioi?iaoe??, ui
ia? i?noea i?e i?iaiico-aaii? iaooiaaciiinieo iieeaae?a .

Oaeei /eiii, ?nio? ?aaeueia iio?aaa a ?ic?iaoe? iiaeo, a?eueo aoaeoeaieo
iaoiae?a iaaoooy ciaiue, ui a?aoiaothoue anth noeoii?noue i?iaeai, ye?
aeieeathoue a i?ioean? ia?aaea/? ciaiue ? noeioeththoue oai?/o
aeoeai?noue aenia?oa, a oaeiae aeei-?enoaiiy iiaeo i?aeoiae?a c
i?aaenoaaeaiiy iaaooeo ciaiue ? cae?eniaiiy eia?/iiai aeniiaeo .

Ca’ycie ?iaioe c iaoeiaeie i?ia?aiaie, ieaiaie,oaiaie. Aeine?aeaeaiiy,
ui io?eiai? a aeena?oaoe?ei?e ?iaio?, o?nii iia’ycai? c aeeiiaiiyi
aea?aeathaeaeaoieo ? ainiiaea?nueei-aeiaia??ieo IAeAeE? eaoaae?e II ca
o/anoth caeiaoaa/a.

Aeena?oaoe?eia ?iaioa aeeiioaaeanue ca ieaiii iaoeiai-aeine?aeieo ?ia?o
aea?aeathaeaeaoii? oaie Ae6/7o “Iaoeia? iniiae ?ic?iaee aenia?oieo
nenoai aeey ia’?eo?a iaooiaaciaiai eiiieaeno” oa iaoeiai-aeine?aeieo
?ia?o oaie 211/96 “?ic?iaea eiii’thoa?eciaaii? aenia?oii? nenoaie aeey
i?iaiicoaaiiy eieaeoi??a iaooe ? aaco “, oaie 89/95 “Nenoaiaoecaoe?y
aaieia?/ii? ?ioi?iaoe?? ii ?iaeiaeuao iaooe ? aaco aeey eiii’thoa?ii?
aace aeaieo”.

Iaoa ? caaea/? aeine?aeaeaiiy: aiae?c aiae?oeei-?ioi?iaoe?eii?
ae?yeueiino? niaoe?ae?noa-aaieiaa aeey ?ic?iaee ? ?aae?caoe?? iiaeo
iaoiae?a ?iaioe c aenia?oii ? ia?iaee iaaooeo ciaiue, ?ica’yceo caaea/
iaaoooy oa i?aaenoaaeaiiy ciaiue ? eia?/iiai aeniiaeo a oiiaao iaiiaii?
? iaoi/ii? ?ioi?iaoe?? iaooiaaciai? i?aaeiaoii? iaeano?.

Caaaeuei? iaoiaee aeine?aeaeaiiy: a iniiao aeine?aeaeaiue iieeaaeaii
eiiieaenia aeei?enoaiiy cania?a ?iaeaia??? ciaiue, oai??? ia/?oeeo
iiiaeei, oai??? eiia??iin-oae, aeaaeoeoe?? ? aeaaa?e eia?ee. Aeey
i?aeoe/ii? ?aae?caoe?? iaea?aeaieo iaoaiaoe/ieo iiaeaeae aeei?enoaii
?ioaa?iaaia na?aaeiaeua Visual Prolog 5.0 .

Iaoeiaa iiaecia io?eiaieo ?acoeueoao?a iieyaa? a ianooiiiio :

?ic?iaeaia ? ?aae?ciaaia iaoiaeeea iaaoooy ciaiue a?ae
niaoe?ae?noa-aenia?oa i?aaeiaoii? iaeano? ia i?eeeaae? iaooiaaciiinieo
iieeaae?a ;

canoiniaaii iia? i?aeoiaee aei aiae?co iaea?aeaieo ciaiue ? ?o
i?aaenoaaeaiiy c aeei?enoaiiyi oai??? ia/?oeeo iiiaeei;

?ic?iaeaii iaoiae aeey i?aai?caoe?? eia?/iiai aeniiaeo a oiiaao iaoi/ii?
? iaiiaii? ?ioi?iaoe?? i?aaeiaoii? iaeano? .

I?aeoe/ia cia/aiiy io?eiaieo ?acoeueoao?a :

cai?iiiiiaai? i?aeoiaee aei ?iaioe c aenia?oii iaooiaaciai? i?aaeiaoii?
iaeano? aeicaieythoue ?ica’ycoaaoe i?iaeaie, ye? aeieeathoue a i?ioean?
oi?ioaaiiy aac ciaiue, i?aeaeuoaaoe oai?/o aeoeai?noue
niaoe?ae?noa-aenia?oa ? cia/ii i?enei?eoe i?ioean ?ic?iaee AN ;

ia aac? iaieiiee aenia?oii? nenoaie ESTA ?ic?iaeaii ? ?aae?ciaaii
aenia?oio nenoaio COLECTOR, ui ia’?aeio? a ?aieao oi?aa?naeueiiai
?ioa?oaeno caniae iaaoooy, aiae?co, oi?iae?caoe?? ? i?aaenoaaeaiiy
aenia?oieo ciaiue oa eia?/-iiai aeniiaeo a oiiaao iaiiaii? ? iaoi/ii?
?ioi?iaoe?? ia i?eeeaae? i?iaiicoaaiiy iaooiaaciaeo eieaeoi??a. AN
COLECTOR oni?oii aeei?enoiao?oueny aeey i?iaiicoaaiiy iaooiaaciaeo
eieaeoi??a a AeAI “Iieoaaiaooiaacaaieia?y” .

