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.
Author(s): Stephen Ernest Rodabaugh, Erich Peter Klement (eds.)
Series: Trends in Logic 20
Edition: 1
Publisher: Springer Netherlands
Year: 2003
Language: English
Pages: 470
Tags: Mathematical Logic and Foundations; Geometry; Order, Lattices, Ordered Algebraic Structures; Group Theory and Generalizations; Logic
Front Matter....Pages i-xi
Introduction....Pages 1-16
Front Matter....Pages 17-17
Uniform Completion In Pointfree Topology....Pages 19-56
Monadic Convergence Structures....Pages 57-79
A Unified Approach To The Concept Of Fuzzy L -Uniform Space....Pages 81-114
Many Valued Topologies And Borel Probability Measures....Pages 115-135
Fuzzy Reals: Topological Results Surveyed, Brouwer Fixed Point Theorem, Open Questions....Pages 137-151
Lattice-Valued Frames, Functor Categories, And Classes Of Sober Spaces....Pages 153-187
Weakening The Requirement That L Be A Complete Chain....Pages 189-197
Axiomatic Foundations For Uniform Operator Quasi-Uniformities....Pages 199-233
Fully Fuzzy Topology....Pages 235-253
Front Matter....Pages 255-255
Fuzzy Logics Arising From Strict De Morgan Systems....Pages 257-276
Structure Of Girard Monoids On [0,1]....Pages 277-308
On The Geometry Of Choice....Pages 309-336
Front Matter....Pages 373-373
On Some Fuzzy Categories Related To Category L -TOP Of L -Topological Spaces....Pages 337-371
Fuzzy Compactness Via Categorical Closure Operators....Pages 375-387
Discrete Triangular Norms....Pages 389-400
Powerset Operators Based Approach To Fuzzy Topologies On Fuzzy Sets....Pages 401-413
Lifting Of Sobriety Concepts With Particular Reference To ( L, M )-Topological Spaces....Pages 415-426
Examples For Different Sobrieties In Fixed-Basis Topology....Pages 427-440
Additive Generators Of Non-Continuous Triangular Norms....Pages 441-454
Front Matter....Pages 373-373
Groups, T-Norms, And Families Of De Morgan Systems....Pages 455-467
Back Matter....Pages 469-470
