Soft Methods for Integrated Uncertainty Modelling PDF
Preview Soft Methods for Integrated Uncertainty Modelling
JonathanLawry,EnriqueMiranda,AlbertoBugarin,ShoumeiLi,MariaAngelesGil, Przemysa(cid:20) wGrzegorzewski,OlgierdHyrniewicz(Eds.) SoftMethodsforIntegratedUncertaintyModelling AdvancesinSoftComputing Editor-in-chief Prof.JanuszKacprzyk SystemsResearchInstitute PolishAcademyofSciences ul.Newelska6 01-447Warsaw Poland E-mail:[email protected] Furthervolumesofthisseries BarbaraDunin-Keplicz,AndrzejJankowski, canbefoundonourhomepage: AndrzejSkowron,MarcinSzczuka Monitoring,Security,andRescue springer.com TechniquesinMultiagentSystems,2005 ISBN3-540-23245-1 TetsuzoTanino,TamakiTanaka,Masahiro BerndReusch(Ed.) Inuiguchi ComputationalIntelligence,Theoryand Multi-ObjectiveProgrammingandGoal Applications:InternationalConference8th Programming,2003 FuzzyDaysinDortmund,Germany, ISBN3-540-00653-2 Sept.29–Oct.01,2004Proceedings,2005 Mieczys(cid:20)awK(cid:20)opotek,S(cid:20)awomirT. ISBN3-540-2280-1 Wierzchon¥,KrzysztofTrojanowski(Eds.) FrankHoffmann,MarioKˆppen,Frank IntelligentInformationProcessingandWeb Klawonn,RajkumarRoy(Eds.) Mining,2003 SoftComputing:Methodologiesand ISBN3-540-00843-8 Applications,2005 AjithAbraham,KatrinFranke,Mario ISBN3-540-25726-8 Kˆppen(Eds.) AjithAbraham,BernarddeBaets,Mario IntelligentSystemsDesignandApplications, Kˆppen,BertramNickolay(Eds.) 2003 AppliedSoftComputingTechnologies:The ISBN3-540-40426-0 ChallengeofComplexity,2006 AhmadLotÝ,JonathanM.Garibaldi(Eds.) ISBN3-540-31649-3 ApplicationsandScienceinSoft-Computing, AshutoshTiwari,JoshuaKnowles,Erel 2004 Avineri,KeshavDahal,RajkumarRoy(Eds.) ISBN3-540-40856-8 ApplicationsofSoftComputing,2006 Mieczys(cid:20)awK(cid:20)opotek,S(cid:20)awomirT. ISBN3-540-29123-7 Wierzchon¥,KrzysztofTrojanowski(Eds.) Mieczys(cid:20)awA.K(cid:20)opotek,S(cid:20)awomirT. IntelligentInformationProcessingandWeb Wierzchon¥,KrzysztofTrojanowski(Eds.) Mining,2004 IntelligentInformationProcessingandWeb ISBN3-540-21331-7 Mining,2006 MiguelLÛpez-DÌaz,MarÌaÁ.Gil, ISBN3-540-33520-X Przemysa(cid:20) wGrzegorzewski,Olgierd JonathanLawry,EnriqueMiranda,Alberto Hryniewicz,JonathanLawry Bugarin,ShoumeiLi,MariaAngelesGil, SoftMethodologyandRandomInformation Przemysa(cid:20) wGrzegorzewski,Olgierd Systems,2004 Hyrniewicz(Eds.) ISBN3-540-22264-2 SoftMethodsforIntegratedUncertainty KwangH.Lee Modelling,2006 FirstCourseonFuzzyTheoryand ISBN3-540-34776-3 Applications,2005 ISBN3-540-22988-4 Jonathan Lawry Enrique Miranda Alberto Bugarin Shoumei Li Maria Angeles Gil Przemys(cid:20)aw Grzegorzewski Olgierd Hyrniewicz (Eds.) Soft Methods for Integrated Uncertainty Modelling ABC JonathanLawry ShoumeiLi AIGroup DepartmentofAppliedMathematics DepartmentofEngineering BeijingUniversityofTechnology Mathematics Beijing100022,P.R.China UniversityofBristol Bristol,BS81TR,UK EnriqueMiranda MariaAngelesGil ReyJuanCarlosUniversity UniversiaddeOviedo StatisticsandOperationsResearch Fac.Ciencias C-Tulip·ns/n Dpto.EstadisticaeI.OyD.M. MÛstoles28933,Spain CalleCalvoSotelos/n 33071Oviedo,Spain AlbertoBugarin Przemysa(cid:20) wGrzegorzewski OlgierdHyrniewicz IntelligentSystemsGroup DepartmentofElectronics SystemsResearchInstitute &ComputerScience PolishAcademyofSciences UniversityofSantiagodeCompostela Newelska6 SantiagodeCompostela,Spain 01-447Warsaw,Poland LibraryofCongressControlNumber:2006928309 ISSNprintedition:1615-3871 ISSNelectronicedition:1860-0794 ISBN-10 3-540-34776-3SpringerBerlinHeidelbergNewYork ISBN-13 978-3-540-34776-7SpringerBerlinHeidelbergNewYork Thisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialis concerned,speciÝcallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting, reproductiononmicroÝlmorinanyotherway,andstorageindatabanks.Duplicationofthispublication orpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9, 1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.Violationsare