lSSN:1327-2314
IntemationalJournalofKnowledge-BasedIntelligentEngineeringSystems
Volume7NmnberLJanuarv2003
CONTENTS
SubmittedPapers
AComparisonofStaticandAdaptiveReplacementStrategiesfbrDistributedSteady-StateEvolutionaryPathPla】minginNon-StationaryEnviromentsG・Dozier
EmergencemCombinedSystemStructureofRoughSetTheoryandNeuralnetworks
Y・Hassan,A・NiimiandETa完aki
AlgebraicMethodsinFoImdationofSoftComputing:SomeApplicationsA、Lettieri
TheBiopolarManFrameworkfOrHUman-CentredIntelligentSystemsF・Amigoni,V・SchiaffbnatiandMSomalvico
RobustLongitudinalAircraft-ControlbasedonanAdaptiVeFUzzy-LogicAlgorithmA-L・E1shafei
DEVEX-AnExlpertSystemfbrCurrencyExchangeAdvisingLj、NedovicandVDevedzic
COnflict-FreePlaImingForAirTra髄cSupportedbyanAgent-BasedlntegratedOperationalDecisionSupportfbrPiIotsandControllersB.N,Iordanova
1
凹
17
喉1
30
38
46
EmergenceiinCombinedSystemStmct、。eof]Ro皿ghSetTheoryandNeIIralNetworks
YasserHassan,AyahikoNiimi,andEiichiroTazaki
Depar”e”qfco”mZα"dSys花加助g加ee7加9,Tb加U>zjve耐zyq/mtohama,
16坪K1z"鋤Qgrme-cAo,Ao6a-肋,I’b肋力α772α225-8502,〃pα".
Abstract
AIノiasmadeg花ats"雄s加CO””α"o"αIpm6Jemsoん加8”"ggxp"cizIy”rese"“jbzowIedgeex”αed加加オノiezzzsk〃w巴CO”""ero“seexp"c"Iyrep花se"redk"owIedgeexc“ivelWbrco”邸”io"αlpmbzemSOん蝿,we'my〃eVerCO”砿α"O"α〃αCCO”"SノiaIeVeZqfPm6IemSOん加gPeZb777ZarzCee9“αZZO",7Zα"S,jr7ze刀ee‘./br”だ城c"veme的o公”geノzerzzzeaノ2‘Ima飯"加o肋ergjo6az"o”'zczio"αJpmpe河ies皿gges応α,zqpproachα"αIo8o"szo伽seqf"α畝mIpmcessgsm6ioIogicazsysre”socjazbehavjo月α"deco"o”cJy師e郷加ge"emt加geme増e"cepmpe汀ies.E雁噌e"Ce‘Sys花加α"o晒咋CO"S”航芯qfrノzeZzzskm6e”だSe"極、Oだれα"7zzノIyα"”e”応o胸perr加e"r郷k叩ec坂ck"owje庵ememe増e加敢eco腿応eqf‘FCM"grhepmbjem.z7zep”er此scr必essomebasjcsqfeme増e"cesys彪加α”jな”Ieme"”lio〃j〃zノzecoノ7z6j"α"o〃Jysre"zqfRo邸gASaZ7ieo可αノzdA廊施cjaノノV”mIノVawo応.WEwi助rese"z沈ede碗o"s”伽"sα”gⅨ雄I加eso"howzoeJリplo〃eme増e"Ce”e"jge"ceroex陀極rhepro6Ie7泥SOM"gcqpa6i”esqfrhなcomb”〃o".
1.Introduction
KnoWledgediscoveryindatabase(KDD)hasbeendefinedas‘‘Thenontrivialexhfactionof
implicit,previouslyunlmown,andpotentiallyusefUlinfblmationfiromdala”[10,14].Inrecentyearsnumeroussuccessfnlapplicationsofroughsetmethodsfbrknowledgediscoveryindatabasehavebeendeveloped[2,4,6,10,11,13,14,15].]hlanotherdirectiontherehasbeenarapiddevelopmentinourunderstandingofthedetailedmechanismsunderlyingtheemergenceofintelligentbehaviorI1,3,4,7,12]、
Thepaperisprimarilyconcemedwithidentifyingandanalyzingofsomewell-definedtypesofemergencethatoccurinthecombinationofroughsettheorywithartificialneuralnetworks[lOllnthismethod,thebehavioroftheoverallsystem
emergesfiromtheinteractionsofthequasi-independentcomputationalagentsorneurons、Eachagentcontainstheentirespecificationfbritsbehavior,whichincludesinteractionsbetweenitand
itscomputationalenvなonmentandotheragents・Thusunlikem世tionalsystemsmodeling[7],血ereisnooverallconhfollingentityorpro厚amsthatordersorotherwiseconstrainstheinteraction
betweenagents,
Themainissuetacldedinlhispaperisauto‐adaptationoccurredinthismethodthatgeneratesthebehaviors丘omthestudyoflocalinteractionsbetweenagentsandtheenvironment、Somekeyissuesassociatedwiththeunderstandingand
representationofsuchemergingbehaviorsinmulti‐agentsystemsareimoduced・
Thepaperisstructuredasfbllows、Weproposetobeginmsection2wilhabIiefintroductionto
EmergenceSystem・Thenwerecallbasicroughset
pleliminaliesinSection3,Infburthsectionwepresent由econceptofincorporatingroughsetmethodsintoconslructionoftheneuralnetworksbyusingsocalledroughneuron、ThedemonstrationsandguidelinesofemergencepropertiesinthecombinationsystemaredescIibedinSection5.Section6showhowtoexploitemergencepropertiestoextendtheproblemsolvingcapabilitiesinthecombinationofroughsettheoryandartifIcialneuralnetworks・SomeapplicationsarepresentedinSection7、ThepaperconcludesmSection8wilhdirectionsfbrfUrtherresearChontheconsidered
topics.
