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OTE/SPH OTE/SPH JWBK123-FM JWBK123-Pedrycz May15,2008 7:2 CharCount=0 HANDBOOK OF GRANULAR COMPUTING Edited by Witold Pedrycz UniversityofAlberta,Canada andPolishAcademyofSciences,Warsaw,Poland Andrzej Skowron WarsawUniversity,Poland Vladik Kreinovich UniversityofTexas,USA A Publication iii OTE/SPH OTE/SPH JWBK123-FM JWBK123-Pedrycz May15,2008 7:2 CharCount=0 ii OTE/SPH OTE/SPH JWBK123-FM JWBK123-Pedrycz May15,2008 7:2 CharCount=0 HANDBOOK OF GRANULAR COMPUTING i OTE/SPH OTE/SPH JWBK123-FM JWBK123-Pedrycz May15,2008 7:2 CharCount=0 ii OTE/SPH OTE/SPH JWBK123-FM JWBK123-Pedrycz May15,2008 7:2 CharCount=0 HANDBOOK OF GRANULAR COMPUTING Edited by Witold Pedrycz UniversityofAlberta,Canada andPolishAcademyofSciences,Warsaw,Poland Andrzej Skowron WarsawUniversity,Poland Vladik Kreinovich UniversityofTexas,USA A Publication iii OTE/SPH OTE/SPH JWBK123-FM JWBK123-Pedrycz May15,2008 7:2 CharCount=0 Copyright(cid:2)C 2008 JohnWiley&SonsLtd,TheAtrium,SouthernGate,Chichester, WestSussexPO198SQ,England Telephone (+44)1243779777 Email(forordersandcustomerserviceenquiries):[email protected] Visit our Home Page on www.wileyeurope.com or www.wiley.com AllRightsReserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystemortransmitted inanyformorbyanymeans,electronic,mechanical,photocopying,recording,scanningorotherwise,except underthetermsoftheCopyright,DesignsandPatentsAct1988orunderthetermsofalicenceissuedbythe CopyrightLicensingAgencyLtd,90TottenhamCourtRoad,LondonW1T4LP,UK,withoutthepermissionin writingofthePublisher.RequeststothePublishershouldbeaddressedtothePermissionsDepartment, JohnWiley&SonsLtd,TheAtrium,SouthernGate,Chichester,WestSussexPO198SQ,England,oremailedto [email protected],orfaxedto(+44)1243770620. Thispublicationisdesignedtoprovideaccurateandauthoritativeinformationinregardtothesubjectmatter covered.ItissoldontheunderstandingthatthePublisherisnotengagedinrenderingprofessionalservices.If professionaladviceorotherexpertassistanceisrequired,theservicesofacompetentprofessionalshouldbesought. OtherWileyEditorialOffices JohnWiley&SonsInc.,111RiverStreet,Hoboken,NJ07030,USA Jossey-Bass,989MarketStreet,SanFrancisco,CA94103-1741,USA Wiley-VCHVerlagGmbH,Boschstr.12,D-69469Weinheim,Germany JohnWiley&SonsAustraliaLtd,42McDougallStreet,Milton,Queensland4064,Australia JohnWiley&Sons(Asia)PteLtd,2ClementiLoop#02-01,JinXingDistripark,Singapore129809 JohnWiley&SonsCanadaLtd,6045FreemontBlvd,Mississauga,ONT,L5R4J3 Wileyalsopublishesitsbooksinavarietyofelectronicformats.Somecontentthatappearsinprintmay notbeavailableinelectronicbooks. LibraryofCongressCataloging-in-PublicationData Pedrycz,Witold,1953– Handbookofgranularcomputing/WitoldPedrycz,AndrzejSkowron,VladikKreinovich. p. cm. Includesindex. ISBN978-0-470-03554-2(cloth) 1.Granularcomputing–Handbooks,manuals,etc. I.Skowron,Andrzej. II.Kreinovich, Vladik. III.Title. QA76.9.S63P4452008 