An Intelligent System for Risk Classification of Stock Investment Projects

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1 A Iellge Syem for R Clafcao of Soc Iveme Proec Aoaea Sergueva a, aaa Kalgaova b, arq Kha a a Deparme of Bue ad Maageme b Deparme of Elecroc ad Compuer Egeerg Bruel Uvery, Uxbrdge UB8 3PH, UK Emal: AoaeaSergueva@bruelacu he propoed paper demorae ha a hybrd fuzzy eural ewor ca erve a a r clafer of oc veme he rag algorhm for he regular par of he ewor baed o bdrecoal cremeal evoluo provg more effce ha drec evoluo he approach compared wh oher crp ad of veme appraal ad radg echque, whle buldg a mulmodel doma repreeao for a ellge deco uppor yem hu he advaage of each model are uled whle loog a he veme problem from dffere perpecve he emprcal reul are baed o UK compae raded o he Lodo Soc Exchage Keyword: face, bdrecoal cremeal evoluo, mulmodel owledge repreeao Iroduco Sadard veme appraal echque have bee cououly reved he crera have bee reopmed due o veme rreverbly [4] ad he mpac of a o he veor oal r [45] I ha bee realed ha he removal of ay of he perfec mare aumpo deroy he foudao ad reduce he effecvee of he mehod Aleravely, a fuzzy crero doe o aemp o cope wh a pecfc drawbac of adard echque bu perm o he calculao a much uceray a he mare could pobly uffer he oucome a effecve mehod uder rerced formao, ucera daa ad mare mperfeco A fuzzy crero ad veme rag echque are fr roduced [5], he codered a broader framewor of accumulao ad dcou model [], ad recely modfed wh a alerave fuzzfcao of he durao [3] Whle hoe ude are heorecal aure, he emprcal reul are a maor empha [3,4,4,43], where oc are evaluaed ad UK compae raded o he Lodo Soc Exchage are codered Smulaeouly, he aaly of he emprcal oluo o he fuzzy crero faclae here he duco of hree geeral cocluo A veme r meaure, a emae of he robue oward mare uceray modelled wh he fuzzfed daa, ad a alerave rag echque baed o he wo meaure Whe compared wh prevou ude, he propoed paper demorae he followg advaage Fr, e repreeave are choe from he daabae employed [4], hu coely emphag he emprcal reul Secod, he are raed accordg o a modfcao of he r meaure uggeed here, exedg furher he developed mehod hrd, a fuzzy-valued crero formulaed ad a regular fuzzy eural ewor, raed wh a geec algorhm, approxmae oluo Hece, he beef of varou of echque are bleded o acheve a yergy hadlg he veme appraal problem I comparo, [5,6,,3,3] oly udy fuzzy crera Forh, he ewor hybrded o dcrmae bewee low-r ad hgh-r he hrehold age-depede, commucag he accepable level of r he varey of mare age wor wh dvere r rage I he exreme, he behavour of a veme fud dffer from he behavour of a dvdual veor Coequely, a age-depede hrehold wll beef he decomaer Ffh, a effce rag algorhm uggeed for he regular par of he fuzzy

2 ewor Geec algorhm are a promg ool rag fuzzy ewor ad rece ude uccefully apply drec evoluo o opme he fuzzy wegh mall regular ewor reemblg parcular ype of uvarable fuzzy fuco [8] I comparo, here he ewor approxmae a mulvarable crero ad he umber of ode deped o he veme horzo he complexy of he problem requre a correpodg evoluoary raegy ad he mplemeao of bdrecoal cremeal evoluo uggeed Icremeal raegy ha bee already appled o evolve eural ewor corollg a robo moo [8] I addo o cremeal evoluo, he bdrecoal raegy furher corporae dvde-ad-coquer evoluo hu he complex a fr gradually dvded o mpler uba, he each uba evolved eparaely, ad laly he evolved uboluo are merged cremeally o opme he overall oluo he echque allow overcomg he allg effec drec evoluo ad ha already proved more effce evolvg logc fuco [4] Fally, he developed clafer compared wh oher clacal ad of veme appraal ad radg mehod, ad he advaage of each approach are uled whle buldg a mulmodel owledge doma for a ellge deco uppor yem h wll allow loog a he veme problem from varou cocepual or purpoe agel ad choog a adequae echque for each uao A beefcal feaure of uch owledge orgaao, comparo wh gle-model repreeao, he flexbly offer overcomg pecfc model drawbac Navgag wh a pace of mulple model ha bee already appled o echcal ad medcal doma [4,6,7,9] here, he creaed capably of he relaed ellge yem upporg uer rough varou a examed, ad parcularly overcomg lmao here moo-model approache I he veme doma, uch yem wll ehace he ably of he deco-maer o aalye from mulple perpecve, ad wll uppor hm olvg problem wh varyg obecve ad complexy he propoed approach developed for he followg reao Fr, here have bee uggeed fuzzy echque for veme appraal ad baed o hem rag procedure [5,4], bu o veme clafer ye codered herefore, a deco would oly be ae afer applyg he fuzzy crero o all avalable, he rag hem accordgly, ad fally choog he accepable opporue he roduco of a clafyg yem wll gfcaly mplfy he proce, epecally for a large umber of cououly updaed ad regularly ae veme deco Oce raed, he ewor wll be a efforle rume he had of he deco-maer, wheever he formao avalable ubec o chage Secod, adard eural ewor have bee uccefully appled o clafy aeover arge [7] hrd, here have bee already developed of ellge radg yem ad arfcal oc mare [,3,46,47,48] ha wll furher beef from he roduco of he mulple modellg-perpecve approach I wll power a veme age o perform prelmary evaluao ad rag, r aaly ad clafcao of admble oc, ad radg mulao Fgure decrbe he errelao bewee facal, of compug ad arfcal ellgece echque, a well a bewee heorecal ad emprcal ude All hee approache are volved o he proce of formulag he veme clafer ad buldg he mulmodel ellge yem he orgaao of he paper follow a ep by ep approach, oulyg he of clafer Seco, buldg he mulmodel owledge repreeao Seco 3, ad preeg he emprcal reul Seco 4 he clafer roduced by fr formulag ubeco a fuzzy-valued crera ha beer capable of veme evaluao uder ucera mare daa he a crp crera Nex, ubeco, he rucure of a hybrd fuzzy eural ewor defed ha effecve approxmag he above crera Fally, ubeco 3, a geec algorhm uggeed ad a bdrecoal cremeal evoluoary raegy developed ha effce rag he fuzzy ewor he ecod par of he paper ed by ag he advaage of he of veme clafer I he hrd par, a mulmodel veme doma bul up cludg he developed clafer Fr, ubeco 3, a umber of releva model are referred o ad her characerc are aalyed he model are choe wh he purpoe o gve he

