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Associative functions : triangular norms and copulas /

The functional equation of associativity is the topic of Abel's first contribution to Crelle's Journal. Seventy years later, it was featured as the second part of Hilbert's Fifth Problem, and it was solved under successively weaker hypotheses by Brouwer (1909), Cartan (1930) and Aczel...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Alsina, Claudi
Otros Autores: Schweizer, B. (Berthold), Frank, Maurice J.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Singapore ; Hackensack, NJ : World Scientific, ©2006.
Temas:
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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.