006.3–dc22 2008002695 BritishLibraryCataloguinginPublicationData AcataloguerecordforthisbookisavailablefromtheBritishLibrary ISBN: 978-0-470-03554-2 Typesetin9/11ptTimesbyAptaraInc.,NewDelhi,India PrintedandboundinGreatBritainbyAntonyRoweLtd,Chippenham,Wiltshire iv OTE/SPH OTE/SPH JWBK123-FM JWBK123-Pedrycz May15,2008 7:2 CharCount=0 Contents Preface ix Foreword xiii Biographies xv PartOne FundamentalsandMethodologyofGranularComputingBasedonInterval Analysis,FuzzySetsandRoughSets 1 1 IntervalComputationasanImportantPartofGranularComputing: AnIntroduction 3 VladikKreinovich 2 StochasticArithmeticasaModelofGranularComputing 33 Rene´AltandJeanVignes 3 FundamentalsofIntervalAnalysisandLinkagestoFuzzySetTheory 55 WeldonA.Lodwick 4 IntervalMethodsforNon-LinearEquationSolvingApplications 81 CourtneyRyanGwaltney,YoudongLin,LukeDavidSimoni, andMarkAllenStadtherr 5 FuzzySetsasaUser-CentricProcessingFrameworkofGranularComputing 97 WitoldPedrycz 6 MeasurementandElicitationofMembershipFunctions 141 TanerBilgic¸andI˙.BurhanTu¨rks¸en 7 FuzzyClusteringasaData-DrivenDevelopmentEnvironmentforInformation Granules 153 PauloFazendeiroandJose´ValentedeOliveira 8 EncodingandDecodingofFuzzyGranules 171 ShounakRoychowdhury 9 SystemsofInformationGranules 187 FrankHo¨eppnerandFrankKlawonn 10 LogicalConnectivesforGranularComputing 205 ErichPeterKlement,RadkoMesiar,AndreaMesiarova´-Zema´nkova´, andSusanneSaminger-Platz v OTE/SPH OTE/SPH JWBK123-FM JWBK123-Pedrycz May15,2008 7:2 CharCount=0 vi Contents 11 CalculiofInformationGranules.FuzzyRelationalEquations 225 SiegfriedGottwald 12 FuzzyNumbersandFuzzyArithmetic 249 LucianoStefanini,LaerteSorini,andMariaLetiziaGuerra 13 Rough-GranularComputing 285 AndrzejSkowronandJamesF.Peters 14 WisdomGranularComputing 329 AndrzejJankowskiandAndrzejSkowron 15 GranularComputingforReasoningaboutOrderedData:TheDominance-Based RoughSetApproach 347 SalvatoreGreco,BenedettoMatarazzo,andRomanSlowin´ski 16 AUnifiedApproachtoGranulationofKnowledgeandGranularComputing BasedonRoughMereology:ASurvey 375 LechPolkowski 17 AUnifiedFrameworkofGranularComputing 401 YiyuYao 18 QuotientSpacesandGranularComputing 411 LingZhangandBoZhang 19 RoughSetsandGranularComputing:TowardRough-GranularComputing 425 AndrzejSkowronandJaroslawStepaniuk 20 ConstructionofRoughInformationGranules 449 AnnaGomolin´ska 21 SpatiotemporalReasoninginRoughSetsandGranularComputing 471 PiotrSynak PartTwo HybridMethodsandModelsofGranularComputing 489 22 ASurveyofInterval-ValuedFuzzySets 491 HumbertoBustince,JavierMontero,MiguelPagola,EdurneBarrenechea, andDanielGo´mez 23 MeasurementTheoryandUncertaintyinMeasurements:ApplicationofInterval AnalysisandFuzzySetsMethods 517 LeonReznik 24 FuzzyRoughSets:FromTheoryintoPractice 533 ChrisCornelis,MartineDeCock,andAnnaMariaRadzikowska 25 OnType2FuzzySetsasGranularModelsforWords 553 JerryM.Mendel 26 