3 ellge yem he ably o perform varou a From prelmary crp evaluao of a, hrough more formave fuzzy veme appraal ad rag, gog o wh r ad robue emao, a age-depede r clafcao ad recommedao of aracve, ad fally uggeg oc-radg raege Nex, ubeco 3, he poo of he model codered accordg o everal cocepual perpecve a rgdy, reoluo, preco, ad a mulperpecve doma pace coruced he paper ed wh preeg emprcal reul baed o UK compae raded o he Lodo Soc Exchage, ad dcug he advaage of he mulmodel ellge yem Fuzzy Logc [5,53,54] veme appraal ad rag, heorecal ad emprcal udy [3,4] veme appraal ad rag, heorecal approache [,5,6,,3] Neural Newor [5,5] NN olvg fuzzy equao [7] NN clafyg merger arge [7] Evoluoary Compuao [3,9] cremeal evoluo [8,] veme appraal ad rag, heorecal ad emprcal udy [4,43] bdrecoal cremeal evoluo [4] Propoed Approach Developme (bold boxe) Facal Egeerg [,,6] Sof Compug [8,5] approxmag capable of fuzzy eural ewor [9,33] of compug facal egeerg [,38] Arfcal Iellgece [44,49] model baed reaog [,3] hybrd ellge oc-radg yem [,3,46,47,48] Hybrd Iellge Syem [3,34] clafyg low-r veme, heorecal ad emprcal ude [4,maucrp] mulmodel owledge repreeao [4,6,7,8,9] a mulmodel ellge yem for oc veme evaluao, rag, r clafcao, ad radg [maucrp] clacal veme echque, emprcal ude [37,39] veme appraal, heorecal modfcao [,4,45] Fgure : echque errelao formulag he veme clafer ad buldg he mulple-model ellge yem Boxe bold follow he developme of he propoed approach 3

4 Sof Clafer Fuzzy valued crero he eed for clacal veme model revo ad he groud for ew ype of model are well recoged Varou modfcao [4,45] elmae oly ome of he problem aocaed wh he adard crera ad ha bee realed ha he removal of ay of he perfec mare aumpo ypcally deroy he foudao of geerally acceped veme-eleco echque I [45], emphaed ha havg rule whch lead o correc deco he preece of capal mare mperfeco would lead o a uao where moder face heory ca be appled coely Furhermore, he mahemac uderlyg he adard facal echque eglec exreme uao ad regard large mare hf a oo ulely o maer Such echque may accou for wha occur mo of he me he mare, bu he pcure hey pree doe o reflec he realy, a maor eve happe he redual me ad veor are urpred by uexpeced mare moveme I reaoed [] ha ha he percepo of cocep here or urroudg he veme proce, whoe characer o prcpally meaurable, be hadled by he of mahemac emergg from he heory of fuzzy e hu, a fuzzy approach allow for mare flucuao well beyod he probably ype of uceray permed by he adard facal mehod I doe o mpoe predefed daa or mare behavour, here oly a aemp o model a much uceray a he evrome ca pobly embody, producg beer emae of he veme r Coderg he above argume, we formulae a fuzzy-valued crero a he fr age of he propoed veme appraal mehod he al po he prce-dvded relaohp, where we coder me-varyg oc reur Prce are oo volale o be raoal foreca of fuure dvded dcoued a a coa rae ad emprcal e have covced may facal ecoom ha oc reur are me-varyg raher ha coa [] Allowg me-varyg reur raform he prce-dvded relao o olear If loglear approxmao codered, ad he reulg equao olved forward for he log oc prce, a prce emao pˆ produced perod, (ee Appedx A for deal) Le be he veme horzo, he a profable whe he emaed hare prce exceed he mare hare prce pˆ > p a Baed o h, he fuzzy-valued crero formulaed followg a procedure four ep Fr, for each, he parameer of learao δ ad λ are obaed ad codered crp Secod, mare uceray roduced o he daa coverg hare prce, dvded yeld ad reur, applyg a pecfc calbrao echque o produce pove olear fuzzy coeffce A ~,B ~,C ~, hrd, he fuzzy-valued log hare prce P ~ a preeed a P ~ λ A ~ g A [( λ)( C ~ dy + A ~ p ) + δ B ~ r ] + + A ~ g A B ~ g B B ~ g A ~ + λ B p + + C ~ g C + g, <, <, () where all g fuco are couou ad defed o he crp mare daa employed o evaluae a hu, he fuzzy log hare prce from [4] raformed o a couou mulvarable fuzzy-valued fuco he modfcao provde ha he fuzzy eural ewor roduced he ex ubeco capable of approxmag P ~ o a arbrary degree of accuracy Forh, applyg he exeo prcple, he olear memberhp fuco of he oluo obaed For he pecfc formulao of P ~, he α -cu Ω P ( α ) equvale o he erval arhmec oluo he deal of he four-ep procedure are decrbed Appedx A 4

5 Solvg equao () defe he e of emaed log hare-prce value correpodg o all fuure log hare prce, dvded yeld ad reur poble a ome level of uceray, u h e uaed a he ame level u herefore, here a crcal level of uceray, u, emboded o he mare daa we ue o evaluae a, ad h level delm he veme r he r meaure α below derved from he memberhp µ P ~ of he mare prce p o he evaluaed fuzzy hare prce P ~ level ( p ) α ( p P ~ ) up{ α y p }, u [,], µ α P he followg reao advocae uch r defo he lower he crcal level of uceray a whch here a chace for he beg uprofable, he hgher he veme r Furhermore, α he memberhp level of he fuzzy log hare prce, below ad a whch he oluo clude value maller or equal o he al log mare prce, ad above whch he profable Fally, a he varey of mare age wor wh dvere r rage, he ame wll be accepable for ome of hem ad oo ry for oher hu, a age-depede hrehold wll beef he deco-maer I cocluo, he veme crero decrbed wh α α age, (3) where α age commucae he admble r value Coequely, for a parcular age, a worh veg f he aocaed r doe o exceed a accepable level Fuzzy eural ewor he ecod age of he mehod co of buldg a regular fuzzy eural ewor, o approxmae he couou mulvarable fuzzy-valued fuco P ~, ad ubequely cludg wo more layer o dcrmae bewee ry he approxmag capable of regular fuzzy ewor have bee evely uded he la few year I demoraed [8,9] ha uch eural e are o able o repree couou fuzzy fuco o a arbrary degree of accuracy O he oher had, [33] prove ha hey are uveral approxmaor for couou fuzzy-valued fuco Le he real umber e, ad F he e of all fuzzy umber o he a couou fuzzy fuco F fuzzy a mappg from ad o he fuzzy umber e F fuzzy : F F A couou fuzzy-valued fuco F fuzzy valued o from he real umber e o he e of fuzzy umber, Ffuzzy : (), o he oher had, a valued F We have coruced he hare prce a a fuco of he ecod ype, a decrbed he prevou ubeco Baed o he heorem proved [33] abou gle-varable fuco, we formulae four Remar cocerg he mulvarable cae Dealed mahemacal explaao gve Appedx A hu a parcular cla of regular fuzzy ewor defed ha are capable of repreeg mulvarable couou fuzzy-valued fuco he eural e rucure clude four layer, wh gmod rafer fuco ad hf erm he fr hdde layer, ad dey rafer fuco wh o hf erm he pu, he ecod hdde ad he oupu layer I order o reduce he complexy of he ewor rag a whou weaeg he approxmag capable of he eural e, he wegh ad he hf erm are rerced o be real umber wh he excepo of he wegh o he oupu layer ha are ragular fuzzy umber 5