Iniaenoee aianie caeiaoaa/a . An? iieiaeaiiy, ye? aeiinyoueny ia
caoeno, iaeaaeaoue iniaenoi aaoi?o ? ia i?noyoue ?acoeueoao?a, ?aeae aai
?ic?iaie, ui iaea-aeaoue ni?aaaoi?ai, ?acii c yeeie iioae?eiaai? iaoeia?
i?aoe?.

Ai?iaaoe?y ?acoeueoao?a aeena?oaoe??. Iniiai? ?acoeueoaoe i?iaaaeaieo
aeine?aeaeaiue aeiiia?aeaeenue ? iaaiai?thaaeenue ia iaoeiai-oaoi?/ieo
eiioa?aioe?yo ?aaii-O?aie?anueeiai aea?aeaaiiai oaoi?/iiai oi?aa?neoaoo
iaooe ? aaco a 1996?., 1997?., ia i?aeia?iaei?e eiioa?aioe?? “Iaooa-aac
Oe?a?ie- 98”(Iieoaaa 15-17 aa?an-iy 1998), ia i?aeia?iaeiiio neiiic?oi?
“Eiii’thoa?e a ?a?ii?: ieioea, no/ania, iaeaooi?”(Ee?a 5-9 aeiaoiy
1998?. ), ia i?aeia?iaei?e eiioa?aioe?? ii iaoaia-oe/iiio iiaeaethaaiith
“Iaoaiaoe/aneea iiaeaee e nia?aiaiiua eioi?iaoeeii-iua
oaoiieiaee”(Oa?nii, 3-6 aa?aniy, 1998?. ) .

Ioae?eaoe??. Iniiai? ?acoeueoaoe aeena?oaoe?eii? ?iaioe iioae?eiaai? o
7 iaoeiaeo noaooyo[1, 2, 3, 4, 5, 6, 7], 7 oacao aeiiia?aeae [8, 9, 10,
11, 12, 13, 14], 1 ca?o? c IAe? .

No?oeoo?a oa ianya aeena?oaoe?eii? ?iaioe. Aeena?oaoe?eia ?iaioa
neeaaea?oueny c anooio, /ioe?ueio ?icae?e?a, aeniiae?a, i?noeoue 130
noi??iie iniiaiiai oaenoo, nienie e?oa?aoo?e c 140 iaeiaioaaiue, 9
?enoie?a, 18 oaaeeoeue ? 5 aeiaeaoe?a.

INIIAIEE CI?NO ?IAIOE

O anooi? iaa?oioiaaii aeooaeuei?noue oaie aeena?oaoe?eii? ?iaioe, aeaii
caaaeueio oa?aeoa?enoeeo ?iaioe, iienaii ?? ca’ycie c iaoeiaeie
i?ia?aiaie , iea-iaie, oaiaie, noi?ioeueiaaia iaoa oa caaea/?
aeine?aeaeaiue, iaaaaeai? a?aeiiino? uiaei iaoeiai? iiaecie, i?aeoe/ii?
oe?iiino? oa ai?iaaaeaeaiiy ?acoeueoao?a ?iaioe, ioa-e?eaoe?e aaoi?a oa
ai?iaaoe?? ?iaioe .

O ia?oiio ?icae?e? aeena?oaoe?? i?iaiae?ciaaii aiae?oeei-?ioi?iaoe?ei?
aniaeoe ae?yeueiino? aenia?oa a iaooiaacia?e i?aaeiaoi?e iaeano? i?e
eeaneo?eaoe?? oei?a ?ic??c?a ? eieaeoi??a, i?iieneia?e ioe?ioe?
i?iaeoeoeaieo ii??ae. Aeae?eaii ?yae iaoiaeee, a?eueo?noue ?c yeeo
oa?aeoa?ecothoueny ia/?oe?noth oa iaaecia/ai?noth ? ca-i?iiiiiaaii
iaoiaeeeo iiaoaiii? oi?iae?caoe?? ciaiue aenia?oa ?c aeei?enoaiiyi
aaee/ei oeio “iaaecia/aii”.

I?iaaaeaii aiae?c noaio ?ia?o a iaeano? ai?iaaaeaeaiiy iiaeo
?ioi?iaoe?eieo oaoiieia?e a iaooiaaciaee eiiieaen ? iaa?oioiaaii
aeooaeuei?noue aeine?aeaeaiue ni?yiiaaieo ia ?ic?iaeo eiiieanieo
?ioi?iaoe?eieo nenoai i?iaiicoaaiiy iaooiaaciaeo iieeaae?a .

O ae?oaiio ?icae?e? i?iaiae?ciaaii noai ?ia?o ? ioae?eaoe?e noiniaii
iniiaieo i?aeoiae?a, uiaei i?iaeooaaiiy ? ?ic?iaee ?ioi?iaoe?eieo
nenoai.

