• Aucun résultat trouvé

Elicitation, evaluation and recommendation in multi-criteria decision making process

N/A
N/A
Protected

Academic year: 2021

Partager "Elicitation, evaluation and recommendation in multi-criteria decision making process"

Copied!
8
0
0

Texte intégral

(1)

HAL Id: hal-02487101

https://hal.archives-ouvertes.fr/hal-02487101

Submitted on 21 Feb 2020

HAL is a multi-disciplinary open access

archive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Elicitation, evaluation and recommendation in

multi-criteria decision making process

Ayeley Tchangani, François Pérès

To cite this version:

(2)

OATAO is an open access repository that collects the work of Toulouse

researchers and makes it freely available over the web where possible

Any correspondence concerning this service should be sent

to the repository administrator:

tech-oatao@listes-diff.inp-toulouse.fr

This is an author’s version published in: http://oatao.univ-toulouse.fr/23609

To cite this version:

Tchangani, Ayeley

and Pérès, François

Elicitation, evaluation

and recommendation in multi-criteria decision making process.

(2017) In: 2017 4th International Conference on Control, Decision

and Information Technologies (CoDIT'17), 5 April 2017 - 7 April

2017 (Barcelona, Spain).

(3)

Holflwdwlrq/ Hydoxdwlrq dqg Uhfrpphqgdwlrq lq

Pxowl0Fulwhuld Ghflvlrq Pdnlqj Surfhvv

D|hoh| S1 Wfkdqjdql dqg Iudqêrlv Sìuëv

Xqlyhuvlwì Iìgìudoh Wrxorxvh 0 Plgl S|uìqìhv

Oderudwrluh Jìqlh gh Surgxfwlrq/

7: Dyhqxh g*D}hluh{/ 98349 Wduehv/ Iudqfh

H0pdlo= d|hoh|1wfkdqjdqlClxw0wduehv1iu> iudqfrlv1shuhvChqlw1iu1

Devwudfw Wudglwlrqqdoo|/ pxowl0fulwhuld ghflvlrq pdnlqj +PFGP, olwhudwxuh kdv ghyrwhg lwv hruw wr wkh hydoxdwlrq dqg uhfrppdqgdwlrq vwdjh ri ghflvlrq dqdo|vlv1 D PFGP sureohp lq wklv frqwh{w lv wkhuhiruh frpsohwo| ghwhuplqhg e| d wdeoh zkhuh wkh hqwu| dw d srvlwlrq ri wklv wdeoh fru0 uhvsrqgv wr wkh ydoxh ri d fulwhulrq iru wkh fruuhvsrqglqj dfwlrq dqg wkh pdlq sxusrvh iru wkh dqdo|vw lv wr ghvljq d surfhgxuh wkdw ghulyh dq rughu ru suh0rughu ryhu wkh dfwlrqv vhw iurp wkdw gdwd wdeoh1 Wklv iudphzrun grhv kdyh vrph gudzedfnv lq sudfwlfh vxfk dv wkh qhfhvvlw| iru dfwlrqv wr eh hydoxdwhg wkurxjk wkh vdph fulwhuld dqg rqh remhfwlyh wr uhdol}h1 Lq wklv frppxqlfdwlrq zh jr ixuwkhu dkhdg wr frqvlghu dovr hohflwdwlrq dqg phdvxuhphqw vwdjh dqg ghulyh d iudphzrun wkdw doorzv dovr lqkrprjhqhlw| ri dwwulexwhv wkdw zloo fkdudfwhul}h dfwlrqv zlwk uhjdug wr sxuvxhg pxowl0 remhfwlyhv1 D fdvh vwxg| lq lqiudvwuxfwxuhv surmhfwv sruwirolr vhohfwlrq xqghu ixqg frqvwudlqwv wr hqkdqfh vxlvwdlqdeoh gh0 yhorsphqw lv frqvlghuhg dv dq looxvwudwlyh dssolfdwlrq ri wkh ghyhorsshg dssurdfk1

Nh|zrugv Ghflvlrq dqdo|vlv/ pxowl0fulwhuld/ pxowl0

remhfwlyhv/ ERFU dqdo|vlv/ Fkrtxhw lqwhjudo1 L1 Lqwurgxfwlrq

Pdq| ghflvlrq pdnlqj sureohpv/ li qrw doo ri wkhp/ lq dq| vrflrhfrqrplf grpdlqv/ qhfhvvlwdwh wr fkrrvh dfwlrqv ru dowhuqdwlyh rswlrqv lq rughu wr vdwlvi| pdq| remhfwlyhv dqg2ru wr rswlpl}h pdq| fulwhuld1 Jhqhudoo|/ ghflvlrq rs0 wlrqv duh uhihuuhg wr dv dowhuqdwlyhv li wkh| duh h{foxvlyh rwkhuzlvh wkh| duh nqrzq dv dfwlrqv/ vhh iru lqvwdqfh ^46` ^59`1 Vxfk sureohpv fdq uhsuhvhqw sudfwlfdo vlwxdwlrqv lq pdq| grpdlqv= lqwhuhvwhg uhdghuv fdq frqvxowv iroorzlqj sxeolfdwlrqv ^4` ^5` ^44` ^46` ^49` ^4<` ^57` ^59` dqg uhihuhqfhv wkhuhlq iru vrph uhdo zruog dssolfdwlrqv lq pdqdjhphqw/ hqjlqhhulqj/ hfrqrplfv/ qdqfh/ hwf1> dv zhoo dv lq srolwlfv/ vhh iru lqvwdqfh ^9` iru dq dssolfdwlrq lq h0ghprfudf|/ hwf1 Dssolfdwlrqv pd| dovr eh irxqg lq vrflhw| surwhfwlrq dqg hphujhqf| pdqdjhphqw vxfk dv ghflvlrq pdnlqj uhodwhg wr surwhfwlrq djdlqvw uh ^58` ru lq kxpdq0pdfklqh lqwhuidfh ghvljq ^43`> pxowlfulwhuld fodvvlfdwlrq sureohpv dv ghflvlrq pdnlqj sureohpv duh hqfrxqwhuhg lq pdq| grpdlqv vxfk dv qdqfh ^8`/ lq vxsso| fkdlq ^4;`/ dprqj rwkhuv1

Wkrxjk ghflvlrq pdnlqj surfhvv lv d pxowlsoh vwdjhv surfhvv jrlqj iurp=

 l, sureohp irupxodwlrq/ wkdw lv wkh lghqwlfdwlrq ri wkh

ryhudoo jrdo wr eh vdwlvhg> wkurxjk

 ll, srvvleo| vsolwwlqj wklv jrdo lqwr pdq| remhfwlyhv wr

vdwlvi|>

 lll, lghqwli|lqj srvvleoh dfwlrqv dqg2ru dowhuqdwlyhv wkdw

pd| uhdol}h wkhvh remhfwlyhv>

 ly, lghqwli|lqj dwwulexwhv ri iruphu dfwlrqv2dowhuqdwlyhv

wkdw zloo eh xvhg wr phdvxuh wkh dghtxdf| ri dfwlrqv zlwk uhjdugv wr sxuvxhg remhfwlyhv>

 y, wr/ hydoxdwlrq dqg uhfrpphqgdwlrq vwdjh> wklv odwhu

vwdjh lv wkh prvw zlgho| vwxglhg e| ghflvlrq dlg dqg rs0 hudwlrqdo uhvhdufk frppxqlwlhv zkhuh d ghflvlrq sureohp lv frpsohwho| ghwhuplqhg e| q  p wdeoh ru pdwul{ [ dv vkrzq e| htxdwlrq +4, [ @ 5 9 9 9 9 7 {44 {45 === {4p === === === === {l4 {l5 === {lp === === === === {q4 {q5 === {qp 6 : : : : 8 +4,

zkhuh urzv fruuhvsrqg wr dfwlrqv ru dowhuqdwlyhv/ froxpqv

ghvljqdwh fulwhuld/ dqg wkh hqwu| [+l> m, @ {lm fruuhvsrqgv

wr wkh hydoxdwlrq ri dowhuqdwlyh ru dfwlrq l zlwk uhjdug wr fulwhulrq m> wklv hydoxdwlrq lv jhqhudoo| grqh ryhu dq| ru0 ghuhg vhw lqfoxglqj elqdu| hydoxdwlrq vxfk dv jrrg2edg1

