Erich Peter Klement, R. Mesiar, E. Pap

Triangular Norms (eBook, PDF)

• Format: PDF

Produktbeschreibung

This book discusses the theory of triangular norms and surveys several applied fields in which triangular norms play a significant part: probabilistic metric spaces, aggregation operators, many-valued logics, fuzzy logics, sets and control, and non-additive measures together with their corresponding integrals. It includes many graphical illustrations and gives a well-balanced picture of theory and applications. It is for mathematicians, computer scientists, applied computer scientists and engineers.

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Produktdetails

• Verlag: Springer Netherlands
• Seitenzahl: 387
• Erscheinungstermin: 17. April 2013
• Englisch
• ISBN-13: 9789401595407
• Artikelnr.: 44183606

Inhaltsangabe

I.- 1. Basic definitions and properties.- 2. Algebraic aspects.- 3. Construction of t-norms.- 4. Families of t-norms.- 5. Representations of t-norms.- 6. Comparison of t-norms.- 7. Values and discretization of t-norms.- 8. Convergence of t-norms.- II.- 9. Distribution functions.- 10. Aggregation operators.- 11. Many-valued logics.- 12. Fuzzy set theory.- 13. Applications of fuzzy logic and fuzzy sets.- 14. Generalized measures and integrals.- A. Families of t-norms.- A.1 Aczél-Alsina t-norms.- A.2 Dombi t-norms.- A.3 Frank t-norms.- A.4 Hamacher t-norms.- A.5 Mayor-Torrens t-norms.- A.6 Schweizer-Sklar t-norms.- A.7 Sugeno-Weber t-norms.- A.8 Yager t-norms.- B. Additional t-norms.- B.1 Krause t-norm.- B.2 A family of incomparable t-norms.- Reference material.- List of Figures.- List of Tables.- List of Mathematical Symbols.

Rezensionen

"The book is very well written and constitutes a valuable addition to the literature on t-norms and, in general fuzzy reasoning. It presents almost all of the most important developments of fuzzy sets and fuzzy logic by focusing on the central concept of triangular norm. It is divided into two parts and an appendix, which gives a summary of the existing families of t-norms."
(Mathematical Reviews, 2002a)