Aeeeaaeaii iniiai? iieiaeaiiy c ?ic?iaee oi?iaeueii-eia?/iiai aia?aoo
aeey i?aaenoaaeaiiy ? aeei?enoaiiy ciaiue. Cai?iiiiiaaia iaoaiaoe/ia
iiaeaeue aiae?co iaaecia/aiino? iiaoaeiaaia ia iniia? oai??? ia/?oeeo
iiiaeei(OII).

Anth iiiaeeio i??eoaaiue i?aaenoaaeythoue o aeaeyae? aeaea?oiaiai
aeiaooeo aaciaeo iiiaeei S1S2, a ci?ii? X i Y, ui i?eeiathoue nai?
cia/aiiy ia S1 i S2 a?ae-iia?aeii, ? aca?iiae?th/eie, aacia? ciaiiy
a?aeia?aaeathoueny aeaea?oiaei aeiaooeii ia-/?oeeo iiiaeei, a noaiai?
iiaeeeaino? ? iaiao?aeiino? ?icieoeo aeneiaethaaiue, ui a?aeiia?aeathoue
ia/?oeei iiae?yi F1F2 i F1+F2 caaeathoueny /a?ac :

FE(F1F2, AABB) = min (FE(F1, AA), FE(F2, BB));

SE(F1F2, AABB) = min (SE(F1, AA), SE(F2, BB));

FE(F1+F2, AABB) = max(FE(F1, AA), FE(F2, BB));

SE(F1+F2, AABB) = max(SE(F1, AA), SE(F2, BB)),

ui aeicaiey? i?aaenoaaeyoe iaeii/anii ?icieoa ? iaaecia/aia
aeneiaethaaiiy c aeiiiiiaith ?iciiae?eo iiaeeeainoae, ui a?aeiia?aea?
iaio oi/iiio, aea a?eueo aeinoia??iiio aeneiaethaaiith.

I?e iayaiino? k ??cieo iaae?eieo aeaea?ae, ui iienothoue iaaia
?iaeiaeua ia?e ioe?iie (FEj(s), SEj(s)) ia’?aeiothoueny a ?aeeiee aeie
?ioi?iaoe?? (FE(s), SE(s)):
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(1)

picscalex930100090000037902000003001500000000000500000009020000000004000
00002010100050000000102ffffff00040000002e0118000500000031020100000005000
0000b0200000000050000000c022006201c1200000026060f001a00ffffffff000010000
000c0ffffffbcffffffe01b0000dc0500000b00000026060f000c004d617468547970650
000300109000000fa02000010000000000000002200040000002d0100000500000014023
c033d070500000013023c03cf1b15000000fb0280fe00000000000090010100000000020
01054696d6573204e657720526f6d616e000070040000002d0101000a000000320ac0034
000020000005345c000eb0009000000320ac003a40201000000730094000a000000320aa
0014b12020000005345c000eb0009000000320aa001451501000000730094000a0000003
20ac704110d020000004645eb00eb0009000000320ac704361001000000730094000a000
000320ac704a516020000005345c000eb0009000000320ac7049f1901000000730094001
5000000fb0220ff0000000000009001010000000002001054696d6573204e657720526f6
d616e000070040000002d01020004000000f001010009000000320ad402db0d010000006
a003d0009000000320a00023214010000006a003d0009000000320aa705950b010000006
a003d0009000000320a2705230f010000006a003d0009000000320aa705e912010000006
a003d0009000000320a27058c18010000006a003d0015000000fb0280fe0000000000009
001000000000002001054696d6573204e657720526f6d616e000070040000002d0101000
4000000f001020009000000320ac0030e02010000002800810009000000320ac0033a030
10000002900810009000000320aa001d00f010000002800810009000000320aa001af140
1000000280081000a000000320aa001db15020000002929810081000d000000320ac7045
d07040000006d6178282401ac00c00081000c000000320ac704830a030000006d696e002
4016900c00009000000320ac704a00f01000000280081000a000000320ac704cc1002000
000292c810060000c000000320ac704d711030000006d696e0024016900c000090000003
20ac7042a14010000002800810009000000320ac704091901000000280081000c0000003
20ac704351a030000002929290081008100810015000000fb02c0fd00000000000090010
00000000002001054696d6573204e657720526f6d616e000070040000002d01020004000
000f00101000c000000320af401380c030000006d696e00b6019e00200110000000fb028
0fe0000000000009001000000020002001053796d626f6c0002040000002d01010004000
000f001020009000000320ac0031c04010000003d00d30009000000320ac003180601000
0002d00d30009000000320aa0012611010000002d00d30009000000320ac704801501000
0002d00d30015000000fb0280fe0000000000009001000000000002001054696d6573204
e657720526f6d616e000070040000002d01020004000000f001010009000000320ac0033
405010000003100c00009000000320aa0014210010000003100c00009000000320ac7049
c14010000003100c0000a00000026060f000a00ffffffff01000000000010000000fb021
000070000000000bc02000000cc0102022253797374656d00cc040000002d01010004000
000f0010200030000000000000000000000
(2) Cia/aiiy ia/?oei? ?noeiiino? aeayei? iineeee, ui i?aaenoaaey?oueny
oa?aeoa-?enoe/iith ooieoe??th ia ?ioa?aae? [0, 1] ?ioa?i?aoo?oueny, ye

zZ, C(z) = sup (B(r) *C(z))* B(r) (3)

rR

Oiae? aeey aeaio ooieoe?iiaeueii caeaaeieo ao?eaoo?a A1 ? A2 i?ney
aeeiiaiiy ia/?oei? o?eueo?aoe?? iaea?aeo?ii a?aeiioaiiy