Lq fodvvlfdo dssurdfkhv/ wkh hydoxdwlrq +dqg uhfrpphq0 gdwlrq, sureohp frqvlvw lq jrlqj iurp gdwd ri wkh suhylrxv wdeoh +4, dqg ghflvlrq pdnhu*v suhihuhqfhv wr hvwdeolvk dq rughu ru suh0rughu ryhu dowhuqdwlyhv2dfwlrqv vhw1 Wr wklv hqg/ wzr pdlq dssurdfkhv kdyh ehhq sursrvhg lq wkh olwhu0 dwxuh=

 ydoxh w|sh dssurdfk= urxjko| vshdnlqj wkhvh whfkqltxhv

frqvlghu d qxphulfdo ixqfwlrq  nqrzq dv ydoxh ru xwlolw| ixqfwlrq, ghqhg rq wkh dfwlrqv2dowhuqdwlyhv vhw vxfk wkdw/ vhh htxdwlrq +5,

+l, +o, / l ( o +5,

3 ?

zkhuh l ( o vwdqgv iru %dfwlrq l lv dw ohdvw dv jrrg/ zlwk uh0

jdug wr ghflvlrq jrdo/ dv dfwlrq o% ohdglqj wr dq rughu ryhu

dfwlrqv vhw1 Wkh hydoxdwlrq prgholqj surfhvv wkhq frq0

vlvwv lq exloglqj vxfk d ixqfwlrq edvhg rq fulwhuld phdvxuhv

dqg ghflvlrq pdnhuv suhihuhqfh +rewdlqhg lq jhqhudo e| dq0

vzhulqj vrph sduwlfxodu txhvwlrqv ri wkh dqdo|vw,> wkhuh duh

pdq| whfkqltxhv hpsor|hg lq wkh olwhudwxuh iru frqvwuxfw0

lqj vxfk d ixqfwlrq zkhuh d qxpehu ri wkhp vxssrvh d sduwlfxodu irup iru  vxfk dv dq h{shfwhg xwlolw| irup ru dq dgglwlyh ydoxh ixqfwlrq +lqwhuhvwhg uhdghu pd| frqvxow

(4)

 rxwudqnlqj phwkrgv= lq wklv fdvh/ d sdlu0zlvh frpsdulvrq

ri dfwlrqv lv fduulhg xs xqghu hdfk fulwhulrq wr ghulyh d suh0 rughu ryhu wkh dfwlrqv vhw/ doorzlqj lqfrpsdudelolw| dqg2ru lqwudqvlwlylw|> phwkrgv vxfk dv HOHFWUH surfhgxuhv dqg SURPHWKHH whfkqltxhv ^6` ^59` ehorqj wr wklv fdwhjru|1 Ehvlghv wkhvh wzr pdlq dssurdfkhv/ wkhuh h{lvwv ghflvlrq ohduqlqj dssurdfkhv zkhuh d vhw ri ghflvlrq uxohv duh gh0 ulyhg e| d ohduqlqj surfhvv iurp d nqrzq ghflvlrq wdeoh zlwk srvvleo| lqfrpsohwh gdwd/ vhh ^;`1 Rqh fdq vhh wkdw wr dsso| vxfk dssurdfk/ lw lv qhfhvvdu| wr glvsrvh ri suhylrxvo| froohfwhg gdwd ri vlplodu sureohpv wr wkdw ehlqj vroyhg> wklv lv jhqhudoo| lpsrvvleoh iru vrph sureohpv1

Doo wkhvh dssurdfkhv gr kdyh vrph olplwdwlrqv zkhq idf0 lqj uhdo zruog ghflvlrq pdnlqj sureohpv/ dprqj zklfk iro0 orzlqj lvvxhv vhhp lpsruwdqw=

 lq jhqhudo/ wkh pdlq ghflvlrq sxusrvh frqvlghuhg e| wkhvh

dssurdfkhv lv uhgxfhg wr vdwlvi|lqj d vlqjoh frpprq remhf0 wlyh zkhuhdv lq sudfwlfh wkh sxusrvh ri ghflvlrq surfhvv pd| qhfhvvlwdwh vdwlvi|lqj pdq| remhfwlyhv= rqh pd| wklqn derxw vhohfwlqj vxvwdlqdeoh ghyhorslqj surmhfwv wkdw pd| vdwlvi| vrfldo/ hfrqrplfdo dqg hqylurqphqw remhfwlyhv dv dgplwwhg e| wkh ghqlwlrq ri vxvwdlqdelolw|>

 qhfhvvlw| iru doo dfwlrqv ru dowhuqdwlyhv wr eh hydoxdwhg

ryhu wkh vdph vhw ri fulwhuld>

 qxphulfdo hydoxdwlrq ri dwwulexwhv zlwk uhjdugv wr sxu0

vxhg remhfwlyh>

 odfn ri vwuxfwxulqj iudphzrun wkdw jxlgh wkh vhdufk iru

qhfhvvdu| lqirupdwlrq1

Lq wklv frppxqlfdwlrq zh sursrvh d vwuxfwxuhg phwkrg wkdw jrhv wkurxjk lpsruwdqw lwhpv ri ghflvlrq pdnlqj surfhvv hqxphudwhg lq wkh suhylrxv vhfwlrq lq rughu wr dg0 guhvv dv pxfk dv srvvleoh olplwdwlrqv ri fodvvlfdo dssurdfkhv udlvhg lq wkh suhylrxv lwhpv1

LL1 Vwuxfwxuhg prgholqj= ERFU dqdo|vlv Zh frqvlghu d ghflvlrq surfhvv wr jr wkurxjk irxu pdlq vwhsv=

l, ghqlwlrq ri wkh ryhudoo jrdo ri ghflvlrq pdnlqj> ll, lghqwlfdwlrq ri remhfwlyhv wr vdwlvi| lq rughu wr uhdol}h wkh ryhudoo jrdo dqg srvvleoh dfwlrqv wr xqghuwdnh> wkrxjk lq vrph fdvhv remhfwlyhv dqg dfwlrqv pd| eh uhodwhg/ khuh zh frqvlghu wkhp wr eh lqghshqghqw vr wkdw wkh| fdq eh holflwhg lq sdudooho>

lll, holflwdwlrq ri dwwulexwhv/ wkdw lv fkdudfwhulvwlfv ri df0 wlrqv wkdw fdq eh xvhg wr hydoxdwh wkhp zlwk uhjdugv wr sxuvxhg remhfwlyhv>

ly, hydoxdwlrq dqg uhfrpphqgdwlrq/ wklv vwhs frqvlvwv lq %djjuhjdwlqj% lqirupdwlrq jdwkhuhg lq suhylrxv lwhpv wr ghulyh d vhohfwlrq surfhgxuh1

Wkh wzr odwh lwhpv lll, dqg ly, duh wkdw frqvlghuhg lq vxevhtxhqw vhfwlrqv1

D1 Holflwdwlrq surfhvv

Zh frqvlghu dw wklv vwdjh wkdw wkh vhw ri remhfwlyhv wr vdwlvi| dv zhoo dv srwhqwldo dfwlrqv2dowhuqdwlyhv wkdw fdq eh xvhg wr vdwlvi| wkhvh remhfwlyhv duh frpsohwho| ghwhuplqhg dqg wkh sxusrvh qrz lv wr ghulyh d iudphzrun wr holflwdwh

