Topological and Algebraic Structures in Fuzzy Sets

TRAMA

This volume summarizes recent developments in the topological and algebraic structures in fuzzy sets and may be rightly viewed as a continuation of the stan­ dardization of the mathematics of fuzzy sets established in the "Handbook", namely the Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory, Volume 3 of The Handbooks of Fuzzy Sets Series (Kluwer Academic Publish­ ers, 1999). Many of the topological chapters of the present work are not only based upon the foundations and notation for topology laid down in the Hand­ book, but also upon Handbook developments in convergence, uniform spaces, compactness, separation axioms, and canonical examples; and thus this work is, with respect to topology, a continuation of the standardization of the Hand­ book. At the same time, this work significantly complements the Handbook in regard to algebraic structures. Thus the present volume is an extension of the content and role of the Handbook as a reference work. On the other hand, this volume, even as the Handbook, is a culmination of mathematical developments motivated by the renowned International Sem­ inar on Fuzzy Set Theory, also known as the Linz Seminar, held annually in Linz, Austria. Much of the material of this volume is related to the Twenti­ eth Seminar held in February 1999, material for which the Seminar played a crucial and stimulating role, especially in providing feedback, connections, and the necessary screening of ideas.

SOMMARIO

1: Uniform Completion In Pointfree Topology.- 2: Monadic Convergence Structures.- 3: A Unified Approach To The Concept Of Fuzzy L-Uniform Space.- 4: Many Valued Topologies And Borel Probability Measures.- 5: Fuzzy Reals: Topological Results Surveyed, Brouwer Fixed Point Theorem, Open Questions.- 6: Lattice-Valued Frames, Functor Categories, And Classes of Sober Spaces.- Appendix to Chapter 6: Weakening The Requirement That L Be A Complete Chain.- 7: Axiomatic Foundations For Uniform Operator Quasi-Uniformities.- 8: Fully Fuzzy Topology.- 9: Fuzzy Logics Arising From Strict De Morgan Systems.- 10: Structure Of Girard Monoids on [0,1].- 11: On The Geometry Of Choice.- 12: On Some Fuzzy Categories Related To Category L-TOP Of L-Topological Spaces.- 13: Fuzzy Compactness Via Categorical Closure Operators.- 14: Discrete Triangular Norms.- 15: Powerset Operators Based Approach To Fuzzy Topologies On Fuzzy Sets.- 16: Lifting Of Sobriety Concepts With Particular Reference To (L, M)-Topological Spaces.- 17: Examples For Different Sobrieties In Fixed-Basis Topology.- 18: Additive Generators Of Non-Continuous Triangular Norms.- 19: Groups, T-Norms, And Families Of De Morgan Systems.

ALTRE INFORMAZIONI

• Condizione: Nuovo
• ISBN: 9789048163786
• Collana: Trends in Logic
• Dimensioni: 240 x 160 mm
• Formato: Brossura
• Illustration Notes: XI, 470 p.
• Pagine Arabe: 470
• Pagine Romane: xi