FE(L(o)?L(y)) = sup min(P(r, t), L(o)(r), L(y)(t)),

(r, t)CL CL

Oiiaiee ?iciiae?e Z|X, ui a?aoiao? iaaecia/ai?noue aeey i?aaee c
iaaecia/aieie aeniiaeaie a aac? ciaiue ?ioi?iaoe?eii? nenoaie o
aeiaaeeo, eiee AA ? AB – cae/aei? iiiaeeie, a dn i ds- ioe?iee
a?aeiia?aeii noaiai? iaiao?aeiino? ? noaiai? aein-

oaoiino? ia? aeaeyae :
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(4)

Aiae?c ia/?oeiai caieoo iiaeaeth?oueny ca aeiiiiiaith neeaaeaiiai
o?eueo?o, ui oyaey? niaith eii’thieoe?th aeaiaioa?ieo o?eueo??a, ui
i?iaiaeyoue ii??aiyiiy iiaeeeaeo cia/aiue ao?eaoo?a ?-ai ia’?eoo (i=1,
…n) c a?aeiia?aeieie ia/?oeeie iiiaeeiaie a aeoeaieo o?eueo?ao.

FE(H1… Hn| G1… Gn) = min FE(Hi, Gi)
(5)

SE(H1… Hn| G1… Gn) = min SE(Hi, Gi)
(6)

Aeey iiaeieaiiy ?ic?eao i?ae i?aaenoaaeaiiyi ciaiue ? ia/?oeei eia?/iei
aeniiaeii i?iiiio?oueny a?a?eaeia eiino?oeoe?y i?aaenoaaeaiiy ia/?oeeo
ciaiue, ui ia? aeaa eiiiiiaioe :iaeei i?aoeth? aeania c ciaiiyie, a
ae?oaee c iaaecia/ai?noth, yeith aiie oa?aeoa?ecothoueny. I?e oaeiio
i?aeoiae? nenoaia ia o?eueee ia? caniae aeey i?aaenoaaeaiiy ia/?oeeo
ciaiue, aea e iiaea cae?enithaaoe ia/?oeee eia?/iee aeniiaie ia
no?oeoo?ao aeaieo . A?a?eaeia no?oeoo?a caaea?oueny o aeaeyae? ei?oaaeo
= , aea oi?iaeueia iiaa ? ? g iaii?iaei? iiiaeeie. ?
?acii ooai?ththoue eiiiiiaio i?aaenoaaeaiiy ciaiue a . C ?ioiai aieo, ie
aeei?enoiao?ii iiiaeeio noaeaeaiue ia iniia? oaeo?a aeey ia/eneaiiy
iaaecia/aiinoae , ? ia?o ooieoe?e (1, 2) , ye? aecia/athoue ?o
aeeiai?/io iiaaae?ieo a i?inoi?? ?ioaineaiino?. Aeaiaioe , ?acii
ooai?ththoue eiiiiiaio ia/?oeiai aeniiaeo a . Aaiaeyoueny ianooii?
iia?aoe?? :

E%[ ] =

A%[a, k] = 1((a), k)

T%[a, x, k]= 2(, k).

aea, true i?aaenoaaey? , ? true i?aaenoaaey? eiao?oe??ioe aeia??e.

Iiaoaeiaa no?oeoo? ciaiue ii/eia?oueny ?c E%[ ], aeae? aeeiio?oueny
iia?aoe?y T% . Oaeei /eiii, ooai?ai? iaie no?oeoo?e ciaiue ? iiiaeeiaie
ia?

, aea p- ?ioaineai?noue, x .

Iiaa ? oi?ioea a c ia?, (a) neeaaea?oueny c iiiaeeie na?o?a, aea a
a?aeiia?-aea? naiaioeoe? aeai?e aeey :

1 = ,

aea TF = oae, i? , g neeaaea? iiiaeeia na?o?a oaeeo, ui M =

? noaiaea?oiith no?oeoo?ith, ui ?ioa?i?aoo?oueny a /eneaii? i?aaeeeao?a
ia?oiai ii?yaeeo:

FOL(a) = | |=FOL a

aea, |=FOL noaiaea?oia ?noeiia a?aeiioaiiy aeey aeaiiai /eneaiiy.

Aaiaey/e ooieoe?? TF oae?, ui

1TF(p, k) = oae yeui aeey an?o k, q p ?iaeoa i?

2TF(

, k)= |k yeui x= oae ?iaeoa k ,

iia?aoe?? iaae no?oeoo?aie ciaiue icia/athoue a oa?i?iao FOL ? TF :
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?ieue iiaeoey i?aaenoaaeaiiy ciaiue iieyaa? a ia/eneaii? (a) aeey
eiaeii? oi?ioee a, ui aoiaeeoue a neeaae iiae i?aaenoaaeaiiy ciaiue.

Neacaia a?aeia?aaea?oueny a?o?oaeoo?ith :

?en. 1 A?o?oaeoo?a a?a?eaeii? no?oeoo?e i?aaenoaaeaiiy ciaiue ?
eia?/iiai

aeniiaeo

A o?aoueiio ?icae?e? i?iaiae?ciaaii i?noea nenoaie eia?/iiai aeniiaeo a
?ioi?iaoe?ei?e nenoai? ? iiaoaeiaaii eiai ia iniia? noaiaea?oieo
i?aaeeeao?a.