dwwulexwhv ri dfwlrqv2dowhuqdwlyhv wkdw fdq eh xvhg wr hydo0 xdwh wkh dghtxdf| ri wkhvh dfwlrqv zlwk uhjdugv wr sxuvxhg remhfwlyhv1 Lq rughu wr glvsrvh zlwk d vwuxfwxuhg iudph0 zrun iru wkh holflwdwlrq dqg hydoxdwlrq surfhvv ri dwwulexwhv/ zh dgrsw dq dssurdfk wkdw kljkoljkwv wkh elsrodulw| ri dw0 wulexwhv zlwk uhjdugv wr remhfwlyhv wkdw zh frqvlghu wr eh lqkhuhqw wr dq| ghflvlrq dqdo|vlv sureohp1 Zh duh prwl0 ydwhg e| wkh idfw wkdw frjqlwlyh sv|fkrorjlvwv kdyh revhuyhg iru orqj wlph wkdw kxpdq/ riwhq/ hydoxdwh dowhuqdwlyhv e| frqvlghulqj vhsdudwho| wkhlu srvlwlyh dvshfwv dqg wkhlu qhj0 dwlyh dvshfwv> wkdw lv rq d elsrodu edvlv/ vhh iru lqvwdqfh ^6`1 Wr wklv hqg/ vxssruwlqj dqg uhmhfwlqj qrwlrqv zhuh lq0 wurgxfhg lq ^56` wkdw uhodwh dwwulexwhv wr remhfwlyhv ohdglqj wr dq hydoxdwlrq prgho lq whupv ri wzr phdvxuhv ru lqglfhv +vhohfwdelolw| dqg uhmhfwdelolw|, iru hdfk dfwlrq2dowhuqdwlyh lq wkh iudphzrun ri vdwlvflqj jdph wkhru| ^4:`1 Wkhvh qr0 wlrqv shuplw wr sduwlwlrq dwwulexwhv vhw lqwr wkuhh vxevhwv jlyhq dq remhfwlyh= dwwulexwhv wkdw vxssruw wklv remhfwlyh/ dwwulexwhv wkdw uhmhfw wklv remhfwlyh dqg dwwulexwhv wkdw duh qhxwudo zlwk uhjdug wr wklv remhfwlyh> ri frxuvh rqo| vxs0 sruwlqj dqg uhmhfwlqj dwwulexwhv duh lqwhuhvwlqj iru hydoxd0 wlrq surfhvv1 E| wdnlqj lqwr dffrxqw xqfhuwdlqw|/ dxwkruv vxjjhvw lq ^56`/ wr holflwdwh dqg dvvhvv dwwulexwhv lq d gh0 flvlrq dqdo|vlv e| sduwlwlrqlqj wkhp lqwr ehqhw +E,= fhu0 wdlq dwwulexwhv wkdw vxssruw ghflvlrq remhfwlyh> rssruwxqlw| +R,= xqfhuwdlq dwwulexwhv wkdw vxssruw ghflvlrq remhfwlyh> frvw +F,= fhuwdlq dwwulexwhv wkdw uhmhfw ghflvlrq remhfwlyh> dqg ulvn +U,= xqfhuwdlq dwwulexwhv wkdw uhmhfw ghflvlrq re0 mhfwlyh> ohdglqj wr d iudphzrun nqrzq dv ERFU dqdo|vlv> wklv holflwdwlrq surfhvv lv uhvxphg e| wkh iroorzlqj Iljxuh

41 Dq dfwlrq l lv wkhuhiruh frpsohwho| fkdudfwhul}hg e|

KďũĞĐƚŝǀĞƐ ĐƚŝŽŶƐ ϭ ͙ ũ ͙ ŵ ϭ ͙ ĞŶĞŝĨŝƚ ĂƚƚƌŝďƵƚĞƐ ;Ϳ KƉƉŽƌƚƵŶŝƚLJ ĂƚƚƌŝďƵƚĞƐ ;KͿ ŽƐƚ ĂƚƚƌŝďƵƚĞƐ ;Ϳ ZŝƐŬ ĂƚƚƌŝďƵƚĞƐ ;ZͿ ͙ Ŷ KǀĞƌĂůů ĚĞĐŝƐŝŽŶ ŐŽĂů KďũĞĐƚŝǀĞƐƚŽƐĂƚŝƐĨLJ WŽƐƐŝďůĞĂĐƚŝŽŶƐ

{

1, 2, ...., , ...,i n

}

ŝ {1, 2, ...., , ...,j m} ůŝĐŝƚĂƚŝŽŶ ŽĨĂƚƚƌŝďƵƚĞƐ

Ilj1 41 Surfhvv iru holflwdwlqj dwwulexwhv

zkdw zh uhihu wr dv lwv ERFU lghqwlw| fdug dv vkrzq e|

Iljxuh 5 wkdw fruuhvsrqgv wr wkh lwk olqh ri wkh wdeoh gh0

slfwhg rq iruphu Iljxuh 41 Qrwlfh wkdw wkh wdeoh jlyhq

(5)

ĐƚŝŽŶͬĂůƚĞƌŶĂƚŝǀĞ;ŝͿ͗ ĚĞƐĐƌŝƉƚŝŽŶĂŶĚƉŽƐƐŝďůĞĐŽŶƐƚƌĂŝŶƚƐ KďũĞĐƚŝǀĞƐ KZĨĂĐƚŽƌƐ ƚƚƌŝďƵƚĞƐ ͙͙ ͙ ͙͘ KďũĞĐƚŝǀĞũ ĞŶĞĨŝƚ ;Ϳ ͲĂ͗ ĚĞƐĐƌŝƉƚŝŽŶ;ǁĞŝŐŚƚ ͕ǀĂůƵĞ Ϳ ͙ KƉƉŽƌƚƵŶŝƚLJ ;KͿ ͲĂ͗ ĚĞƐĐƌŝƉƚŝŽŶ;ǁĞŝŐŚƚ ͕ǀĂůƵĞ Ϳ ͙ ŽƐƚ ;Ϳ ͲĂ͗ ĚĞƐĐƌŝƉƚŝŽŶ;ǁĞŝŐŚƚ ͕͕ǀĂůƵĞ Ϳ ͙ ZŝƐŬ ;ZͿ ͲĂ͗ ĚĞƐĐƌŝƉƚŝŽŶ;ǁĞŝŐŚƚ ͕ǀĂůƵĞ Ϳ ͙ ͙͙ ͙͘ ͙͘ ( )a υ ( )a ω ( )a ω υ( )a ( )a υ ( )a υ ( )a ω ( )a ω

Ilj1 51 ERFU vwuxfwxuhg lghqwlw| fdug ri dq dfwlrq ru dq dowhuqdwlyh Ilqdoo| lq wklv iudphzrun/ hdfk dfwlrq ru dowhuqdwlyh l/ zloo eh fkdudfwhul}hg e| irxu phdvxuhv/ lwv ehqhw phdvxuh E+l,/ lwv rssruwxqlw| phdvxuh R+l,/ lwv frvw phdvxuh F+l,/ dqg lwv ulvn phdvxuh U+l,> zklfk fdq eh frqvlghuhg dv ful0 whuld lq wkh fodvvlfdo zd| ri PFGP> wkhvh phdvxuhv duh rewdlqhg e| djjuhjdwlqj wkh fruuhvsrqglqj phdvxuhv ryhu wkh vhw ri remhfwlyhv zklfk duh rewdlqhg e| djjuhjdwlqj dw0 wulexwhv phdvxuh ri hdfk fdwhjru|1 Jlyhq wkh krprjhqhlw| ri dwwulexwhv rewdlqhg iurp ERFU vwuxfwxulqj wkdw fuhdwhv v|qhuj| ehwzhhq phdvxuh wr djjuhjdwh/ d v|qhujhwlf djjuh0 jdwlrq rshudwru vxfk dv Fkrtxhw lqwhjudo dvvrfldwhg zlwk d zhljkwhg fduglqdo ix}}| phdvxuh +ZFIP,/ vhh ^55`/ wkdw ohdgv wr d vwudljkwiruzdug irupxod iru wklv lqwhjudo/ lv xvhg dw dq| ohyho wkdw qhhgv djjuhjdwlrq1