6 Fgure roduce he ewor rucure clafyg veme accordg o he age-depede r crero (3) he cofgurao co of a regular fuzzy eural ewor par ad a hybrd egme he dahed box oule he regular module I pu layer fed wh crp daa - log oc prce p, log reur r ad log dvded yeld dy - whle he oupu layer produce he olear fuzzy umber P ~ RFNN P ~ q V ~ m q,m, V ~ F, e, θ,w,u, z, (4) RFNN ( p,, p,r,,r,dy,,dy,) e ( w p + u r + z dy ) +, where w l, u l, z l ad e are real wegh, θ are real hf erm, V ~ are ragular fuzzy wegh, σ he gmod rafer fuco, he veme horzo, m ad q are he p p r r dy w w u u m u z w m w θ σ z σ θ e q e e qm V ~ V ~ q P ~ RFNN p <α age < α FNN ϕ α FNN dy z m z m σ θ m RFNN 3-m-q- Fgure : Neural ewor rucure clafyg wh accepable r level Regular Fuzzy Neural Newor ouled he dahed box ewor ze: ( 3 ) m q he veme horzo m ad q are he umber of ode he fr ad ecod hdde layer, repecvely crp pu: log oc prce wegh: real umber e,w,u, z p, log reur r ad log dvded yeld, ad ragular fuzzy umber V ~ fr hdde layer: gmod rafer fuco σ wh real hf erm ecod hdde layer: dey rafer fuco wh o hf erm olear fuzzy oupu P ~ RFNN approxmag he fuzzy log hare prce P ~ a Aached Hybrd Par ϕ a rafer fuco producg a approxmao α of he r α, FNN baed o he regular par oupu P ~ RFNN ad he mare prce p a ψ a hard lm rafer fuco wh a age-depede hrehold dy α age oupu defed accepable-r veme (recommedao buy) oupu reeced a oo ry for he cocered mare age (ell) 6

7 umber of ode he fr ad ecod hdde layer repecvely P ~ RFNN a approxmao of he emaed fuzzy log prce P ~, ad lluraed wh memberhp fuco he ewor dagram below he exeo prcple ad he erval arhmec evaluao of uch fuzzy ewor are equvale ad he α -cu of he oupu P ~ RFNN are compued a Appedx A he hybrd par clude wo ode wh rafer fuco ϕ ad ψ, correpodgly he fr ode produce he veme r α releva o he evaluaed FNN hare prce P ~ RFNN ad he mare prce p a hu ϕ decrbed wh FNN ( P ~, p ) µ ( p P ~ ) up{ y p } FNN α ϕ α, (5) FNN memberhp of p o FNN where µ he olear memberhp fuco of P ~ RFNN, ad FNN P P ~, ( p ) RFNN µ P ~ FNN he level of, α ca ae ay value he cloed erval [ ] Fally, ψ α,α age a hard lm rafer fuco comparg he evaluaed r level FNN of he veme uder coderao ad he accepable r level α age of he cocered mare age he olerable r α ca ae ay value he ope erval (,) age ad ac a a hrehold ψ A a reul, oly ha are admble for he parcular veme age wll be recommeded wh a ewor oucome of, ad he re of he wll be reeced producg ha dcae hey are que ry o be codered a veme opporue Each age ca alo reve he hrehold o u h curre poo hu, recoged ha he ame wll have dffere bearg o he r poo of varou mare player ad her parcular crcumace a ha me Such dffereao ugge ha f we coder he oucome of ad a recommedao o buy ad ell, he he advce alo age-depede h a dcve feaure of he mehod comparo wh he geeral pracce of -relaed oly recommedao 3 Bdrecoal cremeal evoluo A he ex age of he developed echque, he regular par of he fuzzy ewor Fgure raed o approxmae he fuzzy log hare prce P ~, ug a geec algorhm ad followg a bdrecoal cremeal evoluoary raegy he geec algorhm pecfed wh alao, eleco ad recombao operaor he alao ep clude chromoome ecodg ad geerag he fr populao Le a ragular fuzzy wegh V ~ be a b c v,v, v correpodg o uppor ad verex he preeed wh hree real umber a b c he relao v < v < v, q, are vald hu he eural e ca be coded o a chromoome χ of ze M 3m + m + qm + 3q, where M equal o he umber of real wegh ad hf erm plu hree me he umber of fuzzy wegh he ewor he al populao X of dvdual χ geeraed mulaeouly a a marx of ze M he eleme of X are realao of a radom varable wh adard ormal drbuo A bloc repreeao of X help o cocurrely or eleme accordg o he equaly rerco above Nex, a breedg ubpopulao X eleced, whch co of he be-fed chromoome, where fuco f ξ, SUB < he eleco baed o he fe 7

