03304nam 22007094a 450 991077826110332120230828204625.01-281-91934-99786611919344981-277-420-39789812566713(CKB)1000000000480153(OCoLC)614464270(CaPaEBR)ebrary10201442(SSID)ssj0000106892(PQKBManifestationID)11140633(PQKBTitleCode)TC0000106892(PQKBWorkID)10014195(PQKB)10691981(MiAaPQ)EBC1681474(WSP)00006036(Au-PeEL)EBL1681474(CaPaEBR)ebr10201442(CaONFJC)MIL191934(OCoLC)879025280(EXLCZ)99100000000048015320061024d2006 uy 0engurcn|||||||||txtccrAssociative functions[electronic resource] triangular norms and copulas /Claudi Alsina, Maurice J. Frank, Berthold SchweizerSingapore ;Hackensack, NJ World Scientificc20061 online resource (253 p.)Bibliographic Level Mode of Issuance: Monograph981-256-671-6 Includes bibliographical references (p. 223-234) and index.Preface -- Special symbols -- 1. Introduction. 1.1. Historical notes. 1.2. Preliminaries. 1.3. t-norms and s-norms. 1.4. Copulas -- 2. Representation theorems for associative functions. 2.1. Continuous, Archimedean t-norms. 2.2. Additive and multiplicative generators. 2.3. Extension to arbitrary closed intervals. 2.4. Continuous, non-Archimedean t-norms. 2.5. Non-continuous t-norms. 2.6. Families of t-norms. 2.7. Other representation theorems. 2.8. Related functional equations -- 3. Functional equations involving t-norms. 3.1. Simultaneous associativity. 3.2. n-duality. 3.3. Simple characterizations of Min. 3.4. Homogeneity. 3.5. Distributivity. 3.6. Conical t-norms. 3.7. Rational Archimedean t-norms. 3.8. Extension and sets of uniqueness -- 4. Inequalities involving t-norms. 4.1. Notions of concavity and convexity. 4.2. The dominance relation. 4.3. Uniformly close associative functions. 4.4. Serial iterates and n-copulas. 4.5. Positivity.Functional equationsAssociative law (Mathematics)Mathematical analysisFunctional equationsStudy and teachingTextbooksAssociative law (Mathematics)Study and teachingTextbooksMathematical analysisStudy and teachingTextbooksFunctional equations.Associative law (Mathematics)Mathematical analysis.Functional equationsStudy and teachingAssociative law (Mathematics)Study and teachingMathematical analysisStudy and teaching515/.7Alsina Claudi309455Schweizer B(Berthold)368525Frank Maurice J1492828MiAaPQMiAaPQMiAaPQBOOK9910778261103321Associative functions3715536UNINA