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

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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

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0.13 0.29

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