2.EmergenceSystemWemaybeabletosayexactlywhat
‘emerges,inaparticularcasethanwegeneranycaninthecaseofreal-worldsystems・Emergenceisgenerallyunderstoodtobeaprocessthatleadstotheappearanceofstructurenotdirectlydescribedbythedefiningconstraintsandinstantaneousfbrcesthatcontrolasystem、Wecandefineemergencesystem[3,7,12]as:‘systembehaviorthatcomesoutoftheinteractionofmanyparticipants,orclocalinteractionscreatingglobalproperties,、Someofthemost・engagingandperplexingnaturalphenomenaarethoseinwhichhighlystmcturedcollectivebehavioremergesovertimefromtheinteractionofsimplesubSystems,USingemergenceintelligenceallowstheremovalofexplicitlmowledgethatisanaturalconsequenceoftheproblemsolvingprocessinteractingwiththetaskenvironment、Byallowingthetaskenvironmenttobeanintegralcomponentoftheproblem-solvingalgorithm[1],aⅡthenatulalconsbzints,including
3.RoughSetTheox・yTheunderlyingideasofroughsettheory,
proposedbyZdzislawPawlakinlheeallyl980,s[8],havebeendevelopedmtoamanifbldtheoxyfbrthepurposeofdataandlmowledgeanalysis,duetoasystematicgrowthofinterestinthistheoryinscientificcommunity,Theprimarygoalofroughsettheoryhasbeenoutlinedasaclass坂catoryanalysisofdata[91.Themainparadi8mofroughsettheorystatesthattheuniverseofknownobjectsisassumedtobeonlysourceofknoWledgeaboutadomainspecifiedbyourneeds.Databasedreasoningisthenconcemedwiththeanalysisofdependenciesbetweenfbatureslabelinglmowncaseswithvalues丘omsomepre‐defineddomain、LetusrepresentanysampleofknowndataasaninfbrmationsystemlS=(UA),whosecolumnsarelabeledbyattributes,rowsarelabeledbyobjectsofinterestandenbriesofthetable
areatbributesvalues,whereUisnon-emptyfmitesetofohjectscalleduniverse,andAisnon-emptyfinitesetofambutes・
DecisiontableDT=(U,Au{d})isaspecialfbrmofinfbrmationsystem,whereAiscalledcondition
ati工ibutes,anddEAiscalleddecisionattribute・If
VabethevaluesetfbratlributeaEAcalledthe
domainofa,thenattributeaEAisamap;a:U→Va,VaEA・
TablIelhasanexampleofdecisiontablewherethesetofattributesA={Sex,CIinicalStage},valuesofdecisionatmbuteisVin企clion={Yes,NC},皿dU={P1,P2,…,P10}・
LetXCUbeasetofobjectsandBCAbeasetofatlributes,theindiscemiblyrelationcanbedefinedas:
Iの)={(X,y)EUxU:a(x)=a(y),、▽'aEB}.
Objectsx,ysatisfyingtherelationlCB)areindiscemiblebyatlributesfromB,I(B)isreflexive,symmetric,andtransitive.