Wklv prgho doorzv dfwlrqv2dowhuqdwlyhv wr eh fkdudfwhu0 l}hg e| khwhurjhqhrxv dwwulexwhv dqg lqfrpsdudelolw| eh0 wzhhq dowhuqdwlyhv lq whupv ri Sduhwr0htxloleulxp1 Lqghhg/ ghflvlrq pdnlqj vlwxdwlrqv zkhuh dowhuqdwlyhv duh fkdudf0 whul}hg e| dwwulexwhv ri glhuhqw qdwxuh duh shuydvlyh lq uhdo zruog dssolfdwlrqv1 Rqh pd| wklqn derxw d jryhuqphqw hydoxdwlqj surmhfwv wkdw ehorqj wr glhuhqw grpdlqv vxfk dv khdowk/ lqiudvwuxfwxuhv/ vrfldo/ hfrqrplfv/ hwf1 zlwk wkh pdlq remhfwlyh wr hqkdqfh d frxqwu| ghyhorslqj surfhvv ru dq hqwhusulvh sodqqlqj wr lqyhvw lq surmhfwv ri glhuhqw qd0 wxuh1 Lq wkhvh vlwxdwlrqv/ wkrxjk dwwulexwhv fkdudfwhul}lqj surmhfwv pd| eh frpsohwho| glhuhqw/ wkh lpsruwdqw wklqj lv wkhlu dghtxdf| zlwk uhjdugv wr wkh sxuvxhg remhfwlyhv/ vr wkdw dowhuqdwlyh surmhfwv fdq eh xowlpdwho| frpsduhg rq wkh vdph edvlv +ghflvlrq pdnhu ghvluhv,1

Rqfh dwwulexwhv duh holflwhg frphv wkh vwhs ri dvvhvvphqw ri wkhlu txdqwlwdwlyh vwuhqjwk zlwk wrzdug wkh uhdol}dwlrq +iru vxssruwlqj dwwulexwhv, ri sxuvxhg remhfwlyhv ru djdlqvw +iru uhmhfwlqj dwwulexwhv, wkh dfklhyhphqw ri wkhvh remhf0 wlyhv1

E1 Dvvhvvphqw ri sdudphwhuv

Wkh qrupdol}hg ydoxh +d, ri dwwulexwh d iru d jlyhq ERFU frpsrqhqw fdq eh rewdlqhg e| qrupdol}dwlrq ri urz phdvxuh/ e| h{shuw holflwdwlrq iru rshudwlrqdo dwwulexwhv ru e| djjuhjdwlqj vxeohyho dwwulexwhv phdvxuhv> lw uhsuhvhqwv krz zhoo wklv dwwulexwh frqwulexwh wr wkh fruuhvsrqglqj ERFU frpsrqhqw dfklhyhphqw> wkh zhljkw $+d, lq frq0

wudu| uhsuhvhqwv wkh uhodwlyh lpsruwdqfh ghjuhh ri wklv dw0 wulexwh lq frpsdulvrq ri rwkhu dwwulexwhv ri wkh vdph fdw0 hjru| dqg ohyho wkdw fdq hdvlo| eh ghwhuplqhg e| phwkrgv vxfk dv dqdo|wlf klhudufk| surfhvv +DKS,/ vhh ^47`/ e| dq0 vzhulqj txhvwlrqv olnh krz lpsruwdqw lv wkh frqwulexwlrq ri dwwulexwh d lq frpsdulvrq ri lwv frxqwhusduwv lq wkh uhdol}d0 wlrq ri xsshu ohyho dwwulexwh1 Xqfhuwdlq frpsrqhqwv/ rs0 sruwxqlw| dqg ulvn/ lghqwlfdwlrq dqg dvvhvvphqw dssurdfk pd| exlog rq zhoo nqrzq ulvn dvvhvvphqw dssurdfk/ vhh ^<`/ ^53`1

Qrupdol}lqj urz phdvxuhv lv lpsruwdqw lq rughu iru dj0 juhjdwlrq wr rshudwh h!flhqwo|> lq wkh olwhudwxuh/ qrupdol}0 lqj vfkhph hqfrxqwhuhg duh grplqdwhg e| wkh irup jlyhq e| htxdwlrq +6, +dl, @ dl pd{l+dl, ru +dl, @ dl plql+dl, pd{l+dl, plql+dl, +6, wkhvh qrupdol}dwlrq vfkhphv gr ulvh vrph sureohpv lq ds0 solfdwlrqv/ vxfk dv=

 qhfhvvlw| wr qxphulfdoo| hydoxdwh dwwulexwhv> wklv lv qrw

dozd|v wkh fdvh lq sudfwlfh>

 qhfhvvlw| wr nqrz wkh phdvxuhphqw udqjh dw dgydqfh

zkhuhdv lq sudfwlfh dqg pdlqo| lq wkh fdvh ri g|qdplf eh0 kdylru ri sureohp gdwd/ rqh grhv qrw nqrz wklv udqjh lq dgydqfh>

 lqghshqghqfh zlwk uhjdugv wr ghflvlrq pdnhuv dwwlwxgh

ru ihholqj wkrxjk lw lv reylrxv wkdw ydoxh dffrughg e| d ghflvlrq pdnhu wr dq dwwulexwh jlyhq lwv urz phdvxuh rq vrph vfdohv zloo ghshqg rq klv2khu ihholqj/ kdelw/ vlwxdwlrq/ hwf1>

 hwf1

Lq wklv frppxqlfdwlrq/ zh frqvlghu d ydoxh w|sh qru0 pdol}dwlrq vfkhph> lq wklv vfkhph d ghflvlrq pdnhu zloo eh dvnhg wr pds dfwxdo phdvxuhphqw ri dq dwwulexwh wr d ydoxh ehwzhhq 3 dqg 4 srvvleo| xvlqj judsklfdo vxssruw +zkhuh wkh vkdsh ri d fxuyh ghshqgv rq ghflvlrq pdnhu ihholqj, dv vkrzq rq Iljxuh 6 wkdw glvsod|v vrph srvvleoh vkdshv> wkxv/ wkh phdvxuh +d, vkrzq rq wkh suhylrxv Iljxuh 5 zloo eh d qrupdol}hg ydoxh rewdlqhg e| wklv qrupdol}dwlrq vfkhph1 Rqh vkrxog qrwlfh wkdw wklv vfkhph ri qrupdol}d0 Ϭ ϭ ZŽǁ ŵĞĂƐƵƌĞ ŽĨĂƚƚƌŝďƵƚĞ Ă sĂůƵĞŽĨ ĂƚƚƌŝďƵƚĞ Ă ( )a υ

Ilj1 61 Ydoxh w|sh qrupdol}dwlrq vfkhph

(6)

wr dq rughuhg glvfuhwh vhw> wklv qrupdol}dwlrq vfkhph dovr pd| lqwhjudwh wkh qdwxuh +srvlwlyh ru qhjdwlyh, ri wkh dw0 wulexwh1

Ohw xv qrz/ ghqrwh e| er

n+l,> rrn+l,/ frn+l,/ dqg urn+l, wkh

qrupdol}hg ydoxhv ri ehqhw/ rssruwxqlw|/ frvw dqg ulvn dw0 wulexwh n ri dfwlrq l zlwk uhjdug wr remhfwlyh r> dqg e| er+l,/ rr+l,/ fr+l,/ dqg ur+l, yhfwruv jdwkhulqj qrupdol}hg

ehqhw/ rssruwxqlw|/ frvw dqg ulvn phdvxuhv uhvshfwlyho|1 Ohw xv vxssrvh qrz wkdw ghflvlrq pdnhu lv deoh wr vxsso| iru ehqhw/ rssruwxqlw|/ frvw dqg ulvn dwwulexwhv qrupdo0

l}hg uhodwlyh ghjuhhv yhfwruv lq whupv ri $e/ $r/ $f/ dqg

$u wkhq wkh ryhudoo ehqhw +Er+l,,/ rssruwxqlw| +Rr+l,,/

frvw +Fr+l,,/ dqg ulvn +Ur+l,,/ phdvxuhv ri dfwlrq l iru re0

mhfwlyh r duh jlyhq e| htxdwlrqv +7, dqg +8,

Er+l, @ F$zfi pe +er+l,, > Rr+l, @ F$zfi pr +rr+l,, > +7, Fr+l, @ Fzfi p $f +f r+l,, > Ur+l, @ Fzfi p $u +u r+l,, +8, zkhuh Fzfi p

$ +{, vwdqgv iru Fkrtxhw lqwhjudo ri qxphul0

fdo yhfwru { dvvrfldwhg wr zhljkwhg fduglqdo ix}}| phdvxuh zlwk zhljkw yhfwru $/ vhh ^55`1

