Description
Book Synopsis
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.
Trade Review
"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)Table of Contents
Acknowledgments. Introduction. Notations used in this book. Part 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. Part 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. Appendix A: Families of t-norms. B: Additional t-norms. Reference material. List of Figures. List of Tables. List of Mathematical Symbols. Bibliography. Index.
