Triangular Norms
By: by Erich Peter Klement, Radko Mesiar, Endre Pap
Contributors: Mesiar, Radko; Pap, Endre
Series: Trends in Logic, Studia Logica Library -- 8; Trends in Logic, Studia Logica Library -- 8
Publisher: Springer Netherlands
Published: 2000
Place of publication: Dordrecht
Language: eng
Format: [electronic resource] /
Number of pages: 387
ISBN-13: 9789048155071; 9789401595407
Subjects: Philosophy (General); Logic; Symbolic and mathematical Logic; Algebra
Description: Triangular norms were first used in the context of probabilistic metric spaces in order to extend the triangle inequality from classical metric spaces to this more general case. The theory of triangular norms has two roots, viz., specific functional equations and the theory of special topological semigroups. These are discussed in Part I. Part II of the book 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. Part I is self contained, including all proofs, and gives many graphical illustrations. The review in Part II shows the importance if triangular norms in the field concerned, providing a well-balanced picture of theory and applications.
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Table of contents: title: Acknowledgments; title: Introduction; title: Notations used in this book; title: 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; title: 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; title: Appendix A: Families of t-norms. B: Additional t-norms; title: Reference material; title: List of Figures; title: List of Tables; title: List of Mathematical Symbols; title: Bibliography; title: Index.