Tablel:anexample
AnorderpairAS=(U,I(B))iscalledanapproximationspace・Accordingtol(B),wecan
definetwocrispsets星XandBXcalledlowerand
upperapproximationofthesetofobjectsXintheapproximationspaceASas:
星X={xEU:IB(x)二X},and
BX={xEU:IB(x)nX≠ウ}、
BXconsistsofallobjectsofUthatcanbewith
certaintyclassifYedaselementsofsetXgiventheknowledgerepresentedbyattributesfromB,and
BXconsistsofallobjectsthatcanbepossiblyclassifiedaselementsofsetXemployingthelpnowledgerepresentedbyatlributesfiromBThe
differenceBNB(X)=(BX‐且X)iscalledboundaryofX,whichcontainsallobjectsthatcannotbeclassifiedeithertoXorcomplementofXgivenlmowledgeB、Pawlak[8]definedaroUghsettobeafamilyofsubsetsofauniversethathasthesamelowerandupperapproximations、IromTablel,theupperandlowerapproximationofthedecisionathFibute‘‘infbction,,canbefbrmattedas
fbllows:
聖infeaib腕=ye‘={P1,P7}
Xinfeai。"=y“={P1,P2,P4,P5,P6,P7,P10}
茎infecii。"="。={P3,P8,P9}
Xinfec‘i・"="。={P2,P3,P4,P5,P6,P8,1,9,P10}
Decisionrulescanbeperceivedasdatapattems,
whichrepresentrelationshipbetweenattributesvaluesofaclassi負cationsystem、IfDT=(U,Au
{。})isadecisiontableandV=U{va:aEA}Uvd,isasetofvaluesfbrattributes,thenthedecisionruleis
alogicalfbrm:raTHBNβ,orcanbewritten[11]as(α,β),whereαisaconditionpartofthcrule,itisaconjunctionofselectors:fbrnominalatmbutestakethefbrm:(a,=v,A1、.…ANDan=v、)andfbrnumericalatmbutestakethefbrm:v,<a<v2,and
l3isthedecisionpart:(d=vd),itusuallydescribesthepredictedclass,Wecandefinethesetofrulesas:
RuleSet={(αi,βi):i=1,…,k}.
thosetoosubtlefbrthelmowledgeenglneertoextract,虹eavailabletothealgorithmandemergeatappropriatemomentswhilesolvingproblems・Thestudyingofemergencepropertiesinmathematicallywell-definedsystemsmaybe
p麺ticularlyusefUlinconstructingatopologyofemergence,Emergenceastheexistenceof
propertiesofasystemisnotpossessedbyanyofitsparts[31This,ofcourse,issoUbiquitousaphenomenonthatit'snotdeeplyinteresting・Itprobablywillhelptofbcusona企wcoreexamplesofemergencesystems[7】:(A)ThegameofLifも:High-levelpattemsandstructureemerge丘omsimplelow-levelrules(CellularAutomata).
OB)Connectionistnetworks:BUgh-level1'cognitive11behavioremergeshomsimpleinteractionsbetweendumbthresholdlogicunitsOVeuralNetworks).(C)Evolution:Intelligenceandmanyotherinterestingpropertiesemergeoverthecourseofevolutionbygenetlcrecombinationandmutationoperators(GeneticAlgorithm).
rablel:anexample
-1
U
P1
P2
P3
P4
P5
P6
P7
P8
P9
P10
Sex
F
M
F
M
M
M
F
F
M
M
ClinicalStageT
T
B
T
T
T
T
B
B
T
Infection
Yes
Yes
NC
Yes
Yes
NC
Yes
NC
NC
NC
Thereexistseveralmeasurementsinorderto
evaluatethedecisionmle、Theclassification
accuracyandcoverageofruleraredefinedasfbnows[10,11,13,14]:
』"(『)雲'W)f’Cov(r)=|sup(r)nDl
lDlwherelAlisthecardinalityofasetA,Acc(r)istheclassificationaccm・acyoftheruler,Cov(r)isthecoverageoftheruler,sup6)isthenumberofcasesthatmatchtheconditionpartofruler,andlDlisthenumberofcasesthatmatchthedecisionpartofruler,ItisclearthatAcc(r)andCov(r)belongtotheinterval[0,11.