liableforprosecutionundertheGermanCopyrightLaw. SpringerisapartofSpringerScience+BusinessMedia springer.com (cid:1)c Springer-VerlagBerlinHeidelberg2006 PrintedinTheNetherlands Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnotimply, evenintheabsenceofaspeciÝcstatement,thatsuchnamesareexemptfromtherelevantprotectivelaws andregulationsandthereforefreeforgeneraluse. Typesetting:bytheauthorandtechbooksusingaSpringerLATEXmacropackage Coverdesign: ErichKirchner,Heidelberg Printedonacid-freepaper SPIN:11757825 89/techbooks 543210 Preface Theideaofsoftcomputingemergedintheearly1990sfromthefuzzysystemscom- munity, and refers to an understanding that the uncertainty, imprecision and igno- rance present in a problem should be explicitly represented and possibly even ex- ploitedratherthaneithereliminatedorignoredincomputations.Forinstance,Zadeh defined‘SoftComputing’asfollows: Soft computing differs from conventional (hard) computing in that, unlike hard computing, it is tolerant of imprecision, uncertainty and partial truth. Ineffect,therolemodelforsoftcomputingisthehumanmind. Recently soft computing has, to some extent, become synonymous with a hybrid approach combining AI techniques including fuzzy systems, neural networks, and biologicallyinspiredmethodssuchasgeneticalgorithms.Here,however,weadopt a more straightforward definition consistent with the original concept. Hence, soft methodsareunderstoodasthoseuncertaintyformalismsnotpartofmainstreamsta- tisticsandprobabilitytheorywhichhavetypicallybeendevelopedwithintheAIand decisionanalysiscommunity.Thesearemathematicallysounduncertaintymodelling methodologies which are complementary to conventional statistics and probability theory. Inadditiontoprobabilisticfactorssuchasmeasurementerrorandotherrandom effects,themodellingprocessoftenrequiresustomakequalitativeandsubjectjudge- ments that cannot easily be translated into precise probability values. Such judge- ments give rise to a number of different types of uncertainty including; fuzziness if they are based on linguistic information; epistemic uncertainty when their relia- bility is in question; ignorance when they are insufficient to identify or restrict key modelling parameters; imprecision when parameters and probability distributions canonlybeestimatedwithincertainbounds.Statisticaltheoryhasnottraditionally been concerned with modelling uncertainty arising in this manner but soft meth- ods, a range of powerful techniques developed within AI, attempt to address those problemswheretheencodingofsubjectiveinformationisunavoidable.Therefore,a morerealisticmodellingprocessprovidingdecisionmakerswithanaccuratereflec- tionofthetruecurrentstateofourknowledge(andignorance)requiresanintegrated VI Preface framework incorporating both probability theory, statistics and soft methods. This fusionmotivatesinnovativeresearchattheinterfacebetweencomputerscience(AI), mathematicsandsystemsengineering. This edited volume is the proceedings of the 2006 International Workshop on SoftMethodsinProbabilityandStatistics(SMPS2006)hostedbytheArtificialIn- telligenceGroupattheUniversityofBristol,between5-7September2006.Thisis thethirdofaseriesofbiennialmeetingsorganizedin2002bytheSystemsResearch Institute from the Polish Academy of Sciences in Warsaw, and in 2004 by the De- partmentofStatisticsandOperationalResearchattheUniversityofOviedoinSpain. Theseconferencesprovideaforumfordiscussionandresearchintothefusionofsoft methods with probability and statistics, with the ultimate goal of integrated uncer- taintymodellingincomplexsystemsinvolvinghumanfactors. The papers in the volume are organized into a number of key themes each ad- dressing a different aspect of the integration of soft methods with probability and statistics.Theseareidentifiedbothasbeinglongstandingfoundationalproblems,as wellaspromisingavenuesofresearchwiththepotentialofprovidingsignificantad- vancesinthemodellingandrepresentationofknowledgeanduncertainty.Alsovital