Ohw xv qrz ghqrwh e| e+l,/ r+l,/ f+l,/ dqg u+l, yhfwruv jdwkhulqj ehqhw/ rssruwxqlw|/ frvw dqg ulvn phdvxuhv zlwk

uhjdug wr doo remhfwlyhv dqg e| $r/ wkh uhodwlyh lpsruwdqfh

yhfwru ri remhfwlyhv zlwk uhjdug wr ryhudoo jrdo/ wkhq wkh ryhudoo rslqlrq ghflvlrq pdnhu uhjduglqj wkh dfwlrq l lv fdswxuhg e| wkh ehqhw phdvxuh E+l,/ rssruwxqlw| phd0 vxuh R+l,/ frvw phdvxuh F+l,/ dqg ulvn phdvxuh U+l,/ wkdw duh jlyhq e| htxdwlrqv +9, dqg +:,

E+l, @ F$zfi pr +e+l,, > R+l, @ F$zfi pr +r+l,, > +9,

F+l, @ F$zfi pr +f+l,, > U+l, @ F$zfi pr +u+l,, +:,

F1 Uhfrpphqgdwlrq

Uhfrpphqgdwlrq surfhgxuh zloo ghshqg rq wkh sureohp wr vroyh +vhohfwlqj/ udqnlqj/ vruwlqj/ ru fodvvlfdwlrq/ hwf1 ri dfwlrqv2dowhuqdwlyhv lq rughu wr vdwlvi| vrph sxusrvhv,> ohw xv looxvwudwh wkh fdvh ri iruplqj sruwirolr ri dfwlrqv wkdw lv vhohfwlqj d vxevhw ri dfwlrqv lq rughu wr rswlpl}h ERFU frpsrqhqwv ri wkh sruwirolr zkhq uhvshfwlqj vrph

uhvrxufhv olplwdwlrq frqglwlrqv1 Ohw xv ghvljqdwh e| il wkh

qxphulfdo txdqwlw| ri uhvrxufh qhhghg e| dfwlrq l wr eh lp0 sohphqwhg dqg e| i wkh dydlodeoh uhvrxufh ohyho1 Jlyhq wkh vwuxfwxuh ri ERFU dqdo|vlv/ zh sursrvh wzr dssurdfkhv wr vroyh wklv sureohp= elqdu| pxowl0remhfwlyhv surjudp0 plqj +EPRS, dqg elsrodu phdvxuhv dssurdfk iru vkruw olvw +EPVO, vhohfwlrq lq wkh iudphzrun ri vdwlvflqj jdph ^4:`1

F14 EPRS= elqdu| pxowl0remhfwlyhv surjudpplqj

Jlyhq wkh ghvfulswlrq suhvhqwhg lq deryh sdudjudsk/ wkh sureohp/ khuh/ lv wr irup d sruwirolr wkdw pd{lpl}h joredo ehqhw dqg rssruwxqlw| dqg plqlpl}h joredo frvw dqg ulvn zkhq uhvshfwlqj olplwhg uhvrxufh frqglwlrq1 Ohw xv ghqrwh

e| {l d elqdu| yduldeoh lqglfdwlqj zkhwkhu dfwlrq l lv lq0

foxghg ru qrw lq wkh sruwirolr/ wkxv {l @ 4 li l lv lqfoxghg

lq wkh sruwirolr dqg {l @ 3 li qrw1 Wkh sureohp wr vroyh

lv wkhuhiruh d pxowl0remhfwlyhv surjudpplqj sureohp jlyhq e| iroorzlqj irupxodwlrq +;, ; A A A A A A ? A A A A A A = pd{iSql@4+E+l,,{l,j pd{iSql@4+R+l,,{l,j plqiSql@4+F+l,,{l,j plqSiSql@4+U+l,,{l,j q l@4il{l i {l5 i3> 4j +;,

Wr vroyh wklv sureohp/ glhuhqw dojrulwkpv ghyhorshg lq pxowl0remhfwlyh rswlpl}dwlrq olwhudwxuh vxfk dv jhqhwlf do0 jrulwkpv/ hyroxwlrqdu| dojrulwkpv/ frqvwudlqw vdwlvidfwlrq dojrulwkpv/ hwf1/ vhh iru lqvwdqfh ^7` ^5:` dqg uhihuhqfhv wkhuhlq/ fdq eh xvhg1

F15 EPVO= elsrodu phdvxuhv iru vkruw olvw vhohfwlrq Jlyhq wkh zd| wkh lghqwlw| fdug ri hdfk dfwlrq lv vwuxf0 wxuhg lq whupv ri srvlwlyh lqfhqwlyhv +ehqhw dqg rssruwx0 qlw|, dqg qhjdwlyh lpsdfwv +frvw dqg ulvn,/ elsrodu dqdo|0 vlv dssurdfk ghyhorshg e| wkh dxwkruv/ vhh +^4;` ^4<` ^54` ^56`,/ zkhuh dq dfwlrq lq ghflvlrq dqdo|vlv lv fkdudfwhul}hg e| lwv vhohfwdelolw| ghjuhh dqg lwv uhmhfwdelolw| ghjuhh lv zhoo vxlwhg iru iruplqj d sruwirolr ri dfwlrqv> lw phdqv wkdw rqh dyrlg lpphgldwh frpshqvdwlrq ehwzhhq srvlwlyh lqfhqwlyhv

dqg qhjdwlyh lpsdfwv1 Vhohfwdelolw| phdvxuh V+l, dqg uh0

mhfwdelolw| phdvxuh U+l, ri dfwlrq l lq wkh srlqw ri ylhz

ri ghflvlrq pdnhu fdq qdoo| eh rewdlqhg e| htxdwlrqv +<, dqg +43,

V+l, @ S!E+l, . +4 !, R+l,

oi!E+o, . +4  !, R+o,j

+<,

U+l, @ S+4 !, F+l, . !U+l,

oi+4  !, F+o, . !U+o,j

+43, zkhuh 3  !  4 lv wkh ulvn dyhuvh lqgh{ ri ghflvlrq pdnhu> wklv lqgh{ shuplwv wr dgmxvw wkh dwwlwxgh ri d gh0 flvlrq pdnhu wrzdug xqfhuwdlqw|> iru lqvwdqfh d ulvn dyhuvh ghflvlrq pdnhu/ iru zkr ! $ 4/ zloo edodqfh lpphgldwh ehqhw +E, zlwk srwhqwldo kdup +U, uhjdugohvv ri srwhqwldo ehqhw +R, dqg lpphgldwh frvw wr sd| +F,1

Wr vhohfw wkh qdo sruwirolr/ iroorzlqj vwhsv +exloglqj rq vdwlvflqj jdphv wkhru| ^4:`, fdq eh xvhg1

 Irup wkh vdwlvflqj htxloleulxp vhw Vtri dfwlrqv wkdw lv

jlyhq e| htxdwlrq +44,

Vt@ t_ H +44,

zkhuh H lv wkh htxloleulxp vhw +dfwlrqv iru zklfk wkhuh lv qr rwkhu dfwlrqv kdylqj ohvv uhmhfwdelolw| ghjuhh dqg dw ohdvw wkh vdph vhohfwdelolw| ghjuhh ru kdylqj pruh vhohfwdelolw| dqg dw prvw wkh vdph uhmhfwdelolw| ghjuhh> wklv vhw lv dozd|v

qr hpsw| e| frqvwuxfwlrq, dqg tlv wkh vdwlvflqj vhw/ vhh

^4:`/ dw wkh erogqhvv ru fdxwlrq lqgh{ t/ jlyhq e| htxdwlrq +45, ehorz

t@il = V+l, tU+l,j +45,

 Frpsxwh wkh fruuhvsrqglqj uhvrxufh ohyho i+Vt, dv jlyhq

(7)

i +Vt, @

[

l5Vt

il +46,

 Li i+Vt, lv ohvv wkdq i / doo vdwlvflqj htxloleulxp df0

wlrqv duh lqfoxghg lq wkh sruwirolr> li wkh uhpdlqlqj uhvrxufh

i  i+Vt, lv vx!flhqw iru dw ohdvw rqh surmhfw/ lw zloo eh

xvhg lq d vhfrqg vhohfwlrq vwhs zkhuh wkh dfwlrqv douhdg| lqfoxghg lq wkh sruwirolr duh h{foxghg> wkh surfhvv lv uh0 shdwhg xqwlo qr dfwlrq fdq jhw uhvrxufh zlwk wkh uhpdlqlqj uhvrxufh ru dydlodeoh uhvrxufh lv frpsohwho| xvhg1 Rqh pd| dowhuqdwlyho| ghfuhdvh fdxwlrq lqgh{ lq rughu wr lqfoxgh dv pxfk dv htxloleulxp dfwlrqv +li dq|, lq wkh sruwirolr xqwlo uhvrxufh lv frpsohwho| xvhg1