4.Combination0fRoughSetTheoryandNeuralNetworksThissectionisanattempttosummanzeanapproachaimedatconnectingroughsettheorywithartificialneuralnetworks・Artificialneuralnetworkinits
mostgeneralfbrmisattemptedtoproducesystemsthatworkinasimilarwaytobiologicalnervoussystems,Thenatureofconnectionsinneural
networksanddataexchangethroughtheconnectionsdependupontheapplication.Drivenbytheideaofdecomposingthesetofanobjectsintothreeparts:thelowerapproximation,theboundaryreglonandtheupperapproximationwithreSpecttoagwensetXofobjectsinthedecisiontable,Ligras[10]imoducedtheideaofroughneurontoconsmctnetworkcalledRoughNeuralNetwork・
Eachroughneuronrisapalr,onefbrtheupper
boundcalledupperneuronrandanotherfbrlower
boundcaⅡedlowerneuronr・Thosetwoneurons
canexchangeinfbrmationbetweeneachotherand
betweenotherroughorconventjionalneurons;soroughneuralnetworkconsistsofbothconventionalandroughneurons・
Theou印utsofaroughneuronrdependingonapair
ofneurons:lowerneuronrandupperneuronr,
arecalcUlatedusingfbrmula:
o叩”デーmax(jf.(””7),jF(””『))
o叩”r=min(f(””7),f(””r))wherefstandsfbranytransfもrfimction,fbrexample:sigmoidfimction,whichtakesthefbrm:
1
f(x)=,+e-&whereβisthecoefflcientcalledgain,whichdeterminestheslOpeofthefimction.Theconnectionsbetweenconventionalneuronsin
roughneuralnetworkaremadeasinusualcase,Whileconnectionbetweenroughneuronandconventionaloneismadeasconnectinglower
neuronエandupperneuronrseparately,Two
roughneuronsinthenetworkcanbeconnectedtoeachotherusingeithertwoorfburconnections、A
roughneuronrissaidtobefilllyconnectedtorough
neurons,ifrand7arecomectedtobothSand
S、Ifthereexisttwoconnectionsonlyfromneuronr
toneurons,thenthetwoneuronsarepartiallyconnected,Ifaroughneuronrexcitestheactivityofneurons(i、e・increaseintheoutputofrwillresulttheincreaseintheoutputofs),thenweconnect
onlySwithrandSwithr・Intheopposite
situation,ifrinhibitstheactivityofs(i,e,increaseintheoutputofrcolrespondstothedecreaseinthe
outputofs)weconnectonly2withrandSwith
r・
Iftworoughneuronsarepartiallyconnected,thentheexcitatoryorinhibitorynatureoftheconnectionisdeteImineddynamicallybypollingtheconnectionweights・Ifapartialconnectionfromaroughneuronrtoanotherroughneuronsisassumedtobeexcitatoryandweightsofboththeconnections虹enegative,thentheconnectionfromrtosischangedftomexcitatorytoinhibitory,Ontheotherhand,ifr
isassumedtohaveasinhibitorypartialconnectiontosandweightsofboththeconnectionsare
positive,thentheconnectionftomrtosischangedhfominhibitorytoexcitatory、Nowwewillcaneachneuronandlink、inthe
networkas‘‘agenf,、Fromaconectionofagentsobeyingexplicitinsmctions(weighfmodificationandsignalpropagationalgorithms),leamingandpattem-recognitionemerge,Theagentreceivingthisinfbrmationcandescribeobjectsusingitsownatmbutes・Inthiswayadecisiiontableiscreatedand
thereceivingagentcanexなactapproximatedescriptionofconcept・Iftheagentj(conventionalorroughneuron)connectstoagenti(conventionalorroughneuron),thenthecollectedweightedinputofagentiiscalculatedas:
”"r,=Zの,×o"”j
whereのりistheconnectionweightbetweenagentsiandj,
LetthenetworkhereisrepresentedbyasetofagentsAg={a9,,…,agp}・AnyagentfomAgisequippedwithaninfbrmationsystemlSag=(Ulg,AaJwhereUhgisasetofobjectsandAagisasetofatmbutesassociatedwithagentagThedecision
tableisapairDTag=(Uも9,AagU{dag})fbranyagentagEAgwheredagisthelocaldecisionattIibute・Thelowerandupperapproximationsof
anyconceptXdefiningbyagentageAgwithrespecttoconditionatnibutesofDTagdescribethevaguenessinunderstandingofXbyagents・丘omAg・Everyagentisautonomousinthesenseitisnot
αDα、
二■rr■ⅡⅡけ■■■■■
underthecontrolofasupervisor:aIlitsdecisionsarederivedfi「omembodiedrulesdependingonlyuponlocalinfbrmationaccessibletotheagentTheagentsdiffierintheirle2mledbehavior,andtheh・consequentialexperlenceandperfbrmance・Theleamingprocessfbrthenetworkisbasedonanygeneralleamingscheme,sotheweightsinthe
Nowletweglvesmallexampletoshowhowtouse
roughneuron,Table2hasexamplemedicaldata,wheretheattributevaluestakethefbrmofroughpattem(mdnimumandmaximumvalues).Thedataconsistsof6objectseachofwhichhasvaluesfbr3
atmbutes{totalPSA,PSAdensity,PSATZdensity}andonedecision{Patho}withvalueset
{0,1).“0”me2msnoti並ectedand“1”me鉦in企cted.
