Topological and Algebraic Structures in Fuzzy Sets: A Handbook of Recent Developments in the Mathematics of Fuzzy Sets by S.E. RodabaughTopological and Algebraic Structures in Fuzzy Sets: A Handbook of Recent Developments in the Mathematics of Fuzzy Sets by S.E. Rodabaugh

Topological and Algebraic Structures in Fuzzy Sets: A Handbook of Recent Developments in the…

EditorS.E. Rodabaugh, Erich Peter Klement

Paperback | December 4, 2010

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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.
Title:Topological and Algebraic Structures in Fuzzy Sets: A Handbook of Recent Developments in the…Format:PaperbackDimensions:481 pagesPublished:December 4, 2010Publisher:Springer NetherlandsLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9048163781

ISBN - 13:9789048163786

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Table of Contents

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. Gutiérrez 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)-Topological Spaces; W. Kotzé. 17. Examples for Different Sobrieties in Fixed-Basis Topology; A. Pultr, S.E. Rodabaugh. 18. Additive Generators of Non-Continuous Triangular Norms; P. Viceník. 19. Groups, T-Norms and Families of De Morgan Systems; C. Walker, E. Walker.