S.E. Rodabaugh / E.P Klement (eds.)

Topological and Algebraic Structures in Fuzzy Sets

A Handbook of Recent Developments in the Mathematics of Fuzzy Sets
Herausgeber: Klement, E.P, Rodabaugh, S.E.

• Gebundenes Buch

Produktbeschreibung

"Topological and Algebraic Structures in Fuzzy Sets has these unique features:
-strategically located at the juncture of fuzzy sets, topology, algebra, lattices, foundations of mathematics;
-major studies in uniformities and convergence structures, fundamental examples in lattice-valued topology, modifications and extensions of sobriety, categorical aspects of lattice-valued subsets, logic and foundations of mathematics, t-norms and associated algebraic and ordered structures;
-internationally recognized authorities clarify deep mathematical aspects of fuzzy sets, particularly those topological or algebraic in nature;
-comprehensive bibliographies and tutorial nature of longer chapters take readers to the frontier of each topic;
-extensively referenced introduction unifies volume and guides readers to chapters closest to their interests;
-annotated open questions direct future research in the mathematics of fuzzy sets;
-suitable as a text for advanced graduate students. "

Produktdetails

• Trends in Logic 20
• Verlag: Springer Netherlands
• 2003 edition
• Seitenzahl: 470
• Erscheinungstermin: 30. September 2003
• Englisch
• Abmessung: 252mm x 162mm x 30mm
• Gewicht: 879g
• ISBN-13: 9781402015151
• ISBN-10: 1402015151
• Artikelnr.: 22460836

Inhaltsangabe

"Volume Contributors. Preface. Introduction.
I: Topological Structures in Fuzzy Sets. 1. Uniform Completion in Pointfree Topology; B. Banaschewshi. 2. Monadic Convergence Structures; W. Gähler. 3. A Unified Approach to the Concept of Fuzzy L-Uniform Space; J. Gutierrez Garcí, M.A. de Prada Vicente, A.P. Sostak. 4. Many Valued Topologies and Borel Probability Measures; U. Höhle. 5. Fuzzy Reals: Topological Results Surveyed, Brouwer Fixed Point Theorem, Open Questions; T. Kubiak. 6. Lattice-Valued Frames, Functor Categories and Classes of Sober Spaces; A. Pultr, S.E. Rodabaugh. Appendix to Chapter 6: Weakening the Requirement that L be a Complete Chain; U. Höhle, S.E. Rodabaugh. 7. Axiomatic Foundations for Uniform Operator Quasi-Uniformities; S.E. Rodabaugh. 8. Full Fuzzy Topology; L.N. Stout.
II: Algebraic Structures in Fuzzy Sets. 9. Fuzzy Logics Arising from Strict De Morgan Systems; M. Gehrke, C. Walker, E. Walker. 10. Structure of Girard Monoids on [0,1]; S. Jenei. 11. On the Geometry of Choice; C.J. Mulvey. 12. On Some Fuzzy Categories Related to Category LTOP of L-Topological Spaces; A.P. Sostak.
III: Related Topics in Topological and Algebraic Structures. 13. Fuzzy Compactness via Categorical Closure Operators; I.W. Alderton. 14. Discrete Triangular Norms; B. de Baets, R. Mesiar. 15. Powerset Operators Based Approach to Fuzzy Topologies on Fuzzy Sets; C. Guido. 16. Lifting of Sobriety Concepts with Particular Reference to (L, M"