networkareadjustedaccordingtothegeneral
equation:
の"=の拶十α(r).g(”"i)wheregisanytransferfimction,α(t)isaleamingfactor,whiChstartswithahighvalueatthebeginningofthe廿ainingprocessandisgraduallyreducedasafimctionoftime.E,9.theweightsadjustedaccordingtoasimplebachpropagation‐leamingschemetakethefbrm:
の『"=の;!‘+αe叫f1(”蝿)wheref'isthederivativeofsigmoidfUnction,a
istheleamingcoefficientande恥isane[rorfbr
agenti、Duetothepropertiesofsigmoidfimction,
calculationoff1(X)=f(X).(1-/(X))iseasy・LetN(ag)beafimction,whichdeterminesthesetof
immediateneighborsagentsoftheagentagEAg、ThefimctionNcanbedefinedas:
N(ag)={a9,:ag1eAgandag1isimmediateneighborofag}・AnyagentagftomthenetworkcanusefimctionNtodetenninewhichagentwillinteractwithit・
ThecommunicationbetweenagentsisprovidedbymappingE(a9,N(ag))suchthat:
ForxEUhg,thevalueE(a9,N(ag))(x)EUN(ag).AccordingtofimctionEeachagentcansendorreceiveinfbrmationthroughimmediateneighboragents、Perturbationandundirectedcommunications
canbebeneficialtothesuccessandperfbrmanceofemergencesystem・TheinfbrmationcanonlybelransmittedthroughsequencesofimmediateneighborCommunications・Theundirected
communicationsandabsenceofcomPleteinfbrmationpermitsroughneuralnetworkthatsometimesbutnotalwayssucceedinsatisfyingitsgoals・
Figurelshowsanexampleofroughneuralnetwork,whichconsistsoftheinputlayer,whichthepattemispresented,dishibutesthepattemthroughoutthenet,andpropagatesthepattemdowntheirconnectionstothemiddlelayers(oneormore
hiddenlayers).Thepattemismodifiedbyweightsassociatedwitheachconnection・Theagentsinthehiddenlayerpasso、thepatteminanappropriatemanner,againmodifiedbyweightconnections,toevokethedesiredresponseintheoutputlayer、TheOperationsarenaturalinasenselhattheycoIrespondtodifferentviewsonglobalapproximationspacerepresentedbythenetworkThesenewapproximationspacescanbeusedfbrbetterdescriptionofconcepts.
○OutputLayer
r
αDaDaDaD
Hi‘...(…
Figurel:AnexampleofRoughNeuralNetwork
L
InputLayer
TheconstructednetworkisshowninFigure2・Weusehere3roughnemonsasinputlayerco豆espondingto3conditionatなibutes,Onelnddenlayerhas21oughneuronandoneconventionalneuroninoutputlayerfbrdecisionatlribute‘‘Patho,,、TheconnectionsbetweenroughneuroninthisnetworkaretakenasfUllconnection.
5.GuidelinesfbrEmergence
SysteminCombinationofRoughSetsandNeuralNetworks
WeprovidesomeguidelinesfbrdirectedintroductionofemergencepropertiesintothecombinationofroughsettheoryandartiHcialneuralnetworks・Inthissystemtheinteractionofthe
dynamicrepresentationandnon-positionalinterpretationprovidessomeinnateemergencepropertiesthatassistintheacquisitionofsolutions[1,7]、Thosepropeltiesemelgenotbecausetheyweredesignedintotheneuralnetworkitselfbut
becausethedynamicsofthemethoddeterminethemtobeusefUlornecessaryfbrsuccess、Thiscombinationrepresentsemergencetechnologyontwolevels、First,intheleamingprocessitselftheabilitytorecogmizethepattem-set(embodiedintheconnectionaltopologyandweights)emergesiiFomtheinteractionsofagents(neuronsandlinks).Second,oncethenetis廿ained,theappropriatepattemattheoutputlayeremergesftomtheinteractio、sbetweenagentsinthestaticnetwo1k[7]・FourcharacteristicsofthesystemareobservedtodefinetheemergenceprOperties:
|-
i・Noagentcon廿olsgloballythedynamicofallthe
TbIaI
PSA‘●=q
TbtaI
PSA
Patho
PSA
denS町”=●、
PSA
densityJ■、
PSATZ
dcnsiW(min)
PSATz
densiW(min)
Figure2:Theroughnemalnetworkmodelconstructedonexampledataintable2.
11.
111‘
1V.
