Handbook of Granular Computing

1150 Pages·2008·16.81 MB·English

by  Witold Pedrycz

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 [phone]
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([phone].
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