8 , ξ > ξ A fξ, (6) ( ξ A ξ )* ξ B, ξ ξ A where ξ A ad ξ B are parameer relaed o he approxmag preco of he coded ewor, ad ξ repree he error of he fuzzy ewor for he correpodg chromoome Coequely, ξ max ( max ( P ( α ) PRFNN ( α ), P ( α ) PRFNN ( α ) )), (7) α {,,,} [ ] where P ( α ), P ( α ) ad, ( α ) RFNN RFNN [ ] P α P are he α -cu of he oupu RFNN hare prce P ~, correpodgly hu he be ubpopulao ba he recombao proce fally buld he ew geerao P ~ ad he X SUB defed, ad o A mulpo X NEW croover operaor appled o X SUB o produce a emporary full-ze populao X EMP he umber ad poo of croover po radomly choe every geerao A realumber ewor parameer recoged a a gee wh he chromoome, ad a rple repreeg a fuzzy-umber parameer alo codered a a gle gee he croover po are oly e bewee gee Radomly choe chromoome from X are combed a Fgure 3 o oba wo offprg, oly oe of whch cluded EMP SUB X Fr Pare gee ; gee ; ; gee 3m+m+qm+q croover po Secod Pare gee ; gee ; ; gee 3m+m+qm+q Fr Chld gee ;gee ; ; gee 3m+m+qm+q Secod Chld gee ;gee ; ; gee 3m+m+qm+q Fgure 3: Mulpo croover operaor he croover po are oly e bewee gee A gle gee co eher of oe real-umber ewor parameer or of a rple repreeg a fuzzy-umber wegh he pare chromoome belog o he be ubpopulao X SUB Oly he fr-chld chromoome added o X SUB o form he emporary full-ze populao X EMP he muao operaor coclude he recombao ep, raformg he emporary populao o he ew geerao of fuzzy-ewor repreeao h ep volve a coa muao rae τ, where <τ < hu he umber of muaed gee coa τ ( 3 m + m + qm + q), bu her place he chromoome radomly choe every geerao Modfed eleme are geeraed a realao of a radom varable wh adard ormal drbuo All he muaed rple gee are cocurrely ored accordg o he equaly rerco above h geec algorhm appled wh a bdrecoal cremeal evoluoary raegy, uggeed o he followg groud A complex a dffcul o evolve, a o poble o drecly dcover a geeral oluo he allg effec drec evoluo may be defeaed by mplemeg cremeal raege, where eural ewor lear complex behavour whle arg wh mple fucog ad gradually creag he complexy of he a [8,] he problem ha he releva ube of mple a a well a her equece o uformly defed, ad o a cremeal raegy Coequely, approprae o 8

9 defy he effce ube of a ad her effce equece [4] Bdrecoal cremeal evoluo appled here deal wh he queo of effcecy by fr defyg he uba ad her equece, he evolvg hem eparaely, ad fally mergg he a gradually whle followg he effce equece Whe he veme paradgm codered, he doma of uba decrbed a follow If he veme horzo, N he umber of perod whch are avalable, [, + ],, N [ N, + ], ad N he umber of compae, he here N are N N N gle-compay gle-perod coug he fr level of uba wh lowe complexy he ex level volve creag umber of gle hey may cocer he ame compay over everal perod or he ame ype of compae over oe or a umber of perod, or may clude dffere ype of compae Accordg o veme r, here ex hree mode of a gle I ca be profable ad o ry whe α, ry for < α <, or oo ry ad uprofable whe α here are alo fve ype of compae hoe wh veme r over all he perod are que rare, havg md ha he mare modelled a hghly ucera he oher ype clude compae wh cououly mprovg level of r, ad compae wh uable r level α whou a parcular dreco Fally, hoe wh coaly woreg veme r, ad he oe wh α over all perod Provdg he rag e clude compae of all ype ad gle coverg he hree mpora mode of α, he he evolved regular fuzzy eural ewor wll uffcely predc he fuzzy log hare prce P ~ of ew veme opporue he overall dea of he evoluoary raegy preeed below, whle dealed decrpo provded Appedx A3 he fe fuco appled hroughou he evoluo f from defo (6), whle he obecve fuco dyamc ad updaed a each ep ξ of he raegy Fr a radom al populao of ze geeraed ad a fuzzy ewor evolved over he full e of gle for a probg umber of geerao N ug f ξ he, f he obecve, baed o he average value of he error ξ over he reulg ubpopulao of be-fed chromoome, above a e lm max( ξ ( χ )) > ξ DEC, he evoluo ar aga wh a ew radom al populao Oherwe he gle are probed wh a updaed obecve fuco over he be ubpopulao If here doe o ex a gle wh a obecve value below a updaed e lm, he a ew full-ze populao geeraed by recombao of he be ubpopulao ad he evoluo coued for aoher N erao Oherwe, he afyg he codo are ge probed aga oppoe he ecod lm o defy e of maxmum ze raher he gle wh a afyg combed obecve value he he full rag e,,,,,, where J he umber of ube of paroed o ube { } J afyg he ecod lm, ad he ube of gle ha do o afy he codo h he fr decompoo level of he rag e Now J + dffere full-ze populao are geeraed by recombao of he ame breedg ubpopulao ad a eparae fuzzy ewor evolved N geerao for each rag ube of he ge he ep up o here, wh reved obecve fuco, are repeaed for each rag ube hu everal level of decompoo of he rag e are defed, ad each level characered wh a uque parog o ube ad a pecfc umber J he decompoo age of he evoluoary raegy complee whe he eural ewor evolved over each rag ube reache a average value of he error over he fr half of he be ubpopulao below a e lm ξ he, he cremeal par of he evoluo ar DECEND ge 9

10 Geerae a full-ze populao IP by recombao of X radom al populao IP of ze Chooe he complee rag e () of, coverg varou ype of compae, ad evaluae he hare prce P ~ for each eleme of he e Se he decompoo level a EVOLVE: a fuzzy ewor over all () for N ge geerao ug he fe fuco f q Keep he geoype of ubpopulao X of he be-fed chromoome Obecve fuco max ξ( χ ) ξ ha a egave value? ye ye DEC Obecve fuco ξ ( χ ) ξdec ha a egave value for a lea oe gle ()? Group all gle ha doe o mee ξ DEC o Paro he rag e o, { } Obecve fuco max( ξ ( χ )) ξ DEC ha a egave value for a lea oe ube of? ye Idefy all he ube, each of maxmum ze Paro he ube o,,,, { } J where each a gle or a ube of Geerae J full-ze populao by recombao of he ame ubpopulao EVOLVE: a eparae fuzzy ewor for each ube of, N ge geerao ug he fe fuco f q Keep he geoype of ubpopulao X of he be-fed chromoome X Geerae a full-ze populao by recombao of EVOLVE: a fuzzy ewor over he for N ge geerao ug he fe fuco f q Keep he geoype of ubpopulao X of he be-fed chromoome Obecve fuco max( ξ ( χ )) ξ ha a egave value? ye DEC 5 Geerae a full-ze populao by recombao of he evolved be ubpopulao Coder he ube a he full rag e + for he ex decompoo level Se he decompoo level a + X X Geerae a full-ze populao by recombao of he prevou ( ) be ubpopulao X ( ) co of a gle? EVOLVE: a fuzzy ewor over he, ug fe fuco f q, ul he obecve ( ) me max ξ χ < ξ DECEND ye Keep he geoype of he fr half of he evolved be-fed ubpopulao END X Sar he cremeal par Se a he hghe level of paro Kmax() Coder he rag e {,,J, } ad geerae a full-ze populao baed o he be ubpopulao ( ) X,,X EVOLVE: ( K ) a fuzzy ewor over he rag e, ug fe fuco f q, ul he obecve ( ) me max ξ χ < ξinc END END Keep he geoype of he fr half of he evolved be-fed ubpopulao INC X Some of he obecve fuco max ξ( χ ) ξ ha a egave value? ye DEC 3 Geerae a full-ze populao by recombao of he evolved be ubpopulao X Geerae a full-ze populao by recombao of he prevou be ubpopulao EVOLVE: a fuzzy ewor over he ube ug he fe fuco f q, ul he obecve ( ) me max ξ χ < ξdecend Keep he geoype of he fr half of he evolved be-fed ubpopulao END > ye X EVOLVE: a fuzzy ewor over he rag e, ug fe fuco f q, ul he obecve be max ξ χ < ξ me ( INCEND INCEND X Fgure 4: Bdrecoal cremeal evoluo ( ) Coder Decreae he level of paro -, whch equvale o creag he cremeal level Keep he geoype of he of he be-fed be chromoome χ INCEND I repree he compleely evolved ewor