tothedevelopmentofanyacademicdisciplineistheidentificationandexplorationof challengingnewapplicationareas.Itisonlythroughtheapplicationofexistingtools andmethodologiestotheanalysisofuncertaintyinlarge-scalecomplexsystemsthat fundamentalresearchissuescanbeidentifiedandnewcapabilitiesdeveloped. Part I presents abstracts of four keynote presentations by Lotfi Zadeh, Gert de Cooman,JimHallandVladikKreinovich.Prof.Zadeh’stalkprovidesdetailsonthe latestdevelopmentsinhistheoryofgeneraliseduncertainty.Prof.deCooman’stalk describesatheoryoflinguisticprobabilitiesbasedonimpreciseprobabilities.Prof. Hall gives an overview of the application of soft methods in Earth Systems Engi- neering. Prof. Kreinovich describes algorithms for statistical data processing under interval uncertainty and investigates their complexity. Part II on Soft Methods in StatisticsandRandomInformationSystemspresentscurrentresearchleadingtothe developmentofnewstatisticaltoolsincorporatingfuzziness.PartIIIonProbability ofImprecisely-ValuedRandomElementsWithApplicationsfocussesonaspectsof probabilitytheoryincorporatingimprecision.PartIVonApplicationsandModelling ofImpreciseOperatorsconsidershowlinguisticquantifierscanbeusedtodescribe uncertainty. Part V on Imprecise Probability theory concerns the uncertainty mea- surescorrespondingtoupperandlowerprobabilitiesandprevisions.PartVIonPos- sibility,EvidenceandIntervalMethodscontainspapersonpossibilityandevidence theoryaswellasintervalmethods.Finally,partVIIpresentsarangeofchallenging applicationsrequiringtheintegrationofuncertainty,fuzzinessandimprecision. Bristol, JonathanLawry May2006 Contents PartI KeynotePapers GeneralizedTheoryofUncertainty(GTU)–PrincipalConcepts andIdeas LotfiA.Zadeh .................................................... 3 ReasoningwithVagueProbabilityAssessments GertdeCooman .................................................. 5 SoftMethodsinEarthSystemsEngineering JimW.Hall ...................................................... 7 StatisticalDataProcessingunderIntervalUncertainty:Algorithmsand ComputationalComplexity VladikKreinovich ................................................. 11 PartII SoftMethodsinStatisticsandRandomInformationSystems OnTestingFuzzyIndependence OlgierdHryniewicz................................................ 29 VarianceDecompositionofFuzzyRandomVariables AndreasWünsche,WolfgangNäther................................... 37 FuzzyHistogramsandDensityEstimation KevinLoquin,OlivierStrauss........................................ 45 GradedStochasticDominanceasaToolforRankingtheElements ofaPoset KarelDeLoof,HansDeMeyer,BernardDeBaets ....................... 53 VIII Contents OnNeyman-PearsonLemmaforCrisp,RandomandFuzzyHypotheses AdelMohammadpour,AliMohammad-Djafari .......................... 61 FuzzyProbabilityDistributionsInducedbyFuzzyRandomVectors WolfgangTrutschnig............................................... 71 OntheIdentifiabilityofTSKAdditiveFuzzyRule-BasedModels JoséLuisAznarteM.,JoséManuelBenítez ............................. 79 AnAsymptoticTestforSymmetryofRandomVariablesBased onFuzzyTools González-Rodríguez.G.,Colubi,A.,D’UrsoP.,Giordani,P. ............... 87 ExploratoryAnalysisofRandomVariablesBasedonFuzzifications Colubi,A.,González-Rodríguez.G.,Lubiano,M.A.,Montenegro,M.......... 95 AMethodtoSimulateFuzzyRandomVariables González-Rodríguez.G.,Colubi,A.,Gil,M.A.,Coppi,R. ..................103 Friedman’sTestforAmbiguousandMissingData EdytaMrówka,PrzemysławGrzegorzewski.............................111 PartIII ProbabilityofImprecisely-ValuedRandomElements withApplications Measure-FreeMartingaleswithApplicationtoClassicalMartingales S.F.Cullender,W.