system・Theagents虹elimitedandtheyare
unawareofsomepartsoftheglobalsystem・Soeachagenthasalocalenvlronment・Eachparticipantcanneitherreadnorwritedirectlytoagents,inotherword,thesystemcanmakeuseofneitherglobalvisibilitynorcemalconなo1.Theagentsactandmodifylocallythisenvironment・Eachagenthasonlyap鉦tialviewofothersandtheenvironment,inwhichitIs
ilmnersed,andintheabsenceofglobalcontrol,everyagentmustbeabletocommunicatewithitsimmediateneighborswithoutdependiIngon
thelmoWledgeoftheoverallnetworktopology・Interactionisabasismechanismfbragents,and
thesystemconsidersaresultasemergingfi・omexchangesbetweenagents、Eachagentcancommunicatedirectlyonlywithanumberof
immediateneighborsthatislessthanthetot2Jlnumberofagentsinthesystem,whichcalledlocalinteractions・
Emergenceofglobalsolutionsisadaptationofagent0sbehaviortolmoWledgeandenvironment.‘Ihishypothesiscanbeovercomeinconsideringeachcomponentasawholesystem,inwhichthesub-componentsareusingthesameselfLorganizationmelhod・Eachneuronconsistsofapairoflowerneuronandupperneuron・Ifweconsidertheroughneuronaswholesystem,so
lowerandupperneuronsareconsideredassub-componentandeachcanusethesameselfLorg2mizationmethod.§networkhereisa虹ouDofaEents・noneofThenetworkhereisa厚ouporagents,noneot
whichcandealwithadifflcultyalone,butonlydosowheneachcooperates.
6.ExPloitingEmergenceIntenigenceinRoughNeuralNetwork
Wewilldescribeexampleofmodificationtothesystemthathamessinherentdynamicsfbremergenceintelligenceinproblemsolving・Twokindsofdynamicevolutioncouldbeconsidered:modificationofthes(ructurebyre-organizationoftheacquaintancesnetworkormodificationofbehavior・ThegoalhereistodemonstratetheselfLorganizationoftheroughneuralnetwork・Consequently,roughneuralnetworktobeusedinanemergencewayandcan
perfbrmitsroles,aduplicationsystemisrequired、Wewilldefinea・duplicateoperatorlhatanagentcanusetoduplicateitselflnthesamemanner,removableoperatorcanbedefinedwheretheagenthastheabilitytodieanddeleteitselffromthenetworkshncture・
Thisideawasfirstdiscussedin[5]asadaptationofneuralnetworkssbfucturebutindifferentway,wherethisprocesswasundercon杜olofoverallsystemerror・Butinourcombinationsystem,thisprocessislocalfbragentandnoglobalcontrolexist,soeachagenthastheabilitytoproducenewagentandalsoremoveitselfftomthesystemunderlocal
comrolonly.Todefinelocalcontmlfbreachagent,weassignafitnessvaluefbreachagent、Thisfitness
valueisnotonlydependonagentperfbrmance,butalsoonhowthisagent‘‘better,,againstotheragents,Letdefineafitnessfimctioninasimplefbrmassummationoftwoterms:firsttelmisthe
perfbrmanceofanagent,itistheaveragebetweentheinputandtheoutputvaluesofthisagent,andsecondtermfbrmeasurehowthisagentbetteragainstotheragentsinthenetwork、Sothefitnessfimctioncantakethefbrm:
Fag=α,.V+o(2.B,WhereFhgisafitnessfimctionfbragentagEAg,ohanda2areparameters,VistheaverageofinputandoutputvaluesfbragentageAg,andBishowtheagentag‘‘better,,againstotheragentsinAg・DependingonthevalueoffitnessfimctionEg,theneuroncanbespiltintotwousingduplicateoperator,i、e、itproducesanothernemontotheexactIysameinterconnectionofthenetworkasitsparentneuron,satmbutesareinherited・IfaneurondoesnotfOrmthecolrectinterconnectionsbetween
otherneuronsoritisaredundantinthenetwork,
thenitwilldie,Wewilllimitthispropertytohidden
layersonly,andinputlayerandoutputlayerareExed、Wecansaythatroughneuralnetworkisnotdesignedbutevolved.]Fromgenerationtogeneration,thesystemlearnsitssm1cturethroughinteractionswithitsenvlronment・
Byembeddingthismodificationwithinanongoingevolutionaryscenarioandbyallowingprocessesofagent/environmentinteractiontotakeplacewithin
Forcomparingtheresults,weconstructthree
modelsfbrneuralnetworks:firstmodelfbrroughneuralnetworkwithmodificationthatdesclibedin
thispaper,secondmodelfbrstandardroughneuralnelwolkasdefinedin[10Laswenasmodelfbrconventionalneuralnetwork・Forfirstandsecond
models(proposedmodelandstandardroughneuralnetwork),Thenetworkhasthreeinputroughneurons,eachofwhichfbronesection,andone
hiddenlayerwitheightroughneurons・Sincetheoutputisauniquevalue,theoutputlayerusedoneconventionalneuron,Theimportantdifferenceinroughneuralnetworkapproachisthattheytakeasinputstheupperandlowerboundsfbrathfibutes・Soinfactthisnetworkhastwicethenllmherofneurons
空 午
eachagent,slifetime,wecanobtainperfbrmance,ofnewmodelofneuralnetworkisgoingmorewhichisreliablygood.naturalthanstandardroughneuralnetworkand
conventionalneuralnetwork
7.ApplicationThepu[poseoftheexpenmentsdescribed
inthissectionisnottoproposebettermethodsfbrsolvingtheparticularproblem,whileournewmodelofroughneuralnetworkprovidesbetterresults,Butthemodelusedintheexperimentwastoosimplistictomakeanyconcreterecommendations、hlsteadthis
sectionmestoverifytheemergencepropertiesinthiscombination.