 Li i+Vt, lv juhdwhu wkdq wkh wkh dydlodeoh uhvrxufh i/

wkhq lqfuhdvh fdxwlrq lqgh{ t wr uhgxfh wkh qxpehu ri vdw0 lvflqj dfwlrqv dqg uhshdw suhylrxv vwhsv1

LLL1 Fdvh vwxg| 16 Ghvfulswlrq ri wkh sureohp

Dxwkrulwlhv ri d uxudo duhd lq d ghyhorslqj frxqwu| duh frqiurqwhg wr gl!fxowlhv uhodwhg wr d txlfn srsxodwlrq jurzlqj ri wklv duhd lq whupv ri odfn ri lqiudvwuxfwxuh id0 flolwlhv iru wkh zhoo0ehlqj ri wkh srsxodwlrq1 Ixuwkhupruh/ wkh| duh vhqvleoh wr idflolwlhv wkdw hqkdqfh vxvwdlqdeoh gh0 yhorsphqw zklfk lv frqvlghuhg dv wkh prvw lpsruwdqw lv0 vxh iru wkh ixwxuh ri wklv duhd lq sduwlfxodu dqg qdwlrqdo ghyhorsphqw lq jhqhudo1 Iru wklv sxusrvh dqg diwhu odujho| frqvxowlqj srsxodwlrq dqg h{shuwv/ yh ghyhorslqj surmhfwv kdyh ehhq lghqwlhg +vhh ^4<` iru pruh ghwdlov,=

 Surmhfw 4 +exlog dqg rshudwh d zdvwh pdqdjhphqw

idflolw|,= dv srsxodwlrq lv txlfno| jurzlqj/ wkh lvvxh ri pdqdjlqj zdvwh ehfdph lpsruwdqw ehfdxvh dfwxdoo| zdvwh lv ehlqj wkurzlqj hyhu|zkhuh fdxvlqj e| wkh zd| khdowk sureohpv/ vrlo srooxwlrq/ vdqlwdu| frqglwlrqv ghjudgdwlrq/

hwf11 Qhfhvvdu| dprxqw iru wklv surmhfw lv I +S4, @ :8

ploolrq PX zkhuh PX vwdqgv iru prqhwdu| xqlw1

 Surmhfw 5 +exlog dqg pdlqwdlq d eulgjh wkdw frq0

qhfwv wkh duhd wr d pdlq qdwlrqdo urdg,= wkh frq0 vlghuhg uxudo duhd lv vxssolhg lq glhuhqw jrrgv iurp pdlq wrzqv ri wkh frxqwu| yld d uxudo urdg wkdw dfurvv d ulyhu> vr wkdw gxulqj udlqlqj shulrgv/ dffhvvlelolw| lv uhqghuhg gl!fxow fdxvlqj pdq| wurxeohv iru wkh srsxodwlrq ri wklv duhd> d eulgjh ryhu wklv ulyhu zrxog eh d juhdw dgydqfh0 phqw wrzdugv ghyhorslqj surfhvv1 Qhfhvvdu| dprxqw iru

wklv surmhfw lv I +S5, @ 96 ploolrq PX1

 Surmhfw 6 +lqvwdoo dqg rshudwh d zlqg idup wr vxs0

so| hohfwulflw| wr wklv duhd,= dw wkh prphqw/ wkhuh lv qr hohfwulflw| idflolw| lq wklv duhd> dqg lwv lvrodwhg frqglwlrq uhqghu lwv frqqhfwlrq wr qdwlrqdo srzhu vxsso| lqihdvleoh/ zklfk srzhu vxsso|/ lv dfwxdoo| lqvx!flhqw iru wkdw qdwlrq1

Qhfhvvdu| irxqg ri wklv surmhfw lv I +S6, @ :5 ploolrq PX1

 Surmhfw 7 +exlog dqg rshudwh d zdwhu vxsso| idflo0

lw|,= dfwxdoo|/ zdwhu xvhg e| lqkdelwdqwv ri wkh frqvlghuhg duhd iru glhuhqw dfwlylwlhv ri wkhlu grphvwlf olih frphv iurp wkh ulyhu zkhuh fkloguhq dqg zrphq zhqw wr ihwfk zdwhu1 Wkhuhiruh kdylqj d prghuq zdwhu vxsso| idflolw| lq wklv duhd zloo eh yhu| lpsruwdqw iru wkh srsxodwlrq lq glhu0

hqw ylhzsrlqwv1 Wkh surmhfw frqvlvwv wkhuhiruh lq pdnlqj d guloo lq vrph srlqwv wr jhw gulqnlqj zdwhu iurp xqghu0

jurxqg1 Qhfhvvdu| dprxqw iru wklv surmhfw lv I +S7, @ 88

ploolrq PX1

 Surmhfw 8 +exlog dqg rshudwh d gdp iru djulfxo0

wxuh luuljdwlrq,= sulqflsdo dfwlylw| ri srsxodwlrq ri wkh frqvlghuhg duhd lv djulfxowxuh> exw lw lv qrwlfhg wkdw wkh surgxfwlylw| ri fxowlydwhg odqgv lv yhu| orz gxh lq sduw wr lqvx!flhqw udlqlqj1 Wkh lghd lv wkhuhiruh wr exlog dqg rs0 hudwh d gdp lq rughu wr uhwdlq udlq zdwhu wr eh xvhg iru luuljdwlrq e| iduphuv1 Qhfhvvdu| dprxqw iru wklv surmhfw lv

I +S8, @ 63 ploolrq PX

Dv wkh dydlodeoh ixqg ri I @ 483 ploolrq PX fdqqrw ixqg doo surmhfwv/ wkh| pxvw eh hydoxdwhg lq rughu wr vhohfw surmhfwv wkdw pxvw frqvwlwxwh wkh prvw vxvwdlqdeoh surmhfwv sruwirolr1 Lw lv zhoo dffhswhg/ iurp wkh ghqlwlrq ri vxv0 wdlqdeoh ghyhorsphqw sdudgljp +ghyhorsphqw wkdw phhwv wkh qhhgv ri wkh suhvhqw zlwkrxw frpsurplvlqj wkh delolw| ri ixwxuh jhqhudwlrqv wr phhw wkhlu rzq qhhgv, jlyhq e| iruphu Qruyhjldq Sulph Plqlvwhu Jur Kduohp Euxqgwodqg lq 4<;:/ wkdw vxvwdlqdelolw| ri d surmhfw pxvw eh dvvhvvhg wkurxjk wkuhh pdlq remhfwlyhv/ vrfldo remhfwlyh/ hfrqrplfdo remhfwlyh dqg hqylurqphqwdo remhfwlyh> vr wklv wkuhh remhf0 wlyhv duh wkrvh xvhg wr hydoxdwh hdfk surmhfw dqg ERFU idfwruv ydoxhv ri wkhvh surmhfwv duh vkrzq rq wkh iroorz0 lqj Wdeoh L +ghwdlohg fdofxodwlrqv duh rplwwhg khuh ehfdxvh ri odfn ri sodfh/ lqwhuhvwhg uhdghuv fdq frqvxow ^4<` wr wklv hqg,1

Surmhfwv E+Sl, R+Sl, F+Sl, U+Sl,

S4 3=89 3=94 3=9: 3=94

S5 3=95 3=87 3=98 3=87

S6 3=8; 3=97 3=:6 3=77

S7 3=79 3=89 3=94 3=78

S8 3=87 3=:5 3=98 3=9;