11 from he hghe decompoo level Each of he rag ube a h level ha a evolved be ubpopulao aocaed wh A full-ze populao geeraed by recombao baed o all ubpopulao he evoluo coue over he whole rag e exg a he hghe decompoo ep ul a reved obecve fuco ge below ξ INC h he fr cremeal ep he he ecod hghe decompoo level codered he rag e exg a h level clude by defo he whole rag e from he hghe decompoo ep ad ome furher ube of Aga oe full-ze populao geeraed by recombao of he breedg ubpopulao aocaed wh each rag ube here he ube equvale o he hghe decompoo e of preeed wh he be ubpopulao evolved a he fr cremeal level he obecve lm aga ξ INC bu he obecve fuco clude more h he ecod cremeal level he procedure coue by aalogy ul he fr decompoo ep reached, where he parog wa appled over he al full rag e I wll be he fal cremeal level A eural ewor evolved ul he error of oe chromoome oly, raher ha over a ubpopulao of chromoome, bu cludg all he, fall below ξ where INCEND be ξ INCEND < ξ INC h be chromoome χ INCEND repree he compleely evolved regular fuzzy eural ewor Fgure 4 above repree he evoluoary raegy For mplcy, he decompoo par lghly geeraled he dagram omg he e lm ξ DEC4, (ee Appedx A3) he bdrecoal cremeal algorhm mpleme a dyamc obecve fuco I fe fuco f, o he oher had, wll be he ame over all ep, ad equal o he oe ued ξ drec evoluo, for a eay comparo of he reul 4 Cocluo I cocluo, he advaage of he developed mehod cover he followg apec he veme clafer baed o a fuzzy-valued crero ha beer hadle ucera mare daa ha crp crera [] Whaever reao oe ha for modfyg he clac reul [4,45], he allowace provded by he fuzzy-valued crero wll cover hee pecfc crcumace ad wll clude he modfed value, a well a oher poble value, creag he flexbly of he volved calculao Moreover, a meaure for he r aocaed wh each uggeed, hu provdg groud for a alerave veme rag h reul emphae he mehod a more formave o he deco-maer, comparo wh oher fuzzy approache [5,6,,3] Nex, a fuzzy eural ewor rucure defed capable of approxmag he mulvarable crera he cofgurao derved by developg furher he reul for gle-varable fuzzy-valued fuco from [33] he, a geec algorhm uggeed for opmg he parameer of he ewor Sarg wh a procedure from [8] for a mple ewor cofgurao, ad recurvely eg o ad modfyg for he more complex rucure from Fgure, he algorhm developed o demorae creaed peed ad effcecy Fally, a bdrecoal cremeal evoluoary raegy ouled ha parcularly effecve rag fuzzy ewor wh a larger umber of ode ad layer Drec evoluo fal o olve he a We ca compare our emprcal reul (ee ubeco 4) wh oher applcao of geec algorhm o opmg fuzzy ewor parameer I [8] que a mpler rucure raed, wh drec evoluo oly, o approxmae a elemeary gle-varable fuzzy fuco Opmg he clafer me-coumg ad he complexy of he a creae wh expadg he veme horzo Sll, o a dadvaage of he mehod, a he model oly corporaed o he ellge yem afer rag, ad he aly provde uppor o he deco-maer Moreover, everal of clafer ca be cluded o he mulmodel baed yem (ee Seco 3), each raed o gve recommedao over dffere horzolegh Aoher beefcal feaure he age-depede recommedao Raher ha provdg a abrac advce, he model relae every veme o he poble crcumace or preferece of each maor ype of mare age

12 3 Mulmodel owledge repreeao 3 Model eleco he facal echque o be corporaed o he mulmodel doma are choe wh he purpoe o gve he ellge yem he ably o uppor a deco-maer hrough varou veme qure Sarg wh a hare-prce emao baed o he loglearao of he prce-dvded relao whch olved forward over he legh [] h wll provde a prelmary evaluao, hadlg me-varyg reur If he emaed fgure ecouraggly dverge povely from he mare prce, furher vegao ca be uderae A lghly more flexble crero wll be employed o acle he mg of he al oulay I how [4] ha f he value of he a he me evaluaed ochacally flucuag ad depedg o a radom ar me, he here ex a rade-off bewee a larger veru a laer e beef hu he opmal mg of buyg he hare wll be defed, ag o accou veme rreverbly he be ar perod equal he me a whch he beef reache a hrehold I comparo, f he adard crero were ued, he he age would ve ooer bu rely o larger rae o ge he ame prof Up ul ow he deco-maer ha a dea whch could be beefcal ad e o ge more relable evaluao Alhough wh creag flexbly comparo wh adard veme crera, all model above are crp ad herefore worg uder relavely arrow preumpo abou he uderlyg drbuo ad mare behavour Nex ome fuzzy crera wll be roduced o he mulmodel doma ha are effecve uder a hgh level ad dvere form of uceray, e mare mperfeco, abece of complee or prece daa, ad preece of huma volveme prce formao I [5] a evaluao echque uggeed ha ca be appled here he followg apec Ug he adard arhmec of fuzzy umber, ad modellg ucera amou he cahflow a well a he emaed rae wh olear rapezum memberhp fuco, wo dffere formulae are appled whe a amou pove or egave For example, f he volve buyg hare he begg ad ellg hem he ed, he fr formula wll be oly releva If he precrbe varou opmal po me for buyg ad ellg dffere hare, he he wo formulae wll be volved Oher fuzzy model exed eve furher he flexbly of he evaluao echque I [], he opo of aocag a dffere rae o each amou offered he ma corbuo [3] co fuzzfyg he durao over he releva me perod Uually fuzzfed durao preeed a a dcree fuzzy e wh a memberhp fuco defed by a colleco of pove eger each correpodg o he ed of a me perod accordg o he acceped me dvo, eg moh, wee, day Aleravely [3], he durao a real fuzzy umber allowg for he o fh a ay mome, o oly a he ed of a me perod, e he mddle of he moh or hroughou he wee Fally, amog h group of fuzzy crera maly baed o he ocprce evaluao, he echque from [36] fd place here, a hybrd ewor developed ad a fuzzy memberhp array embedded o a eural ewor Alhough he approach appled o predcg a oc dex, effecvely ca be ued gle-ae or porfolo prce evaluao he ou-of-ample foreca of he hybrd e up o 4 moh ahead whou updag he model are compared wh hee of everal crp regreo ad he euro-fuzzy model foud o perform ubaally beer he ex group of model wll pree he deco-maer wh ll relable bu furher progrevely formave oluo, comparg wh he above echque Queo codered clude fuzzy rag, veme r evaluao, meaurg robue oward mare uceray, ad age-depede clafcao of aracve Ug a procedure uggeed [5], he ca be raed accordg o he evaluaed memberhp fuco for he fuzzy crero Furher [3,43], a r meaure propoed ad a alerave r-baed rag echque decrbed he oluo procedure here volve a mulple erval aaly, whch eable veor o coder a ad ae deco baed o varyg level of uceray Icreag he rage of uceray modelled o he fuzzy daa, oe ca deerme he robue of he veme r aocaed wh each

