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1、MATHEMATICSINSCIENCEANDENGINEERINGVOLUME144FuzzySetsandSystems:TheoryandApplicationsDidierDuboisHenriPradeFUZZYSETSANDSYSTEMSTheoryandApplicationsThisisVolume144inMATHEMATICSINSCIENCEANDENGINEERINGASeriesofMonographsandTextbooksEditedbyWilliamF.Ames,GeorgiaInstituteofTechnologyThecompletelistingofbo
2、oksinthisseriesisavailablefromthePublisheruponrequest.FUZZYSETSANDSYSTEMSTheoryandApplicationsDidierDuboisDepartmentofAutomatics(DERA)ONERA-CERTToulouse,FranceHenriPradeCNRS,LanguagesandComputerSystems(LSI)UniversitéPaulSabatierToulouse,FranceACADEMICPRESS,INC.SanDiegoNewYorkBostonLondonSydneyTokyoT
3、orontoThisbookisprintedonacid-freepaper.¥COPYRIGHT©1980BYACADEMICPRESS,INC.ALLRIGHTSRESERVED.NOPARTOFTHISPUBLICATIONMAYBEREPRODUCEDORTRANSMITTEDINANYFORMORBYANYMEANS,ELECTRONICORMECHANICAL,INCLUDINGPHOTOCOPY,RECORDING,ORANYINFORMATIONSTORAGEANDRETRIEVALSYSTEM,WITHOUTPERMISSIONINWRITINGFROMTHEPUBLISH
4、ER.ACADEMICPRESS,INC.ADivisionofHarcourtBrace&Company1300BoylstonStreet,ChestnutHill,MA02167UnitedKingdomEditionpublishedbyACADEMICPRESSLIMITED24–28OvalRoad,LondonNW17DXLibraryofCongressCataloginginPublicationDataDubois,DidierJFuzzysetsandsystems.(Mathematicsinscienceandengineering;v.)Includesbiblio
5、graphiesandindexes.1.Settheory.2.Systemanalysis.I.Prade,HenriM.,jointauthor.II.Title.III.Series.QA248.D74511’.379–25992ISBN0–12–222750–6PRINTEDINTHEUNITEDSTATESOFAMERICA94959697QW9876Themore,thefuzzier.ContentsForewordxiiiPrefacexvAcknowledgmentsxviiPartIIntroductionIntroduction1Appendix:SomeHistori
6、calandBibliographicalRemarks4References5PartIIMathematicalToolsChapter1FuzzySetsA.Definitions9B.Set-TheoreticOperations11C.a-Cuts19D.CardinalityofaFuzzySet20E.InclusionsandEqualitiesofFuzzySets21F.ConvexFuzzySetsandFuzzyStructuredSets25G.L-FuzzySets27H.MeasuresofFuzziness32References34Chapter2Extens
7、lonPrlnciple,ExtendedOperations,andExtendedFuzzySetsA.ExtensionPrinciple36B.ExtendedRealOperations41C.ExtendedFuzzySets62References67viiFuzzySetsandSystems:TheoryandApplicationsbyDidierDuboisandHenriP