Wdeoh L= ERFU hydoxdwlrq ri surmhfwv D1 Uhvxowv

Iurp gdwd ri suhylrxv Wdeoh L/ sruwirolr iruplqj sureohp kdv ehhq frqvlghuhg lq wzr ohyhov/ e| ydu|lqj wkh ulvn dyhuvh lqgh{ ! iurp ulvn| ghflvlrq pdnlqj +! @ 3 ,> phdq ulvn wdnlqj +! @ 3=8, dqg ulvn dyhuvh ghflvlrq pdnlqj +! @ 4,> dqg iroorzlqj Iljxuh 7 vkrzv rewdlqhg uhvxowv lq wkh fdvh ri EPVO uhfrpphqgdwlrq prgho zlwk d erogqhvv lqgh{ ri t @ 41

Iru ! @ 3/ V4@iS8j> wkdw lv/ rqo| surmhfw 8 lv d vdwlvf0

lqj htxloleulxp +frpsdulvrq ri rssruwxqlw| wr lpphgldwh

frvw,> e| glvuhjduglqj surmhfw S8/ surmhfwv S4/ S6 dqg S7

ehfrph htxloleulxpv iru d wrwdo dprxqw ri 535 ploolrq PX wkdw fdqqrw vlpxowdqhrxvo| eh ixqghg e| wkh uhpdlqghu ri 483  63 @ 453 ploolrq PX> ixuwkhupruh rqh fdq hdv0 lo| vhh wkdw rqo| rqh ri wkhvh surmhfwv fdq eh ixqghg zlwk wkh uhpdlqghu ixqg> e| uhdvrqlqj rq pd{lpxp erogqhvv

lqgh{ edvlv/ wkh qh{w surmhfw wr ixqg lv surmhfw S7 zlwk d

uhpdlqghu ixqg ri 98 ploolrq XP wkdw fdq fryhu qdqfldo

dprxqw ri surmhfw S5 +wkdw ehfrphv htxloleulxp zkhq S7

lv glvuhjdughg, vr wkdw lq wklv fdvh wkh sruwirolr frqvlvwv

(8)

R µ S µ 0 .16 0.17 0.18 0.19 0.2 0 .21 0.2 2 0 .23 0.24 0.25 0.16 0.17 0.18 0.19 0.2 0.21 0.22 0.23 0.24 0.25 Re jectability d eg ree S e le c ta b ili ty d e g re e φ = 0 φ = 0.5 φ = 1 P 1 P2 P3 P 4 P 5 P1 P2 P 3 P4 P5 P1 P 2 P 3 P 4 P5

Ilj1 71 Uhsuhvhqwdwlrq ri uhvxowv lq wkh sodq +U> V,

! @ 3=8/ wkh vdwlvflqj htxloleulxp vhw dw erogqhvv lqgh{

t @ 4 lv V4@iS6> S8j zklfk wrwdo ixqg lv 435 ploolrq XP

dqg wkh uhpdlqghu ixqg ri 7; ploolrq XP fdqqrw qdqfh dq| ri wkh uhvw ri surmhfwv1 Iru ulvn dyhuvh ghflvlrq pdnlqj/

! @ 4/ wkh vdwlvflqj htxloleulxp surmhfwv vhw lviS5> S6j

wkdw lv ixqghg iru 468 ploolrq PX dqg wkh uhpdlqghu ri 48 ploolrq PX fdqqrw ixqg d ixuwkhu surmhfw1

LY1 Frqfoxvlrq

D vwuxfwxuhg iudphzrun iru pxowl0fulwhuld ghflvlrq pdn0 lqj surfhvvhv kdv ehhq frqvlghuhg lq wklv frppxqlfdwlrq1 Wkh pdlq frqwulexwlrq ri wklv frppxqlfdwlrq frqfhuqv wkh fodulfdwlrq ri remhfwlyhv qrwlrq/ dwwulexwhv qrwlrq dqg ful0 whuld qrwlrq frpsduhg wr h{lvwlqj dssurdfkhv lq wkh olwhu0 dwxuh1 Wkh sursrvhg dssurdfk shuplw wr fkdudfwhul}h df0 wlrqv e| khwhurjhqhrxv dwwulexwhv zlwk uhjdug wr sxuvxhg remhfwlyhv1 Lqghhg/ lq wklv frppxqlfdwlrq/ dq remhfwlyh lv vrphwklqj ghflvlrq pdnhu vhhnv wr dfklhyh wr dwwdlq vrph xowlpdwh jrdo/ dq dwwulexwh lv d ihdwxuh ri dq dfwlrq wkdw pd| dfw wrzdug ru djdlqvw wkh uhdol}dwlrq ri vrph remhfwlyhv dqg d fulwhulrq lv rewdlqhg e| %djjuhjdwlqj% wkh vwuhqjwk ri vrph dwwulexwhv ryhu doo remhfwlyhv wr uhsuhvhqw dq lqgl0 fdwru ri krz zhoo ru uhvlvwdqw lv dq dfwlrq zlwk uhjdug wr ryhudoo ghflvlrq jrdo1 Ixuwkhupruh wkh sursrvlwlrq wr dv0 vhvv wkh vwuhqjwk ri dwwulexwh e| d ydoxh ixqfwlrq shuplwv hqodujhv srvvlelolwlhv ri vfdohv dqg zd|v ri phdvxuhphqw ri urz gdwd1

Uhihuhqfhv

^4` G1 Erx|vvrx/ W1 Pdufkdqw/ S1 Shuq|/ P1 Sluorw/ D1 Wvrxnlãv/ dqg S1 Ylqfnh/ Hydoxdwlrq dqg Ghflvlrq Prghov= D fulwlfdo Shu0 vshfwlyh/ Gruguhfkw= Noxzhu Dfdghplf/ 53331

^5` \1 Erx}durxu0Dprnudqh/ D1 Wfkdqjdql/ dqg I1 Shuhv/ %Ghflvlrq hydoxdwlrq surfhvv lq hqg0ri0olih v|vwhpv pdqdjhphqw%/ Mrxuqdo ri Pdqxidfwxulqj V|vwhpv/ 6:/ ss1 :480:5;/ 53481

^6` M1 W1 Fdflrsr dqg J1J1 Ehuqwvrq/ %Uhodwlrqvkls ehwzhhq dwwl0 wxghv dqg hydoxdwlyh vsdfh= D fulwlfdo uhylhz/ zlwk hpskdvlv rq wkh vhsdudelolw| ri srvlwlyh dqg qhjdwlyh vxevwudwhv/% Sv|fkrorj0 lfdo Exoohwlq/ 448/ ss1 7340756/ 4<<71

^7` F1D1 Frhoor Frhoor/ J1JE1 Odprqw/ dqg G1D1 Ydq Yhogkx}lhq/ Hyroxwlrqdu| Dojrulwkpv iru Vroylqj Pxowl0Remhfwlyhv Sureohpv/ Vsulqjhu/ 533:

^8` P1 Grxpsrv/ V1K1 ]dqdnlv/ dqg F1 ]rsrxqlglv/ %Pxowlfulwhuld suhihuhqfh glvdjjuhjdwlrq iru fodvvlfdwlrq sureohpv zlwk dq ds0

solfdwlrq wr joredo lqyhvwlqj ulvn/% Ghflvlrq Vflhqfhv/ 65+5,/ ss1 6666;9/ 53341

^9` M1 Jhoghupdqq/ R1 Uhqw} / %Hqylurqphqwdo ghflvlrqv dqg hohf0 wurqlf ghprfudf|/% Mrxuqdo ri Pxowl0Fulwhuld Ghflvlrq Dqdo|vlv/ 45+56,/ ss1 ::<5/ 53361

^:` P1 Judelvfk/ %Wkh dssolfdwlrq ri ix}}| lqwhjudov lq pxowlfulwhuld ghflvlrq pdnlqj/% Hxurshdq Mrxuqdo ri Rshudwlrqdo Uhvhdufk/ ;< +6,/ ss1 7780789/ 4<<91

^;` V1 Juhfr/ E1 Pdwdud}}r/ dqg U1 Vorzlqvnl/ %Urxjk vhwv wkhru| iru pxowlfulwhuld ghflvlrq dqdo|vlv/% Hxurshdq Mrxuqdo ri Rshud0 wlrqdo Uhvhdufk/ 45<+4,/ ss1 47:/ 53341

^<` \1 Kdlphv/ V1 Ndsodq/ dqg M1 Odpehuw/ %Ulvn Ilowhulqj/ Udqnlqj/ dqg Pdqdjhphqw Iudphzrun Xvlqj Klhudufklfdo Krorjudsklf Prgholqj/% Ulvn Dqdo|vlv 55 +5,/ ss1 ;606<:/ 53351

