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Advances in Intelligent and Soft Computing 107 Editor-in-Chief:J.Kacprzyk Advancesin Intelligentand Soft Computing Editor-in-Chief Prof.JanuszKacprzyk SystemsResearchInstitute PolishAcademyofSciences ul.Newelska6 01-447Warsaw Poland E-mail:[email protected] Furthervolumesofthisseriescanbefoundonourhomepage:springer.com Vol.93.M.P.Rocha,J.M.Corchado, Vol.100.S.Li,X.Wang,Y.Okazaki,J.Kawabe, F.Fernández-Riverola,and T.Murofushi,andLiGuan(Eds.) A.Valencia(Eds.) NonlinearMathematicsforUncertaintyand 5thInternationalConferenceonPractical itsApplications,2011 ApplicationsofComputationalBiology& ISBN978-3-642-22832-2 Bioinformatics6-8th,2011 ISBN978-3-642-19913-4 Vol.101.D.Dicheva,Z.Markov, andE.Stefanova(Eds.) Vol.94.J.M.Molina,J.R.CasarCorredera, ThirdInternationalConferenceonSoftware, M.F.CátedraPérez,J.Ortega-García,and ServicesandSemanticTechnologies A.M.BernardosBarbolla(Eds.) S3T2011,2011 User-CentricTechnologiesand ISBN978-3-642-23162-9 Applications,2011 ISBN978-3-642-19907-3 Vol.102.R.S.Choras´(Ed.) ImageProcessingandCommunications Vol.95.R.Burduk,M.Kurzyn´ski, Challenges3,2011 M.Woz´niak,andA.Z˙ołnierek(Eds.) ISBN978-3-642-23153-7 ComputerRecognitionSystems4,2011 ISBN978-3-642-20319-0 Vol.103.T.Czachórski,S.Kozielski,and U.Stan´czyk(Eds.) Vol.96.A.Gaspar-Cunha,R.Takahashi, Man-MachineInteractions2,2011 G.Schaefer,andL.Costa(Eds.) ISBN978-3-642-23168-1 SoftComputinginIndustrialApplications,2011 ISBN978-3-642-20504-0 Vol.104.D.JinandS.Lin(Eds.) AdvancesinComputerScience,IntelligentSystem Vol.97.W.Zamojski,J.Kacprzyk, andEnvironment,2011 J.Mazurkiewicz,J.Sugier, ISBN978-3-642-23776-8 andT.Walkowiak(Eds.) DependableComputerSystems,2011 Vol.105.D.JinandS.Lin(Eds.) ISBN978-3-642-21392-2 AdvancesinComputerScience,IntelligentSystem andEnvironment,2011 Vol.98.Z.S.Hippe,J.L.Kulikowski,and ISBN978-3-642-23755-3 T.Mroczek(Eds.) Human–ComputerSystemsInteraction: Vol.106.D.JinandS.Lin(Eds.) BackgroundsandApplications2,2011 AdvancesinComputerScience,IntelligentSystem ISBN978-3-642-23186-5 andEnvironment,2011 ISBN978-3-642-23752-2 Vol.99.Z.S.Hippe,J.L.Kulikowski,and T.Mroczek(Eds.) Vol.107.P.Melo-Pinto,P.Couto,C.Serôdio, Human–ComputerSystemsInteraction: J.Fodor,andB.DeBaets(Eds.) BackgroundsandApplications2,2011 Eurofuse2011,2011 ISBN978-3-642-23171-1 ISBN978-3-642-24000-3 Pedro Melo-Pinto, Pedro Couto, Carlos Serôdio, János Fodor, and Bernard De Baets (Eds.) Eurofuse 2011 Workshop on Fuzzy Methods for Knowledge-Based Systems ABC Editors Prof.PedroMelo-Pinto Prof.JánosFodor CITAB-UTADUniversity ÓbudaUniversity QuintadosPrados Bécsiút96/B 5000-911VilaReal H-1034Budapest Portugal Hungary E-mail:[email protected] E-mail:[email protected] Prof.PedroCouto Prof.BernardDeBaets CITAB-UTADUniversity KERMIT QuintadosPrados ResearchUnitKnowledge-basedSystems 5000-911VilaReal UniversiteitGent Portugal Coupurelinks653 E-mail:[email protected] 9000Gent Belgium Prof.CarlosSerôdio E-mail:[email protected] CITAB-UTADUniversity QuintadosPrados 5000-911VilaReal Portugal E-mail:[email protected] ISBN978-3-642-24000-3 e-ISBN978-3-642-24001-0 DOI 10.1007/978-3-642-24001-0 AdvancesinIntelligentandSoftComputing ISSN1867-5662 LibraryofCongressControlNumber:2011936640 (cid:2)c 2011Springer-VerlagBerlinHeidelberg