Theneuralnetworkshaveshowntobemore
effectivethantheexistingmethodsfbrestimationofmanyapplications,sowechooseadatacontainsinfbrmationabouttherepresentationofstudentsfifomCalifbmiaStateUniveristytakingtheeqUjIvalelntofal5-unitcourseload,andthetaskistopredictthevolumeofstudentsfbryear2000usingdataaboutthisvolumeftomthelastyears、Theinputtotheroughneuralnetworkmodelconsistsofroughpattem,i,e・upperandlowerboundsofyearlyvolumesofstudents・Wedividedthedataintosectionseachsectionfbrthreeyears,andtaketheupperandlowerboImdofvaluesthate麺stineachsectiolLワ[hedatabegin金oml991until2000、Sothesectionsweredeterminedasfbnows:
Sectionl:1991-1993,Section2:1994-1996,Section3:1997-1999.
Figure3:TheaverageerrorthmuEjllOO,000generationsproducedbytheproposednewrough
neuralnetwork.
Figure4:TheavelageerrorthrougillOO,O00generationsproducedbystandardroughneural
network.
ascomparedtotheconventionaIone,
Forconventionalneuralnetwork,theinputs虹etheaveragevaluefbreachsectionofdata・Themodel
consistsofthreeinputneurons,onehiddenlayer
Figure5:nleaverageexrorthrou邸100,000generationsproducedbyconventionalneural
networkmodel.
witheightneurons,andoneneuroninoutputlayer, Table3showsthecomparisonbetweenaverageNowwementionthediscussionofexperimental errorsofeachneuralnetworkmodelthroughallresultwiththreemodels・
generations・Bromthetableweobservethatsecondlnitially,fbreachnetwork,theconnectionsare
model(standardroughneuralnetwork)hasbestassignedsomewhatrandomweights・The廿aining
averageelroranditisveryClosetotheaverageeITorsetofinputispresentedtolhenetworkseveral
ofournewmodelaswellastheyarebetterthantimes、
conventionalneuralnetwork・Table4showsthe画gures3,4,2md5showtheavelagereductionelror maxlmumelror血oughthreemodelsofneuralofglobaloutputduring杜ainingpmcessevelylOOO networkslhroughlOO,O00genemtion,ourproposedgenerationsfbreachmodelofneuralnetworks・ modelandstandardroughneuralnetworkhavetheFromthefigures,weobservethattheaverageerror
’1
』◎差山①、、』①ンく
0.0050
0.0040
0.0030
0.0020
0.0010
0.0000Mliw血LJJ-lO’0I
0200004000060000800001E+05
Generations
LIUU
543210
000000
000000
●●●●●凸
000000
』○瞳山①回、』のシく
000010500000
Generations
』o瞳山の、四①シく
0.06
妬四囲唾例叩
■●。●●●
000000
0.04
0.01
ZL
:燦ルポ05 00 00 10 00 00
Generations
一
samevalueofmaximumelroranditisbetterthan
theerrorvalueofconventionaione・Table5shows
themmmmmelrorvaluesthrougillOO,O00generationsfbreachmodelofneuralnetworks・
Fromthetableweobservethatourproposedmodelprovidesverygoodresult,wherethevalueproducedfromournewmodelisbetterthanvaluesof
standardroughneuralnetworkandconventionalneuralnetwork
Table3:AverageerrorlhrouE血100,000genemtionsfbrproposedmodelofroughneuralnetwork,standardroughneuralnetwork,andconventionalneuralnetwork.
Proposed StandardRoughNeural ConvemionalNeural
Model NetworkModel NetworkModgl
0.00055 0.00044 0.02866.
Table4:MaximumerrorthrougjllOO,O00generationsfbrproposedmodelofroughneuralnetwork,standardroughneuralnetwork,andconventionalneuralnetwork.