DesignofIntelligentSystemswithIntervalType-2FuzzyLogic 575 OscarCastilloandPatriciaMelin OTE/SPH OTE/SPH JWBK123-FM JWBK123-Pedrycz May15,2008 7:2 CharCount=0 Contents vii 27 TheoreticalAspectsofShadowedSets 603 GianpieroCattaneoandDavideCiucci 28 FuzzyRepresentationsofSpatialRelationsforSpatialReasoning 629 IsabelleBloch 29 Rough–NeuralMethodologiesinGranularComputing 657 SushmitaMitraandMohuaBanerjee 30 ApproximationandPerceptioninEthology-BasedReinforcementLearning 671 JamesF.Peters 31 FuzzyLinearProgramming 689 JaroslavRam´ık 32 AFuzzyRegressionApproachtoAcquisitionofLinguisticRules 719 JunzoWatadaandWitoldPedrycz 33 FuzzyAssociativeMemoriesandTheirRelationshiptoMathematical Morphology 733 PeterSussnerandMarcosEduardoValle 34 FuzzyCognitiveMaps 755 E.I.PapageorgiouandC.D.Stylios PartThree ApplicationsandCaseStudies 775 35 RoughSetsandGranularComputinginBehavioralPatternIdentificationand Planning 777 JanG.Bazan 36 RoughSetsandGranularComputinginHierarchicalLearning 801 SinhHoaNguyenandHungSonNguyen 37 OutlierandExceptionAnalysisinRoughSetsandGranularComputing 823 TuanTrungNyuyen 38 InformationAccessandRetrieval 835 GloriaBordogna,DonaldH.Kraft,andGabriellaPasi 39 GranularComputinginMedicalInformatics 847 GiovanniBortolan 40 EigenFuzzySetsandImageInformationRetrieval 863 FerdinandoDiMartino,SalvatoreSessa,andHajimeNobuhara 41 RoughSetsandGranularComputinginDealingwithMissingAttributeValues 873 JerzyW.Grzymala-Busse 42 GranularComputinginMachineLearningandDataMining 889 EykeHu¨llermeier OTE/SPH OTE/SPH JWBK123-FM JWBK123-Pedrycz May15,2008 7:2 CharCount=0 viii Contents 43 OnGroupDecisionMaking,ConsensusReaching,Voting,andVotingParadoxes underFuzzyPreferencesandaFuzzyMajority:ASurveyandaGranulation Perspective 907 JanuszKacprzyk,S(cid:2)lawomirZadroz˙ny,MarioFedrizzi,andHannuNurmi 44 FuzzJADE:AFrameworkforAgent-BasedFLCs 931 VincenzoLoiaandMarioVeniero 45 GranularModelsforTime-SeriesForecasting 949 MarinaHirotaMagalha˜es,RosangelaBallini,andFernandoAntonio CamposGomide 46 RoughClustering 969 PawanLingras,S.Asharaf,andCoryButz 47 RoughDocumentClusteringandTheInternet 987 HungSonNguyenandTuBaoHo 48 RoughandGranularCase-BasedReasoning 1005 SimonC.K.Shiu,SankarK.Pal,andYanLi 49 GranulationinAnalogy-BasedClassification 1037 ArkadiuszWojna 50 ApproximationSpacesinConflictAnalysis:ARoughSetFramework 1055 SheelaRamanna 51 IntervalsinFinanceandEconomics:BridgebetweenWordsandNumbers, LanguageofStrategy 1069 ManuelTarrazo 52 GranularComputingMethodsinBioinformatics 1093 JulioJ.Valde´s Index 1113

Description:
Although the notion is a relatively recent one, the notions and principles of Granular Computing (GrC) have appeared in a different guise in many related fields including granularity in Artificial Intelligence, interval computing, cluster analysis, quotient space theory and many others. Recent years
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1150 Pages·2008·16.81 MB·English