This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations,recitation,broadcasting,reproductiononmicrofilmorinanyotherway,and storageindatabanks.Duplicationofthispublicationorpartsthereofispermittedonly undertheprovisionsoftheGermanCopyrightLawofSeptember9,1965,initscurrent version,andpermissionforusemustalwaysbeobtainedfromSpringer.Violationsare liabletoprosecutionundertheGermanCopyrightLaw. Theuseof general descriptivenames, registered names, trademarks, etc.in thispubli- cationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesare exemptfromtherelevantprotectivelawsandregulationsandthereforefreeforgeneral use. Typeset&CoverDesign:ScientificPublishingServicesPvt.Ltd.,Chennai,India Printedonacid-freepaper 543210 springer.com Preface ThisbookcomprisesthepapersfromEUROFUSE2011WorkshoponFuzzyMeth- odsforKnowledge-basedSystems. EUROFUSEwasestablishedin1998astheEURO(theAssociationofEuropean OperationalResearch Societies) Working Group on Fuzzy Sets, as a successor of the former European Chapter of IFSA (the International Fuzzy Systems Associa- tion). The working group is coordinated by Bernard De Baets (KERMIT, Ghent University,Belgium)andJa´nosFodor(O´budaUniversity,Hungary). EUROFUSE 2011 is the next in a series ofEUROFUSE workshops, including the successfulEUROFUSE 1999(Budapest,Hungary),EUROFUSE 2000(Mons, Belgium),EUROFUSE2001(Granada,Spain),EUROFUSE2002(Varenna,Italy), EUROFUSE2004(Warsaw,Poland),EUROFUSE2005(Belgrade,Serbia),EURO- FUSE2007(Jaen,Spain)andEUROFUSE2009(Pamplona,Spain). The present edition is held in Re´gua, Portugal, in the World Heritage Site of the Douro Wine Region and is organised by Pedro Melo-Pinto and Pedro Couto. The theme of the workshop is Fuzzy Methods for Knowledge-based Systems. As was the case for previous editions, the aim of the workshop is to bring together researchersandpractitionersinaninformalatmosphere.Forthisreason,thenumber ofparticipantsislimitedandallpresentationsareplenary. EUROFUSE 2011 has three distinguished invited speakers: Francisco Herrera (Granada,Spain),RadkoMesiar(Bratislava,Slovakia)andJose´LuisGarciaLapresta (Valladolid,Spain).Nexttotheinvitedspeakers,thethreedayprogramconsistsof 37lectures.Intotal,thereare70participantsfrom10countries.Thiseditedvolume contains the final revised manuscripts on the basis of which the program was put together. VI Preface Wearegratefultotheinvitedspeakers,theauthorsandallreviewersforcontribut- ingtothesuccessofthisworkshop.We alsowanttothankallthepeoplefromthe organizingcommitteefortheinvaluablehelp,whichhelpedturningthisworkshop intoasuccessfulone. BernardDeBaets Ja´nosFodor PedroCouto PedroMelo-Pinto ThisconferencewaspartiallysupportedbyProgramOperacionalRegionaldoNorte (ON.2) Organisation OrganisingCommitee Chairmen Members • B.deBaets • J.Matias • J.Fodor • P.Mestre • P.Melo-Pinto • R.Ribeiro • P.Couto • C.Serodio InvitedSpeakears • Jose´LuisGarc´ıa-Lapresta • FranciscoHerrera • RadkoMesiar VIII Organisation Scientific Program Committee