sed StandardRoughNeuml ConventionalNeural
NetworkModel NetworkModel
0.00397 0.00397 0.04804
Table5:MmimmnelrorthrougillOO,O00generationsfbrproposedmodelofroughneuralnetwork,standardroughneuralnetwork,andconventionalneuralnetwork
ProPOSedModel
0.000046
StandardRoughNeuralNetworkModel
0.000203
ConventionalNeuml
NetworkModel
0.027472
Toseemoreinourproposedmodel,weobservesomeemergencepropertiesinthismodel・From
generationtogeneration,thegroupofagentsinteractswitheachother,Eachagenthastheabilitytoproduceitselfwiththesameconnectionandalsohastheabilitytodieanddeleteitself丘omthenetworkstructure、Throughtheinteractionsbetweenagents,theweightsofconnections,i、atheattributes
ofagentsaremodifIed・Inthisexperimentfbrnewmodelofroughneuralnetwork,wefindthroughlOO,O00generations,thelargestusingoneofduplicateoperatoristheagentnumberl2,whi9hitusesas31%血oug世loveranagents,andfbrremovableoperatorneuronsmmlberl5andl6useitasthesamelate31%againstallagentsinlhenetwork・
Regardingtheapplicationweintroduced,thecombinationofroughsettheoryandartifIcialneuralnetworkrepresentsemergencecomputationinthestrictsense.
8.Concllusions
lnrecentyears,anapproachtermedemergencecomputationhasgainedpopUlarityinavarietyoffields・TY1ispaperthusprovidesa‘‘bigpicture,,storyaboutthewayinwmchthedevelopmentofcomplexintenigentbehaviorsmightinvolveevolutionaryprocesses,leamingprocesses,agent/envkonmentinteraction,andrepresentationdevelopment・Theleimmingmethodprovidedby
roughsetfbrmsabridgebetweentheneuralnetwork
paradigmsontheonehandandtherepresentationlistparadigmontheother,Webegininthispaperwithimoductiontoemergencesystemandillus杜atewhatarethe
prOpertiesofemergencesystemwithsomeexamplesofexistingemergencesystems、Followedthatぅwe
summarizedtheapproachofcombiningroughsettheorywithartificialneuralnetworks,whichcalledroughneuralnetworka、dgivenewdescriptiontothiscombination丘omroughsetview、Innextpart
ofthispaper,weillustratetheemergencepropertiesthatexistinroughneuralnetwork,andshowhowtoexploitemergencepropertiestoextendtheproblemsolvingcapabilitiesinthecombinationofroughsettheoryandartificialneuralnetworks・Whereweadd
twonewoperators:duplicateandremovableOperators,anddefinenewfimctiontoassignfItnessvaluefbreachagentinthenetwork・Byusingthesenewmodifications,roughneuralnetworkcanperfbrmitsrolesandbeusedinemergenceway、Inlastpartofthepaper,wedescribeindetailssomeexperimentswithreallifbdata丘omCalifbmiaStateUniveristy、Thetaskofexperimentistopredictthevolumeofstudentusingdataaboutthevolumesfiromlastyears・Wecomparebetweenconventionalneuralnetwork,roughneuralnetwork,andnewmodelofroughneuralnetwork・Weneedtocontinuethisdirectionofresearchwherewewill
extendthisideatobeingeneralcasefbrroughsettheorywhenitcombineswithanyothermethod
Reference
[1]Angeline,PeterJ.,GenelicProg反ammingandEmergentlntelligence,inKinne註,Jr.,KE、値di.),AdvancesinGeneticPro厚amming,MitPress,1994.
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[3]Gotts,N、,EmergentphenomenainlargesparserandomalTysofConway,s‘GameofLi企,,IntemationalJoumalofSystemScience,vol、31no,7,pp873-894,2000.[4]Hassan,Y、,andTazaki,E,,EmergenceinCombinedSystemS杜uctureofRoughSetTheoryandGeneticPiro厚amming,SubmittedtoKESIntemationalConference,2001.
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I
|-
[8]Pawlak,Z.,RougilSets,IntemalionalJoumalofComputerandmnfbrmationScience,V01.11,N0.5,1982.
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Table2:anexampleofroughvaluesindecisiontable‘Table2:anexampleofroughvaluesindecisiontable.
Objects TotalPSA
(min)
P1 2.07
P2 4
P3 6
P4 4
P5 2.07
P6 4
TotalPSA
(max)
3.84
24
20
24
3.84
24
density(min)
PSAPSA
density(min)
0.07
0.22
0.4
0.14
0.29
0.22
SetModel,PrinciplesofDataMiningandKnowledgeDiscovery.SecondEuropean
Symposium,PKDD'98,pp468-76,1998[14]Ziamko,W,Ed、RoughSets,R1z可sets,andKnowledgeDiscovery,SpringerVerlag,Berlin,1994.
[15lZiarako,W、,DiscovelyThroughRoughSetTheory,CommmlicationsoftheACMVO1.42.No.11,1999,pp54-57.
PSA PSATZ
density density(max) (min)
0.13 0.29
0.07 0.13
0.07 0.13
0.11 0.21
0.07 0.13
0.11 0.21
PSATZ
density(max)0.53
0.13
0.13
0.89
0.13
0.29
Patho
1
0
I
0
0
1
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