A ?aieao i?iiiiiaaiiai i?aeoiaeo cia/aiiy ?noeiiino? i?aaeea eia?/iiai
aeniiaeo “yeui A? oi A? ” ?ioa?i?aoo?oueny a oa?i?iao oiiaii? ?noeiiino?
. Oea cia/aiiy ?noeiiino? caieno?oueny o aeaeyae? verify(A?|A?), ui
aea?aaeaioii iiiaeei? ?ica’yce?a ??aiyiiy

verify(A?A?) = min(verify(A?|A?), verify(A?)). (7)
Ine?eueee, verify(A?)verify(A?A?), oi verify(A?) min(verify(A?|A?),
verify(A?)). sseui A?=“Z=w” i Ai=“Q=r”, i?e/iio Z|Q(w, r)=FE(A?|A?),
? Z – i?iaeoe?y aeaioi??-iiai ?iciiae?eo iiaeeeainoae Q, Z = Z|Q*Q ia
aaciao iiiaeeio BS ci?iii? Z, oi i?aaeei “yeui Q ? AA, oi Z ? AB”
ae?aaeaoeiaoueny ia??ai?noth:

wBS, BB(w) sup Z|Q (w, r)* AA(r) (8)

Cai?iiiiiaaiee iaoai?ci aeniiaeo i?eeia? ia/?oe? iiene niinoa?aaeaiue
?

aeaiaeeoue ia/?oe? iiene i?iaiic?a ca aeiiiiiaith ia/?oeeo a?aeiioaiue
/a?ac aeei?enoaiiy oaeeo i?aaee eiiiiceoe?? aeey aeniiaeo i?iaiico FCj,
aeey ?iaeiaeua DEq, ?c iaai?o niinoa?aaeaiue OBi :

1) Eiiiiceoe?y aeey OBiFCj (a?iioace ? i?aeoaa?aeaeaiiy) :

W1DEFC =WDEOB WCOBFC ,
(9)

ui aecia/a?oueny

W1DEFC (DEq, FCj) = max min[Wdeob(DEq, OBi) ; Wcobfc(OBi, FCj) ]

OBi

2) Eiiiiceoe?y aeey OBiFCj (aeeeth/aiiy (iayaieie niinoa?aaeaiiyie)) :

W2DEFC = WDEOB (1 – WCOBFC ) , (10)

ui aecia/a?oueny

W2DEFC (DEq, FCj) = max min[Wdeob(DEq, OBi) ;1- Wcobfc(OBi, FCj) ]

OBi

3) Eiiiiceoe?y aeey OBiFCj (aeeeth/aiiy (a?aenooi?ie niinoa?aaeaiiyie))
:

W3DEFC = (1-WDEOB ) WOBFC , (11)

ui aecia/a?oueny ianooiiei /eiii :

W3DEFC (DEq, FCj) = max min[1- Wdeob(DEq, OBi) ; WOBFC(OBi, FCj) ]

OBi

I?iaiic aaaaea?oueny i?aeoaa?aeaeaiei, yeui

W1DEFC (DEq, FCj) = 1.00 (12)

I?iaiic iiaeeeaee, yeui

W1DEFC (DEq, FCj) 0.99, (13)

aea oyaey? niaith aa??noe/ia cia/aiiy, yea c aeoaea iaeith
i/aaeaei?noth (iai?ee-eaae, = 0.1000) aeeeth/a? i?iaiic.

I?iaiic aeeeth/a?oueny, yeui

W2DEFC (DEq, FCj) = 1.00 aai W3DEFC (DEq, FCj) = 1.00 (14)

Aeey a?a?eaeii? no?oeoo?e

2 = ,

aea FOL, FOL, g oae? nai?, ye ? a 1 , DS oaia? iaeaaeeoue aei
?ioa?aaeo [0, 1]. No?oeoo?a ciaiue 2 ? iiiaeeiith ia?

, aea p
i?aaenoaaey? iaaio iiiaeeio na?o?a, ? , x[0, 1].

1DS(p,k) iiaa?oa? cia/aiiy c i?ii?aeeo [0,1], ui caaeia?eueiy?
i?aaenoaaeaiiy:
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Aiaaiai?noue aenia?oa a oi/iino? ciaiue i?aaenoaaeaieo /a?ac p ? noiith
an?o iieaciee?a i?eienaieo aei cia/aiue ?ioaineaiino? a k. Oiae? :

2DS(

, k) = k

,

Iia? icia/aiiy aeey E2, A2, T2 iaoeiooue aeaeyae :

E2[] =

A2[a, k] = x | k i qFOL(a)

T2[a, x, k] = k,

Aeey iiiaeeie na?o?a W= , d, a, da, aea D i?noeoue cia/aiiy “eieaeoi?”
ia?ii

k0 = E2[] =

k1 = T2[(ii?iaea ?iaeiaeua), 0.9, k0] = ,

k2 = T2[(ii?iaea eieaeoi?), 0.7, k1] = , ,

,

Ca?aeee :

A2[(?iaeiaeua eieaeoi?), k2] = 0.63

?icaeyaeathoueny icia/aiiy oi?i oeio (def Mi Mj), ui ?ioa?i?aoo?oueny ye
“Mi ? i?aeiiiyooyi Mj” ? oaeoe oi?ie (Mi mj), ui ?ioa?i?aoo?oueny ye
“mj ? i?eeeaaeii iiiyooy Mi” :

|=Z(Mi mj) yeui T(mj, s)T(Mi , s)

|=Z(def Mi Mj) yeui aeey an?o s i sRs, F(Mi, s)F(Mj , s)

Aeei?enoaiiy a?aeiioaiiy R aa?aioo? caeaaei?noue i?ae oaeoaie ?
i?inoeie caieoaie , ui ia?iaeythoueny ca noaiith :

?en. 2 Noaia ia?iaee oe?e?