by  Witold Pedrycz
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OTE/SPH OTE/SPH JWBK123-FM JWBK123-Pedrycz May15,2008 7:2 CharCount=0 HANDBOOK OF GRANULAR COMPUTING Edited by Witold Pedrycz UniversityofAlberta,Canada andPolishAcademyofSciences,Warsaw,Poland Andrzej Skowron WarsawUniversity,Poland Vladik Kreinovich UniversityofTexas,USA A Publication iii OTE/SPH OTE/SPH JWBK123-FM JWBK123-Pedrycz May15,2008 7:2 CharCount=0 ii OTE/SPH OTE/SPH JWBK123-FM JWBK123-Pedrycz May15,2008 7:2 CharCount=0 HANDBOOK OF GRANULAR COMPUTING i OTE/SPH OTE/SPH JWBK123-FM JWBK123-Pedrycz May15,2008 7:2 CharCount=0 ii OTE/SPH OTE/SPH JWBK123-FM JWBK123-Pedrycz May15,2008 7:2 CharCount=0 HANDBOOK OF GRANULAR COMPUTING Edited by Witold Pedrycz UniversityofAlberta,Canada andPolishAcademyofSciences,Warsaw,Poland Andrzej Skowron WarsawUniversity,Poland Vladik Kreinovich UniversityofTexas,USA A Publication iii OTE/SPH OTE/SPH JWBK123-FM JWBK123-Pedrycz May15,2008 7:2 CharCount=0 Copyright(cid:2)C 2008 JohnWiley&SonsLtd,TheAtrium,SouthernGate,Chichester, WestSussexPO198SQ,England Telephone (+44)1243779777 Email(forordersandcustomerserviceenquiries):[email protected] Visit our Home Page on www.wileyeurope.com or www.wiley.com AllRightsReserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystemortransmitted inanyformorbyanymeans,electronic,mechanical,photocopying,recording,scanningorotherwise,except underthetermsoftheCopyright,DesignsandPatentsAct1988orunderthetermsofalicenceissuedbythe CopyrightLicensingAgencyLtd,90TottenhamCourtRoad,LondonW1T4LP,UK,withoutthepermissionin writingofthePublisher.RequeststothePublishershouldbeaddressedtothePermissionsDepartment, JohnWiley&SonsLtd,TheAtrium,SouthernGate,Chichester,WestSussexPO198SQ,England,oremailedto [email protected],orfaxedto(+44)1243770620. Thispublicationisdesignedtoprovideaccurateandauthoritativeinformationinregardtothesubjectmatter covered.ItissoldontheunderstandingthatthePublisherisnotengagedinrenderingprofessionalservices.If professionaladviceorotherexpertassistanceisrequired,theservicesofacompetentprofessionalshouldbesought. OtherWileyEditorialOffices JohnWiley&SonsInc.,111RiverStreet,Hoboken,NJ07030,USA Jossey-Bass,989MarketStreet,SanFrancisco,CA94103-1741,USA Wiley-VCHVerlagGmbH,Boschstr.12,D-69469Weinheim,Germany JohnWiley&SonsAustraliaLtd,42McDougallStreet,Milton,Queensland4064,Australia JohnWiley&Sons(Asia)PteLtd,2ClementiLoop#02-01,JinXingDistripark,Singapore129809 JohnWiley&SonsCanadaLtd,6045FreemontBlvd,Mississauga,ONT,L5R4J3 Wileyalsopublishesitsbooksinavarietyofelectronicformats.Somecontentthatappearsinprintmay notbeavailableinelectronicbooks. LibraryofCongressCataloging-in-PublicationData Pedrycz,Witold,1953– Handbookofgranularcomputing/WitoldPedrycz,AndrzejSkowron,VladikKreinovich. p. cm. Includesindex. ISBN978-0-470-03554-2(cloth) 1.Granularcomputing–Handbooks,manuals,etc. I.Skowron,Andrzej. II.Kreinovich, Vladik. III.Title. QA76.9.S63P4452008 