E.Barrenechea(Spain) J.M.Ben´ıtez(Spain) U.Bodenhofer(Austria) H.Bustince(Spain) J.Carvalho(Portugal) J.Chamorro(Spain) F.Chiclana(UK) O.Cordo´n(Spain) C.Cornelis(Belgium) I.Couso(Spain) P.Couto(Portugal) B.DeBaets(Belgium) S.Diaz(Spain) J.Dombi(Hungary) D.Dubois(France) P.Fazendeiro(Portugal) M.Fedrizzi(Italy) J.Fernandez(Spain) J.Fodor(Hungary) J.L.Garcia-Lapresta(Spain) G.Georgescu(Romania) D.Go´mez(Spain) M.Grabisch(France) F.Herrera(Spain) E.Herrera-Viedma(Spain) E.Hu¨llermeier(Germany) J.Kacprzyk(Poland) E.Kerre(Belgium) E.P.Klement(Austria) A.Kolesa´rova´(SlovakRepublic) J.Liu(UK) V.Loia(Italy) L.Mart´ınez(Spain) G.Mayor(Spain) P.Melo-Pinto(Portugal) R.Mesiar(SlovakRepublic) J.Montero(Spain) S.Montes(Spain) E.Montseny(Spain) J.A.Olivas(Spain) V.Oliveira(Portugal) M.Pagola(Spain) E.Pap(Serbia) I.Perfilieva(CzechRepublic) H.Prade(France) DaRuan(Belgium) P.Salgado(Portugal) D.Sa´nchez(Spain) P.Sobrevilla(Spain) E.Szmidt(Poland) V.Torra(Spain) J.Torrens(Spain) J.L.Verdegay(Spain) Contents Invited Talks 1 OntheUsefulnessofIntervalValuedFuzzySetsforLearningFuzzy RuleBasedClassificationSystems................................. 3 FranciscoHerrera UsingAggregationFunctionsforMeasuringSocialInequalityand Poverty ....................................................... 5 Jose´ LuisGarc´ıa-Lapresta FuzzyIntegralsasaToolforMulticriteriaDecisionSupport .......... 9 RadkoMesiar PartI:Theory 17 APossibilisticLogicViewofSugenoIntegrals....................... 19 DidierDubois,HenriPrade,Agne`sRico DecompositionofPossibilisticBeliefFunctionsintoSimpleSupport Functions ..................................................... 31 MatthieuChemin,Agne`sRico,HenriPrade GeneralizedAttanasov’sOperatorsDefinedonLatticeIntervals ....... 43 I.Lizasoain,C.Moreno Modalities..................................................... 53 Jo´zsefDombi OnthePropertiesofProbabilisticImplications...................... 67 PrzemysławGrzegorzewski X Contents RobustnessofN-DualFuzzyConnectives........................... 79 RenataHaxSanderReiser,Benjam´ınRene´ CallejasBedregal TransitivityandNegativeTransitivityintheFuzzySetting ............ 91 SusanaD´ıaz,BernardDeBaets,SusanaMontes PartII:AggregationOperators 101 A CharacterizationTheoremfort-Representablen-Dimensional TriangularNorms .............................................. 103 Benjam´ınBedregal,GlebBeliakov,HumbertoBustince,TomasaCalvo, JavierFerna´ndez,RadkoMesiar A ConstructionMethodofAggregationsFunctionsonthe Set of DiscreteFuzzyNumbers......................................... 113 J.VicenteRiera,J.Torrens DefiningAggregationFunctionsfromNegations..................... 125 I.Aguilo´,J.Sun˜er,J.Torrens DiscreteKernelAggregationFunctions ............................ 137 M.Mas,M.Monserrat,J.Torrens OnaGeneralizationoftheNotionofaSurvivalCopula............... 147 B.DeBaets,H.DeMeyer,R.Mesiar One-VerticalGeneratedImplications ............................. 157 S.Massanet,J.Torrens Some Propertiesof Consistency in the Families of Aggregation Operators..................................................... 169 KarinaRojas,DanielGo´mez,J.TinguaroRodr´ıguez,JavierMontero PartIII:KnowledgeExtraction 177 Fuzzy Ontologies to Represent Background Knowledge. Some ExperimentalResultsonModellingClimateChangeKnowledge ....... 179 Emilio Fdez-Vin˜as, Mateus Ferreira-Satler, Francisco P. Romero, JesusSerrano-Guerrero,JoseA.Olivas,NataliaSaavedra OntheSemanticsofBipolarityandFuzziness....................... 193 J.TinguaroRodr´ıguez,CamiloA.Franco,JavierMontero

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