A1. (def Mi Mj)

R1. C (Mi mk) i (def Mi Mj) (Mj mk)

R2. C (def Mi Mj) i (def Mj Mk) (def Mi Mk)

Neeaaeai? caieoe ooai?ththoueny /a?ac ia’?aeiaiiy i?inoeo oe?eae.
No?oeoo?a neeaaea?oueny c oe?eae, aii?yaeeiaaieo ce?aa iai?aai, ?
ie?aii? oaaeeoe? , ui i?noeoue iioi/i? cia/aiiy ca’ycaieo ci?iieo.
Ia?aaea/a oi?aae?iiy a?aeaoaa?oueny a cai?ioiueiio iai?yi? , a?ae oe?e?
aei oe?e? , eiee nenoaia iaiaaa?oueny ciaeoe cia/aiiy ci?iieo, ui
caaeiaieueiythoue caieo. Aeey eiaeii? oe?e? ao?ae ? aeo?ae c ia?
iiaeeeaee /a?ac a?aeiia?aeiee ii?o ce?aa /e ni?aaa . I?ioean
ii/eia?oueny c aeeeeeo ia?oi? oe?e? ce?aa . sseui oey oe?eue oni?oii
aeinyaa?oueny , oi ianooiia oe?eue aeeeeea?oueny c aeiii-iiaith
ca’ycaii? ci?iii? , yea iaea?aeaea nai? cia/aiiy i?e aeeiiaii?
iiia?aaeiuei? oe?e? . I?ioean i?iaeiaaeo?oueny aei oeo i??, iiee ia
aoaea cae?eniaii aeo?ae /a?ac exit-ii?o naii? i?aai? oe?e? .

Aeey i?aaeeeao?a, ui aeeeeeathoueny c aeaiia a?aoiaioaie i?iiiio?oueny
/ioe-?e iiaeeeaeo aeaee oaaeii?a iioieo :

(i, i) (i, o) (o, i) (o, o)

Aeey i?enei?aiiy ia?iaee aace aeaieo eiaeia ii?oe?y ?ioi?iaoe??
?ici?uo?oueny o aeaniiio aeiiai? :

?iaeiaeua(C)
( o )

?iaeiaeua(aeeaeia_caeyaaiiy(Iacaa, Aeeaeia))aeeaeia_caeyaaiiy ( o,
o )

?iaeiaeua(a?e(“Aiaaoienueea”, A?e))a?e
( i, o )

?iaeiaeua(e?oieia?y(“Aaiiyee”)
( i )

Aeey iioei?caoe?? i?ioeaaeo? iiooeo ?ioi?iaoe?? a aac? aeaieo
i?aai?ciaothoueny ?aeo?neai? a?ia?i? aea?aaa iiooeo. ?icaeyaeath/e
aoaeue-yeo eii??eo aea?aaa, iiaeia ia?aaeaa/eoe a yeiio c ?? i?aeaea?aa
i?noeoueny iio??aiee o?aaiaio ?ioi?iaoe?? . Oaeee aoaeo aeinyaa?oueny ca
?aooiie caaeaiiy ia noeoiiino? aeaieo iaaiiai ii?yaeeiaiai
a?aeiioaiiy(aeoaa?oiiai /e oeeo?iaiai). Aeaiaioe e?aiai i?aeaea?aaa
ia?aaeoaaoeiooue iioi/i?e eii??oe?, a aeaiaioe i?aaiai i?aeaea?aaa
ne?aeoaaoeiooue ca iath .

I?ney aeeiiaiiy ia?iaee eiaeii? eiie?aoii? eii??ee i?ae /an i?ioeano
iiooeo, iieiaeia eii??ie ui caeeoeeanue, onoaa?oueny c iiaeaeueoiai
?icaeyaeo ? oei naiei oaeaee?noue aeeiiaiiy iiooeo ca?eueoo?oueny . Oiio
yeui ?ici?? aea?aaa ca?eueoeany, iai?eeeaae, aaea?/?, oi iiooe ii
iiaiio aea?aao iio?aaoaaoeia eeoa iaeiiai aeiaeaoeiaiai e?ieo .
Oaeaee?noue iiooeo i?iii?oe?eia eiaa?eoio /enea N, aea N- /enei eii??ie
.