13 , a [4,4] hu he rag echque refed ad baed o boh he r ad robue evaluao Aalogou r meaure ued [4] ad Seco here, whe buldg he of clafer Several uch fuzzy ewor ca be cluded o he mulmodel ellge yem, each ewor raed over wh dffere durao All he clafer wll be raed pror o eerg he yem, ad ready o provde agedepede recommedao he clafyg model ca go oe ep furher by corporag o he eural ewor rucure he robue meaure a well hu here wll be agedepede hrehold for boh veme r ad robue, followg he uo ha wh a mall ad a hghly robu veme r are preferable Coequely, he fuzzy crero evolve o a coderably formave mehod able : Seleced model for he mulperpecve ellge yem model characerc maor Good for prelmary evaluao Hadle me-varyg rae Slghly creaed flexbly ad accuracy, comparo wh prelmary adard veme crera log-leared prce evaluao [] opmal rule for rreverble veme [4] fuzzy pree value [5] geeraled fuzzy crero [] geeraled fuzzy crero [3] euro-fuzzy prce evaluao [36] fuzzy rag [5] veme r evaluao [3,43] robue evaluao [4,4] clafyg lowr [4,maucrp] clafyg hghlyrobu [fuure rreearch] porfolo eleco [46] Help defy he opmal me of buyg he ae, coderg veme rreverbly ad a beef hrehold Icreaed flexbly hadlg mare daa A crp crero Icreaed relably mare evaluao A fuzzy crero Allow a dffere rae o be aocaed wh each amou he cahflow Provde alerave fuzzfcao of he durao Explo facal mare effcece ad exrac olear paer ha eve ophcaed ecoomerc model ca o cope wh Combe fuzzy logc wh a eural ewor Sugge a echque for rag fuzzy umber ad coder he memberhp fuco of fuzzy pree value Apple α -cu arhmec fuzzy prce evaluao, ead of adard fuzzy arhmec Derve a veme r meaure ad ra he accordgly Ue wo calbrao procedure whe fuzzfyg he mare daa, hu modellg a creaed rage of uceray Idefe whch are more robu baed o he chage he veme r meaure uder varyg daa calbrao Sugge a alerave rag ug boh he r ad robue meaure Develop a geec algorhm ad a bdrecoal evoluoary raegy o ra a fuzzy eural ewor o clafy oc accordg o he veme r meaure ad a age-depede hrehold Wll corporae he meaure of he robue o he ofclafyg model, followg he heurc ha low-r ad hghlyrobu are preferable Iveme exper owledge refleced o he oc reur pobly or fuzzy probably drbuo Seleco baed o mmg correpodg parameer he porfolo drbuo dyamc porfolo Maage a opmal oc porfolo a fuzzy dyamc evrome maageme [35] by olvg a fuzzy lear racg problem radg model [3] Iegrae eural e ad fuzzy Delph mehod A effecve radg approach whou ad uder raaco co radg model [] A geec-fuzzy model for dcoverg radg owledge arfcal oc mare [] arfcal oc mare [47] A age-baed arfcal oc mare evolvg ucceful rader Sugge ha he age have he ably o compre umerou crp radg rule ad codo o a few fuzzy oo ad aalye hem ug fuzzy logc evaluao, crp crera relable evaluao, fuzzy or of echque formave rag ad clafcao, fuzzy ad of echque porfolo eleco ad oc radg, of or hybrd echque 3