006.3–dc22 2008002695 BritishLibraryCataloguinginPublicationData AcataloguerecordforthisbookisavailablefromtheBritishLibrary ISBN: 978-0-470-03554-2 Typesetin9/11ptTimesbyAptaraInc.,NewDelhi,India PrintedandboundinGreatBritainbyAntonyRoweLtd,Chippenham,Wiltshire iv OTE/SPH OTE/SPH JWBK123-FM JWBK123-Pedrycz May15,2008 7:2 CharCount=0 Contents Preface ix Foreword xiii Biographies xv PartOne FundamentalsandMethodologyofGranularComputingBasedonInterval Analysis,FuzzySetsandRoughSets 1 1 IntervalComputationasanImportantPartofGranularComputing: AnIntroduction 3 VladikKreinovich 2 StochasticArithmeticasaModelofGranularComputing 33 Rene´AltandJeanVignes 3 FundamentalsofIntervalAnalysisandLinkagestoFuzzySetTheory 55 WeldonA.Lodwick 4 IntervalMethodsforNon-LinearEquationSolvingApplications 81 CourtneyRyanGwaltney,YoudongLin,LukeDavidSimoni, andMarkAllenStadtherr 5 FuzzySetsasaUser-CentricProcessingFrameworkofGranularComputing 97 WitoldPedrycz 6 MeasurementandElicitationofMembershipFunctions 141 TanerBilgic¸andI˙.BurhanTu¨rks¸en 7 FuzzyClusteringasaData-DrivenDevelopmentEnvironmentforInformation Granules 153 PauloFazendeiroandJose´ValentedeOliveira 8 EncodingandDecodingofFuzzyGranules 171 ShounakRoychowdhury 9 SystemsofInformationGranules 187 FrankHo¨eppnerandFrankKlawonn 10 LogicalConnectivesforGranularComputing 205 ErichPeterKlement,RadkoMesiar,AndreaMesiarova´-Zema´nkova´, andSusanneSaminger-Platz v OTE/SPH OTE/SPH JWBK123-FM JWBK123-Pedrycz May15,2008 7:2 CharCount=0 vi Contents 11 CalculiofInformationGranules.FuzzyRelationalEquations 225 SiegfriedGottwald 12 FuzzyNumbersandFuzzyArithmetic 249 LucianoStefanini,LaerteSorini,andMariaLetiziaGuerra 13 Rough-GranularComputing 285 AndrzejSkowronandJamesF.Peters 14 WisdomGranularComputing 329 AndrzejJankowskiandAndrzejSkowron 15 GranularComputingforReasoningaboutOrderedData:TheDominance-Based RoughSetApproach 347 SalvatoreGreco,BenedettoMatarazzo,andRomanSlowin´ski 16 AUnifiedApproachtoGranulationofKnowledgeandGranularComputing BasedonRoughMereology:ASurvey 375 LechPolkowski 17 AUnifiedFrameworkofGranularComputing 401 YiyuYao 18 QuotientSpacesandGranularComputing 411 LingZhangandBoZhang 19 RoughSetsandGranularComputing:TowardRough-GranularComputing 425 AndrzejSkowronandJaroslawStepaniuk 20 ConstructionofRoughInformationGranules 449 AnnaGomolin´ska 21 SpatiotemporalReasoninginRoughSetsandGranularComputing 471 PiotrSynak PartTwo HybridMethodsandModelsofGranularComputing 489 22 ASurveyofInterval-ValuedFuzzySets 491 HumbertoBustince,JavierMontero,MiguelPagola,EdurneBarrenechea, andDanielGo´mez 23 MeasurementTheoryandUncertaintyinMeasurements:ApplicationofInterval AnalysisandFuzzySetsMethods 517 LeonReznik 24 FuzzyRoughSets:FromTheoryintoPractice 533 ChrisCornelis,MartineDeCock,andAnnaMariaRadzikowska 25 OnType2FuzzySetsasGranularModelsforWords 553 JerryM.Mendel 