-C.Kuo,C.C.A.LabuschagneandB.A.Watson............121 ANoteonRandomUpperSemicontinuousFunctions HungT.Nguyen,YukioOgura,SantiTasenaandHienTran ................129 OptionalSamplingTheoremandRepresentationofSet-ValuedAmart ShoumeiLi,LiGuan...............................................137 OnaChoquetTheoremforRandomUpperSemicontinuousFunctions YukioOgura .....................................................145 AGeneralLawofLargeNumbers,withApplications PedroTerán,IlyaMolchanov ........................................153 PartIV ApplicationsandModellingofImpreciseOperators FuzzyProductionPlanningModelforAutomobileSeatAssembling J.Mula,R.Poler,J.P.Garcia-Sabater .................................163 Contents IX OptimalSelectionofProportionalBoundingQuantifiersinLinguistic DataSummarization IngoGlöckner ....................................................173 ALinguisticQuantifierBasedAggregation foraHumanConsistent SummarizationofTimeSeries JanuszKacprzyk,AnnaWilbik,SławomirZadroz˙ny.......................183 EfficientEvaluationofSimilarityQuantifiedExpressions intheTemporalDomain F.Díaz-Hermida,P.Cariñena,A.Bugarín .............................191 PartV ImpreciseProbabilityTheory ConditionalLowerPrevisionsforUnboundedRandomQuantities MatthiasC.M.Troffaes ............................................201 ExtremeLowerProbabilities ErikQuaeghebeur,GertdeCooman ..................................211 EquivalenceBetweenBayesianandCredalNetsonanUpdatingProblem AlessandroAntonucci,MarcoZaffalon ................................223 VaryingParameterinClassificationBasedonImpreciseProbabilities JoaquínAbellán,SerafínMoral,ManuelGómezandAndrésMasegosa.......231 ComparingProportionsDatawithFewSuccesses F.P.A.Coolen,P.Coolen-Schrijner....................................241 AUnifiedViewofSomeRepresentationsofImpreciseProbabilities S.Destercke,D.Dubois ............................................249 PartVI Possibility,EvidenceandIntervalMethods EstimatinganUncertainProbabilityDensity YakovBen-Haim ..................................................261 TheoryofEvidencewithImperfectInformation J.Recasens ......................................................267 ConditionalIF-probability KatarínaLendelová ...............................................275 OnTwoWaysfortheProbabilityTheoryonIF-sets BeloslavRiecˇan...................................................285 X Contents AStratificationofPossibilisticPartialExplanations SaraBoutouhami,AichaMokhtari....................................291 FiniteDiscreteTimeMarkovChainswithIntervalProbabilities DamjanŠkulj.....................................................299 EvidenceandCompositionality WagnerBorges,JulioMichaelStern...................................307 HighLevelFuzzyLabelsforVagueConcepts ZengchangQinandJonathanLawry ..................................317 PartVII IntegratedUncertaintyModellinginApplications PossibilisticChannelsforDNAWordDesign LucaBortolussi,AndreaSgarro ......................................327 TransformationofPossibilityFunctionsinaClimateModel ofIntermediateComplexity HermannHeld,ThomasSchneidervonDeimling ........................337 FuzzyLogicforStochasticModeling ÖzerCiftciogluandI.SevilSariyildiz .................................347 ACUSUMControlChartforFuzzyQualityData DabuxilatuWang..................................................357 AFuzzySynset-BasedHiddenMarkovModel forAutomaticTextSegmentation VietHa-Thuc,Quang-AnhNguyen-Van,TruHoangCaoandJonathanLawry..365 ApplyingFuzzyMeasuresforConsideringInteractionEffects inFineRootDispersalModels WolfgangNäther,KonradWälder ....................................373 Scoring Feature Subsets for Separation Power in Supervised Bayes Classification TatjanaPavlenko,HakanFridén .....................................383 IntervalRandomVariablesandTheirApplicationinQueueingSystems withLong–TailedServiceTimes BartłomiejJacekKubica,KrzysztofMalinowski .........................393 OnlineLearningforFuzzyBayesianPrediction N.J.Randon,J.Lawry,I.D.Cluckie ...................................405 Index ............................................................. 413
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