14 he fal e of model ugge porfolo-eleco ad oc-radg raege I [46], wo porfolo eleco model are propoed where veme exper owledge refleced o he fuzzy probably or pobly drbuo of oc reur Drbuo are obaed depedg o oc pobly grade offered by exper he am o mme he varace of he fuzzy probably drbuo or o mme he pread of he pobly drbuo of he reur o he porfolo Furher [35], a dyamc porfolo eleco ouled A fuzzy corol model ued o maage a porfolo a fuzzy dyamc evrome he preece of facal cora Oe rle ad ry ae are employed, modellg he facor mpreco wh fuzzy e A fuzzy lear racg problem olved ug he Kalma fler Nex, he effor [3] o develop a oc-radg yem, egrag eural e ad fuzzy Delph mehod he reul how ha whou ad uder raaco co he egraed model ouperform he gle eural ewor Alhough he geec-fuzzy model [] appled o currecy radg, o furher adume eceary o ue oc radg, a he echque ha all he feaure o cope wh he problem effcely he approach provde a auomaed mehod for dcoverg radg owledge Fally, a archecure for a arfcal oc mare uggeed [] ha age-baed ad clude evolvg ucceful rader I [47] aoher arfcal oc mare model roduced I proved here ha mlar reul ca be obaed, eher coderg rader capable of hadlg a large umber of rule wh umerou codo, or allowg he reaog proce o be everely lmed I he aer cae he reul are eve mproved h cae alo cloer o realy, ad age have he ably o compre formao o a few fuzzy oo ha hey ca proce ad aalye wh fuzzy logc All eleced model are cluded able he yem ll ope for more model, bu each choce hould be ufed 3 Buldg he mulperpecve model pace A mulmodel veme doma wll help he deco-maer wh he proce of mulperpecve aaly ad mullevel reaog Beg expoed o a varey of poble erpreao, wll efforlely erche h vocabulary of relaohp ad elarge h earch pace for hypohe coruco He wll be able o loo a he veme problem from varou agle hu mprovg h ably o uderad ad olve pecfc quere Buldg he mulmodel pace ar wh choog he modellg dmeo [6,7,8,9] h he e of propere ha repree fudameal characerc aocaed wh he coex or framg of he veme problem Each dmeo - e cope, reoluo, rgdy - deoe a dffere coex, whch drec he mulperpecve reaog For example, cope cocered wh he exe of he problem beg modelled We may mply wa o evaluae a Broadeg he cope, a opmal porfolo ca be defed Fally, he fucog of a arfcal oc mare may be uder queo Furher, reoluo dcae how much deal cluded a model A a llurao, he facor aaly whe maagg a dyamc porfolo may be baed o a few maor deerma oly Icreag he reoluo, ome mor facor wll be cluded, or he maor deerma ca be decompoed o everal maller oe ad her effec uded eparaely Whe rgdy codered, we focu o he ably of he model o hadle ucera daa ad real-mare uao I h ee, he crp model are mo rgd, ad progreg alog he fuzzy ad of echque, he hybrd approache are mo flexble he mulmodel pace ca be vualed a a geomercal hape wh everal axe or dmeo I eaer o h of a cubcal form ad Fgure 5 pree he hree dmeo decrbed above: cope, reoluo ad rgdy I pracce, here are more perpecve ad each compoe cube explode o aoher cubcal rucure h me axe are dffere, eg geeraly, preco ad accuracy, ad provde uppor for coderg addoal apec of coex By choog a value for every dmeo, oe ca avgae o a pecfc model he mulple rucure Neghbourg model dffer oly lghly, e wo of clafer recommedg over dffere veme horzo Daly relaed echque, o he oher had, are que ule 4

15 RESOLUION PRECISION ACCURACY GENERALIY RIGIDIY SCOPE Fgure 5: Mulple model rucure Each compoe cube compre maller cube h approach o owledge repreeao produce a doma rucure wh a valuable here qualy he mulmodel pace provde ehaced flexbly problem olvg For example, a lower-reoluo echque wll be uffce oe uao, whle a larger-cope model wll be requred aoher, ad a le rgd mehod ye aoher cae hu poo o each of he modellg dmeo wll be aocaed wh he demad of a parcular veme problem Moreover, chagg model beefcal pracce eeg alerave durg he oluo proce For ace, movg from a arfcal oc mare wh umerou crp radg rule ad codo o a mare model wh oly a few effce fuzzy rule, ca provde a mproved oluo o he al problem, ad help he mare age beer reao abou he reul Furher, he mulmodel approach alo caer for he dyamc owledge mmae he eraco bewee dffere model o llurae, he decomaer may o u loo for he awer o a gle queo, bu raher wor ou he reul of a e of problem, or e a veme raegy volvg everal model Navgag hrough he model pace, h challege comforably me 4 Emprcal reul ad cocluo 4 Emprcal reul he emprcal daa volve hree UK compae - Goodw, Dxo Group ad Mar&Specer - over he perod from Jue 998 o December 999 hey are choe from a daabae of 35 frm o repree hree maor ype of compay behavour I Fgure 6, he fuzzy log-dvded me-raecory relaed o each frm llurae modelled mare uceray Furhermore, a x-moh veme horzo eleced, producg hree per compay ad e oal h e of dvded o hree ube, ued correpodgly for rag, eg ad predcg wh he fuzzy eural ewor able roduce he dvo of he daa e ad he acceped oao able 3 pree he r level for each evaluaed wh he fuzzy crera 5

16 Memberhp Fuco Log Dvded per Share Dec 99 Oc 99 Aug 99 Jue 99 Aprl 99 Feb 99 Dec 98 Oc 98 Aug 98 Fgure 6a: Goodw Fuzzy log-dvded: July 98 Dec 99 Memberhp Fuco Dec 99 Oc 99 Aug 99 Jue 99 Aprl 99 Feb 99 Dec 98 Oc 98 Aug 98 Fgure 6b: Dxo Group Fuzzy log-dvded: July 98 Dec 99 6 Log Dvded per Share 4 Memberhp Fuco Fgure 6c: Mar&Specer Fuzzy log-dvded: July 98 Dec 99 6 Log Dvded per Share Dec 99 Oc 99 Aug 99 Jue 99 Aprl 99 Feb 99 Dec 98 Oc 98 Aug 98 Memberhp Fuco p le α crcal Fuzzy Log Share Prce Fgure 7: Iveme r α 858 Proec 9: Dxo Group, July Dec 99 able : Daa dvo perod / compay Goodw Dxo Group Mar&Specer July-December, 998 Proec : rag Proec 3: rag Proec 5: rag Jauary-Jue, 999 Proec : rag Proec 4: rag Proec 6: rag July-December, 999 Proec 7: eg Proec 9: predcg Proec 8: eg perod / compay able 3: Iveme r evaluao Goodw Dxo Group : r α : r α Mar&Specer : r α July-December, 998 Proec : Proec 3: Proec 5: Jauary-Jue, 999 Proec : 683 Proec 4: Proec 6: July-December, 999 Proec 7: Proec 9: 858 Proec 8: I he ecod colum of able 3, Goodw demorae a cououly mprovg r meaure, reachg α for 7 I he hrd colum, Dxo Group dcae ocllag level α, whou a parcular dreco over he relaed Fally, Mar&Specer exhb he hghe r level α all over hu, provded ha hree maor ype of compae are repreeed I alo guaraeed ha he rag e clude gle coverg he hree mpora r mode: α ( 4), he ope erval < α <, ad α (,3,5 ad 6) 6