26 DesignofIntelligentSystemswithIntervalType-2FuzzyLogic 575 OscarCastilloandPatriciaMelin OTE/SPH OTE/SPH JWBK123-FM JWBK123-Pedrycz May15,2008 7:2 CharCount=0 Contents vii 27 TheoreticalAspectsofShadowedSets 603 GianpieroCattaneoandDavideCiucci 28 FuzzyRepresentationsofSpatialRelationsforSpatialReasoning 629 IsabelleBloch 29 Rough–NeuralMethodologiesinGranularComputing 657 SushmitaMitraandMohuaBanerjee 30 ApproximationandPerceptioninEthology-BasedReinforcementLearning 671 JamesF.Peters 31 FuzzyLinearProgramming 689 JaroslavRam´ık 32 AFuzzyRegressionApproachtoAcquisitionofLinguisticRules 719 JunzoWatadaandWitoldPedrycz 33 FuzzyAssociativeMemoriesandTheirRelationshiptoMathematical Morphology 733 PeterSussnerandMarcosEduardoValle 34 FuzzyCognitiveMaps 755 E.I.PapageorgiouandC.D.Stylios PartThree ApplicationsandCaseStudies 775 35 RoughSetsandGranularComputinginBehavioralPatternIdentificationand Planning 777 JanG.Bazan 36 RoughSetsandGranularComputinginHierarchicalLearning 801 SinhHoaNguyenandHungSonNguyen 37 OutlierandExceptionAnalysisinRoughSetsandGranularComputing 823 TuanTrungNyuyen 38 InformationAccessandRetrieval 835 GloriaBordogna,DonaldH.Kraft,andGabriellaPasi 39 GranularComputinginMedicalInformatics 847 GiovanniBortolan 40 EigenFuzzySetsandImageInformationRetrieval 863 FerdinandoDiMartino,SalvatoreSessa,andHajimeNobuhara 41 RoughSetsandGranularComputinginDealingwithMissingAttributeValues 873 JerzyW.Grzymala-Busse 42 GranularComputinginMachineLearningandDataMining 889 EykeHu¨llermeier OTE/SPH OTE/SPH JWBK123-FM JWBK123-Pedrycz May15,2008 7:2 CharCount=0 viii Contents 43 OnGroupDecisionMaking,ConsensusReaching,Voting,andVotingParadoxes underFuzzyPreferencesandaFuzzyMajority:ASurveyandaGranulation Perspective 907 JanuszKacprzyk,S(cid:2)lawomirZadroz˙ny,MarioFedrizzi,andHannuNurmi 44 FuzzJADE:AFrameworkforAgent-BasedFLCs 931 VincenzoLoiaandMarioVeniero 45 GranularModelsforTime-SeriesForecasting 949 MarinaHirotaMagalha˜es,RosangelaBallini,andFernandoAntonio CamposGomide 46 RoughClustering 969 PawanLingras,S.Asharaf,andCoryButz 47 RoughDocumentClusteringandTheInternet 987 HungSonNguyenandTuBaoHo 48 RoughandGranularCase-BasedReasoning 1005 SimonC.K.Shiu,SankarK.Pal,andYanLi 49 GranulationinAnalogy-BasedClassification 1037 ArkadiuszWojna 50 ApproximationSpacesinConflictAnalysis:ARoughSetFramework 1055 SheelaRamanna 51 IntervalsinFinanceandEconomics:BridgebetweenWordsandNumbers, LanguageofStrategy 1069 ManuelTarrazo 52 GranularComputingMethodsinBioinformatics 1093 JulioJ.Valde´s Index 1113

Description:
Although the notion is a relatively recent one, the notions and principles of Granular Computing (GrC) have appeared in a different guise in many related fields including granularity in Artificial Intelligence, interval computing, cluster analysis, quotient space theory and many others. Recent years
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