Iiaoaeiaa ?ioa?i?aoaoi?a ii/eia?oueny c oa?i?a aTerms ? sTerms, ye?
aeei?enoiaothoueny i?ioeaaeo?ith ioe?ithaaiiy :

1. I?i/eoaiee iioa?i?aoaoi?ii aeo?aeiee eiae iiae?ey?oueny
ia noaoe/i? oa?ie.

2. I?ney oeueiai eiaeiee noaoe/iee oa?i ia?aoai?th?oueny a
aTerm, ui ? iiaea aooe ioe?iaiee.

I?ioean ioe?iee ii/eia?oueny c ii/aoeiaiai oa?ia . Aoaeue-yea
oaa?aeaeaiiy aianaia a aaco aeaieo caa??aa?oueny o aeaeyae? sOerm. Eiee
oe?eue ia?aoai?th?oueny a aeoeaiee oa?i, iioa?i?aoaoi? i?aaee (
iaoai?ci aeniiaeo ) ioe?ith? aOerm ? aeeiio? ii-a’ycaio c iei ae?th.
Ae?y iieyaa? a iiooeo a aac? aeaieo noaoe/iiai oa?ia ( oaa?aeaeaiiy
), ui a?aeiia?aea? aeoeai?e oe?e?. sseui nenoaia ciaoiaeeoue
a?aeiia?aeia oaa?aeaeaiiy, oi aiia c/eoo? oeae sOerm ?
ia?aoai?th? eiai a aOerm, oiio?eoth/e oe?eue ? oaa?aeaeaiiy, a
i?ney oeueiai, yeui oaa?aeaeaiiy ? i?aaeeii, iiaoi?th? i?i-oean aeey
eiaeii? i?aeoe?ei a o?e? oaa?aeaeaiiy .

Iniiaith iaoeie aeniiaeo ? i?aaeeeao unify_term. A?i iaea?aeo? ia
aoiae? noaoe/i? oa?ie, ae?eni? oa?ie, a oaeiae na?aaeiaeua, a ia
aeoiae? aea? oiio?eaoe?th aeaio ??ciiiai?oieo oei?a oa?i?a .

Aeeeee i?aaeeeaoo member caaacia/o? caycoaaiiy aOerm1 ?c ci?iiith
?aeaioeo?eaoe??, i?ney /iai oiio?eaoe?y oa?i?a aOerm ? aOerm1
cae?enith?oueny iaeiei ?c o?ueio niinia?a :

1. sseui iaeaeaa oa?ie ca’ycai?, oi a caeaaeiino? a?ae ?o
cia/aiue oiio?eaoe?y cae?i/o?oueny oni?oii, aai i? .

2. sseui ca’ycaiee o?eueee iaeei oa?i, oi oiio?eaoe?y
i?ieaea oeyoii anoa-iiaeaiiy aeaio oa?i?a iaeia ia iaeiiai .

3. sseui iaeaeaa oa?ie ? a?eueieie ci?iieie, oi aiie
iiae?eythoueny (ui icia/a?, ui aiie aoaeooue i?aaenoaaeai? aeac?aieeaie
? eiaeiee aeac?aiee aoaea aea-coaaoe ia iaeei ? oie aea a?eueiee
aae?an).

I?aaeeeao unify_body ? aoiaeii aeuiai ii?yaeeo iioa?i?aoaoi?a;
aeey iioa?i?aoaoei? aace i?aaee i?aaeeeaoo unify_body caaea?oueny
oe?eue, yeo o?aaa caaeia?eueieoe ( a?iioaca ) ? a?eueia na?aaeiaeua.
I?ney oeueiai oeae i?aaeeeao aeinyaia oe?e?, aai i? a caeaaeiino?
a?ae oiai, /e iiaeia aeiaanoe a?iioaco. Unify_body a?aeiia?aea?
ca iioa?i?aoaoe?th no?oeoo?e o?ea i?aaeea ca?aeii aeai?eoio :

1. Iiae?e o?ea ia i?aeoe?ei – a?aeiia?aeii aei ii?yaeeo
ioe?ithaaiiy, ui aec-ia/a?oueny aoaeiaith o?ea .

2. Aeeeeeo ?ioiai i?aaeeeaoo, ui a?aeiia?aea? ca oaeoe/ia
aeeiiaiiy ie?a-ieo i?aeoe?eae .

Aeeiiaiiy aace i?aaee a?aeaoaa?oueny /a?ac noiaeaeaiiy :

– a?ae a?iioace

– /a?ac ?? i?aeoe?ei

– ? ?o i?aeoe?ei

– ? o.ae.

– aei oaeo?a, ui iathoue o?ei true , yea aeeiiaeiny a
ia?oiio ?a/aii?.

sseui a?iioaco ia iiaeia aeiaanoe c aeiiiiiaith oaeo?a ?
i?aaee aace aeaieo, oi oea i?ecaaaea aei iaaeeiiaiiy aeeeeeo
unify_body ia ??ai? a?iioace. Oea aeei-iaiiy /e iaaeeiiaiiy ? ?aeeiei
?acoeueoaoii iioa?i?aoaoe?? aace i?aaee; ia oaeee ?acoeueoao
iaeaaiaeaeaia ia?aa??ea eiio?ieueii? i?ia?aie.

Aecia/aiiy oe??? iaieiiee aeeth/a? o?e aeiiae, ui aeoiaeyoue ca iaae?
iiae-eeainoae eaioethaa cai?ioi?o i??eoaaiue, i?eeiyoiai a I?ieic? :

1. Oaeoi? aiaaiaiino? oi?io? /anoeio i?aaee ? aeniiae?a c
ieo.

2. sseui ei?enooaa/o caaeaii ieoaiiy, oi nenoaia caaaeaee
iiaea iiynieoe, /iio aiia eiai caaeaea.