^43` N1 Ndedvvl/ G1N1 Ghvsrwlv/ P1 Yluyrx/ %D pxowlfulwhuld dssurdfk wr g|qdplf uhdvrqlqj lq dq lqwhooljhqw xvhu lqwhuidfh/% Lqwhuqd0 wlrqdo Mrxuqdo ri Lqirupdwlrq Whfkqrorj| ) Ghflvlrq Pdnlqj/ 7+4,/ ss1 5467/ 53381

^44` O1 Ndqdshfnlhqh/ D1 Ndnodxvndv/ H1N1 ]dydgvndv/ dqg V1 Udvodqdv/ %Phwkrg dqg v|vwhp iru pxowl0dwwulexwh pdunhw ydoxh dvvhvvphqw lq dqdo|vlv ri frqvwuxfwlrq dqg uhwurw surmhfwv/% H{0 shuw V|vwhpv zlwk Dssolfdwlrqv/ 6;+44,/ ss1 474<94753:/ 53341 ^45` F1 H1 Rvjrrg/ J1 Vxfl/ dqg S1 K1 Wdqqhqedxp/ Wkh Phdvxuh0

phqw ri Phdqlqj/ Fklfdjr= Xqly1 ri Lolqrlv Suhvv/ 4<8:1 ^46` E1 Ur| dqg G1 Erx|vvrx/ Dlgh Pxowlfulwhuh d od Ghflvlrq= Phwk0

rghv hw Fdv/ Sdulv= Hglwlrq Hfrqrplfd/ 4<<61

^47` W1 Vddw|/ Wkh Dqdo|wlf Qhwzrun Surfhvv= Ghflvlrq Pdnlqj zlwk Ghshqghqfh dqg Ihhgedfn/ UZV Sxeolfdwlrqv/ 53381

^48` K1 D1 Vlprq/ Dgplqlvwudwlyh Ehkdylru= D vwxg| ri ghflvlrq0 pdnlqj surfhvvhv lq dgplqlvwudwlyh rujdql}dwlrqv/ Irxuwk Hgl0 wlrq/ Wkh Iuhh Suhvv/ 4<<:1

^49` U1H1 Vwhxhu/ Pxwlfulwhuld Rswlpl}dwlrq= Wkhru|/ Frpsxwdwlrq/ dqg Dssolfdwlrq/ Qhz \run= Zlooh|/ 4<;91

^4:` Z1F1 Vwluolqj/ Vdwlvflqj Jdphv dqg Ghflvlrq Pdnlqj= Zlwk Dssolfdwlrqv wr Hqjlqhhulqj dqg Frpsxwhu Vflhqfh/ Fdpeulgjh Xqlyhuvlw| Suhvv1Vwluolqj/ Z1F1/ 53361

^4;` D1 S Wfkdqjdql/ %Ix}}| Qrplqdo Fodvvlfdwlrq xvlqj Elsrodu Dqdo|vlv/% lq= Ix}}| Rswlplvdwlrq dqg Pxowl0Fulwhuld Ghflvlrq Pdnlqj lq Gljlwdo Pdunhwlqj/ Dqlo Nxpdu dqg Pdqrm Nxpdu Gdvk/ Hgv1/ LJL Joredo/ 5349/ ss1 56605861

^4<` D1 S Wfkdqjdql/ %ERFU Dqdo|vlv= d Iudphzrun iru Iruplqj Sruwirolr ri Ghyhorslqj Surmhfwv/% lq= Pxowlsoh Fulwhuld Ghfl0 vlrq Pdnlqj lq Ilqdqfh/ Lqvxudqfh/ dqg Lqyhvwphqw/ Plqzlu Do0Vkdppdul dqg Kdwhp Pdvul/ Hgv1/ Vsulqjhu/ ss1 4;<0537/ 53481

^53` D1 S Wfkdqjdql/ %Lqwhjudwlqj Kxpdq Dwwlwxgh lq Ulvn Dvvhvv0 phqw Surfhvv/% Mrxuqdo ri Xqfhuwdlq V|vwhpv <= 61 ss1 4:804;5/ 53481

^54` D1 S Wfkdqjdql/ %Elsrodulw| lq Ghflvlrq Dqdo|vlv= d zd| wr frsh zlwk kxpdq mxgjphqw/% lq= H{sorulqj Lqqrydwlyh dqg Vxffhvvixo Dssolfdwlrqv ri Vriw Frpsxwlqj/ Dqwrqlr G1 Pdvhjrvd/ Sdeor M1 Yloodfruwd/ Fduorv Fux}0Frurqd/ P1V1 Jdufld0Fdvfdohv/ Pduðd W1 Odpdwd/ dqg Mrvì O1 Yhughjd|/ Hgv1/ LJL Joredo/ ss1 549 0 577/ 53471

^55` D1 S1 Wfkdqjdql/ %Elsrodu Djjuhjdwlrq Phwkrg iru Ix}}| Qrp0 lqdo Fodvvlfdwlrq xvlqj Zhljkwhg Fduglqdo Ix}}| Phdvxuh +ZFIP,/% Mrxuqdo ri Xqfhuwdlq V|vwhpv/ :+5,/ ss1 46;0484/ 53461

^56` D1S1 Wfkdqjdql/ \1 Erx}durxu0Dprnudqh/ dqg I1 Sìuëv/ %Hydo0 xdwlrq Prgho lq Ghflvlrq Dqdo|vlv = Elsrodu Dssurdfk/%1 LQ0 IRUPDWLFD = dq Lqwhuqdwlrqdo Mrxuqdo1 56 +6,/ ss1 79407;8/ 53451

^57` ]1 Wxuvnlv dqg H1N1 ]dydgvndv/ %D qryho phwkrg iru pxowl0 soh fulwhuld dqdo|vlv= juh| dgglwlyh udwlr dvvhvvphqw +DUDV0J, phwkrg/% Lqirupdwlfd/ 54+7,/ ss1 8<:943/ 53431

^58` H1U1 Ydlgrjdv dqg M1 Vdnhqdlwh/ %Pxowl0dwwulexwh ghflvlrq0 pdnlqj lq hfrqrplfv ri uh surwhfwlrq/% Lq}lqhulqh Hnrqrplnd0 Hqjlqhhulqj Hfrqrplfv/ 55+6,/ ss1 5955:3/ 53441

^59` Sk1 Ylqfnh/ O*dlgh pxowlfulwhuh ã od ghflvlrq/ Eux{hoohv= Hglwlrqv XOE/ 4<;<1

^5:` H1 ]lw}ohu dqg O1 Wklhoh/ %Pxowlremhfwlyh Hyroxwlrqdu| Dojr0 ulwkpv= D Frpsdudwlyh Fdvh Vwxg| dqg wkh Vwuhqjwk Sduhwr Dssurdfk/% LHHH Wudqvdfwlrqv rq Hyroxwlrqdu| Frpsxwdwlrq/ 6 +7,/ ss1 58:05:4/ 4<<<1

Références

Documents relatifs

Rotations (A) Solutions Dessinez l’image de la rotation d´ecrite.. Rotation dans le sens horaire de 90 ◦ autour du point

There is no necessity to work with a refined frame in DSmT framework which is very attractive in some real-life problems where the elements of the refined frame do not have

A particular attention is paid to the automation of the information phase in the decision-making process: movie comments cartography according to users’ evaluation criteria

47`/ lq d erxqghg0huuru frqwh{w1 Lw kdv dovr ehhq xvhg wr ghdo zlwk urexvw frqwuro dqg dqdo|vlv ri olqhdu v|vwhpv ^;/ 4;/ 4/ 53`1 Qrz/ wkh sureohp ri qglqj d ihdvleoh frqwuro vhtxhqfh

to the criteria defined in action pool. These values are used to calculate the average scores of action pool items using LOWA. The values can either be

We conjecture that the change in the deep water formation in the Eastern Mediterranean sea is attributed to a switch between the different states on the thermoha- line circulation;

For the Advanced LIGO interferometric gravitational wave observatory, where the relevant test mass is a suspended 340 mm diameter cylindrical end mirror, the force noise power

Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of