17 Fgure 7 llurae how he r meaure for a derved baed o he emaed fuzzyvalued log hare prce P ~ ad he mare prce p Nex, he geec algorhm ad he bdrecoal cremeal evoluoary raegy from ubeco 3 are appled o ra he regular fuzzy ewor module o approxmae he fuzzyvalued log hare prce over he rag e, o 6 Each compre xmoh daa o log hare prce, reur ad dvded yeld Coequely, he umber of ode he pu layer of he ewor he expermeg wh everal ewor rucure ad coderg he rade-off bewee a mpler cofgurao ad evoluo covergece, he value m 5 ad q 3 are eleced, for he umber of ode he fr ad ecod hdde layer correpodgly Dealed reul for each ep of he evoluoary raegy from Appedx A3 are provded Appedx A4 Here, oly he maor cocluo are dcued he raegy volve a decompoo ad a cremeal par Durg he decompoo par, he problem accordgly dvded o uba of decreag complexy by parog he rag e of a everal level Fgure 8 pree he defed parog he he uba are merged cremeally revere dreco full-ze rag e {,, 3, 4, 5, 6} hrd cremeal level evoluo oward creag complexy a fr-level parog! " # $ %! " # & %! " # ' %! " # ) ( ecod cremeal level ecod-level parog! " # $ %! " # & %! " # ' ( fr cremeal level evoluo oward decreag complexy a hrd-level parog * +, - / 3 Fgure 8: rag-e parog ad creme durg bdrecoal cremeal evoluo Decompoo par: he rag e paroed a everal level, evolvg he fuzzy ewor oward a wh decreag complexy Icremeal par: he rag ube are merged cremeally revere dreco, evolvg he ewor oward olvg he egral problem A dyamc obecve fuco appled a each decompoo ad cremeal level he umber of level ad he parog a each level uque o every mulao of he bdrecoal raegy Coequely, o poble o average he performace of he raegy over everal mulao, a he fe fuco raecory over he geerao wll go hrough dffere rag ube addreed a dffere me O he oher had, drec evoluo ealy averaged For more repreeave comparo, Fgure 9 pree a mulao of bdrercoal cremeal evoluo aga he averaged reul from fve drecevoluo mulao Maxmum fe per geerao preeed for each raegy he bdrecoal raegy evolve a fully fucoal fuzzy ewor 48,43 geerao Drec evoluo reache oly 4633% maxmum fe 5, geerao hu, he emprcal reul prove decvely he effcecy of he developed evoluoary raegy 7

18 RFNN Fucoaly,,3,4,5, decompoo par ,3, 4, ,3, cremeal par 3 4 6,,3, 4,5, Geerao bdrecoal cremeal evoluo drec evoluo Fgure 5: Performace of bdrecoal cremeal evoluo ad drec evoluo maxmum fe per geerao Blac le: bdrecoal cremeal evoluo advace hrough everal decompoo ad cremeal a ad olve he geeral problem 48,43 geerao Lgher le: drec evoluo mae ome al progre ad he all Oce he regular fuzzy ewor module opmed over he rag e, appled o he e e, 7 ad 8 (ee able ) hu, he ou-of-ample performace of he module examed approxmag he fuzzy-valued log hare prce he error ξ from defo (7) appled o meaure he dvergece of P ~ RFNN from P ~, ad coequely he performace of he module he e reul, provded able 4, correpod o que afacory approxmag capable Coequely, we ca ue ow he hybrd ewor over he predcg ube, 9, o emae he veme r I able 5, he predced r value approache he rue value from Fgure 7 able 4: e reul for he regular fuzzy ewor module (RFNN) Goodw Mar&Specer perod / compay : RFNN error ξ : RFNN error ξ July-December, 999 Proec 7: 9< Proec 8: 4< able 5: Predcg veme r wh he hybrd fuzzy ewor Dxo Group perod / compay : predced r α FNN Dxo Group : rue r α July-December, 999 Proec 9: 88 Proec 9: 858 Fally, f he age-depede hrehold a 9 r level, ha he wll be acceped O he oher had, f he lm a 8, he h ae wll be reeced over he relaed veme horzo 8

19 4 Cocluo A of clafer ha bee coruced ha recommed accordg o her evaluaed r ad a age-depede hrehold for he accepable r level he model developed hree age Fr, a alerave veme crero formulaed, cludg a fuzzyvalued hare prce emae he approach more relable ha aalogou crp echque, a derved allowg mare flucuao well beyod he probably ype of uceray permed by adard facal mehod he crero alo more formave comparo wh oher fuzzy approache, a furher ugge a veme r meaure he ecod age he of model developme volve defyg a fuzzy ewor rucure capable of approxmag he crero formulaed a age oe Buldg o prevou ude of fuzzy ewor approxmag quale cocerg mple fuzzy fuco or gle-varable fuzzyvalued fuco, we deduce a rucure adequae for he mulvarable crero he fal age focue o rag he ewor A geec rag algorhm developed ha demorae hgh peed ad effcecy he, a effecve bdrecoal evoluoary raegy elaboraed, a drec evoluo fal o rch a oluo o he complex problem of opmg he wegh ad hf erm he fuzzy ewor over a e of veme he raegy volve a decompoo ad a cremeal par he egral problem fr dvded o uba of decreag complexy by parog accordgly he rag e of he he uba are merged cremeally o opme he egral oluo We ex expla how he clafer, oce developed ad raed, ca be ued problem olvg I wll be corporaed o a mulmodel doma owledge rucure ha o be he exper module a ellge yem Buldg he yem clude hree age Fr, releva model are eleced o gve he evrome he ably o geerae awer o a varey of quere wh creag complexy From gle- evaluao, hrough rag ad age-depede r-clafcao of avalable oc, up o radg recommedao ad mare mulao I addo o addreg varou hough relaed veme queo, he model have dffere mahemacal groud From crp, hrough fuzzy ad of compug echque, up o arfcal ellgece ad hybrd mehod hu he ame problem ca be olved ug more or le rgd mahemacal approache Furhermore, each model he umber of parameer may be reduced or creaed accordg o he aure of he qury he ecod age buldg he mulple exper rucure of he yem cocer he defcao of maor coexual perpecve We have recoged he dmeo of cope, reoluo, rgdy, geeraly, preco, ad accuracy All model are arraged alog hee axe, creag a cubcal rucure where each hree-dmeoal compoe explode o a ecodary cubcal rucure, hu accommodag all x dmeo So coruced, he mulmodel doma faclae a mulperpecve aaly of a gle problem I furher provde a powerful evrome, comparo wh moo-model baed ellge yem, for olvg a varey of problem raher ha oe parcular query Fally, veme raege ca be eed ha volve a ordered e of quere ad requre a deco a each ep Navgag hrough he model pace, he opmal oluo raecory wll be draw he hrd age developg he evrome he ofware deg of a ellge-age archecure for he yem, where he mulmodel exper module corporaed h ep o addreed here, bu he wor o progre I [5], dea o obec-oreed paer for model-baed reaog are preeed ha are parcularly uable for degg he mulmodel doma, ad [4] a ellge-age archecure decrbed for a yem baed o uch exper module Oe furher qualy of he mulmodel baed yem he flexbly ca provde dagog uer behavour order o provde a beer deco uppor, ad h a opc for fuure reearch Acowledgeme h wor wa parly uppored by he Nuffeld Foudao ad by he Egeerg ad Phycal Scece Reearch Coucl Gra GR/R5346/ 9

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