3. An? aeniiaee iiaeooue aooe iiyniai? ca aeiiiiiaith
iineeaiue ia iiia?aaei? i??eoaaiiy .

Oe? aeiiae noiothoueny a o?ueio aeiaeaoeiaeo a?aoiaioao
i?aaeeeaoo unify_body.

1. Real , ui ? oaeoi?ii aiaaiaiino?, noai?aiei a ?acoeueoao?
aeniiaeo.

2. Oa?i, ui ? caaieiaeii i?aaeea, ui aeeiio?oueny a aeaiee iiiaio; a?i
aeicaiey? nenoai? noi?ioethaaoe o?aco : ” ss caaeath oea ieoaiiy , ai
iaiaaathny anoaiiaeoe .

3. Noaoe/iee oa?i , ui cae?enith? i?inoaaiiy aia?aae o?an??iaee; a?i
aoaea iaea?aeoaaoe anoaiiaeaio aa?n?th o?ea, iaae yeith i?aoeth?
unify_body, a?aoiaoth/e, ui oa?ie, ye? ? ci?iieie a i?ioean?
ia?aoiaeo o?ea a unify_body ? call, aoaeooue ci?ia-i? ia o? cia/aiiy,
ye? aiie iaea?aeaoue a i?ioean? aeeiiaiiy. Iayai?noue oeeo onoa-iiaie a
aac? aeaieo, aeicaiey? iiynieoe aoaeue-yea caeeth/aiiy /a?ac
iineeaiiyi ia ?ai?oa aeiaaaeai? iieiaeaiiy.

Ia?aoai?aiiy i?aaeea a oaeo, i?i yeee a?aeiii, ui a?i
i?aeoaa?aeaeaiee, ?nioth/eie a aac? aeaieo oaeoaie, cae?enith?oueny
aeaiia niiniaaie :

1. Aeeo/aiiy i?aaeea ? onoaiiaee eiio a?aeiia?aeiiai oaeoo .

2. Iii?/aiiy i?aaeea ye i?aeoaa?aeaeaiiai .

Oe? iiaeeeaino? aeeiiothoueny /a?ac cai?iaaaeaeaiiy iioeiicaoe??, a
ye?e eiaeiiio i?aaeeo i?eienaiee na?e aeaniee iiia?. Oeae iiia?
ca aeiiiiiaith i?aaeeeaoa aace aeaieo, ui iaceaa?oueny proven
( ), aoaea aeacoaaoe , /e i?aeoaa?aeaeaii i?aaeei ye oaeo.
Oea ia o?eueee i?enei?th? ?iaioo, aea e aeicaiey? aeeiioaaoe iiooe
aeueoa?iaoeaieo ??oaiue .

A /aoaa?oueiio ?icae?e? aeaii ioe?ieo aoaeoeaiino? canoinoaaiiy
?ic?iaeaiiai oi?iaeueii-eia?/iiai aia?aoo aeey aaoiiaoecaoe?? i?ioeano
??oaiiy ae?aaiinoeei-i?iaiicoe/ieo caaea/ niaoe?ae?no?a-aaieia?a.

?ic?iaeaia eiiieaenia iaoiaeeea iaaoooy ciaiue a oiae? ?ioa?aeoeaiiai
ae?aeiao “aenia?o –?iaeaia?-eiai?oieia– ?ioi?iaoe?eia nenoaia”
aeicaiey? aeae?eeoe eeth/aa? ia’?eoe i?aaeiaoii? iaeano? /a?ac iiaoaeiao
iine?aeiaiinoae ia? “a?iioaca-niinoa?aaeaiiy” ? noi?ioaaoe iiaeaeue
i?aaeiaoii? iaeano?.

Caeiaoo? ciaiiy i?iiiio?oueny i?aaenoaaeyoe o aeaeyae? o?aei?a,
o?eieao?a ia’?eo-ao?eaoo-cia/aiiy, ?aeyoe?eieo a?aeiioaiue, ? i?aaee ?c
ci?iieie, ui cia/ii iieaaoeoue ianooiio ?o oi?iae?caoe?th.

?icaeyaeathoueny /ioe?e eeane ia’?eo?a :

– niinoa?aaeaiiy, iciaee, ?acoeueoaoe aaio?ce/ieo aeine?aeaeaiue ?
iaea?aeai? aeai?(OBi);

– a?iioace ? noeaia???(FCj) ;

– i?ii?aei? eiia?iaoe?? (ICk);

– eiia?iaoe?? niinoa?aaeaiue (OCl).

Niinoa?aaeaiiy OBi i?eeiathoue cia/aiiy OBi ?c [0, 1]. Cia/aiiy OBi
iieaco? , a ye?e noaiai? i?iyaeythoueny niinoa?aaeaiiy OBi . I?ney
oeueiai aoaeo?oueny a?ia?ia ia/?oea a?aeiioaiiy WOB , ui aecia/a?oueny
oiiaith Wdeob(DEq, OBi)=OBi aeey ?iaeiaeua DEq, aea DEq (=DE1, …, DEr )
? OBi( = OB1, …, OBm).

I?iaiice oaeiae i?eeiathoue cia/aiiy ?c [0,1]. Ia/?oe? cia/aiiy 0.00

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