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Topological and Algebraic Structures in Fuzzy Sets

A Handbook of Recent Developments in the Mathematics of Fuzzy Sets

  • Book
  • © 2003

Overview

Editors:
  1. Stephen Ernest Rodabaugh

    1. Department of Mathematics and Statistics, Youngstown State University, Youngstown, USA

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  2. Erich Peter Klement

    1. Institut für Algebra, Stochastik und wissensbasierte mathematische Systeme, Johannes Kepler Universität, Linz, Austria

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Trends in Logic (TREN, volume 20)

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Table of contents (21 chapters)

  1. Front Matter

    Pages i-xi
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  2. Introduction

    1. Introduction

      • Stephen Ernest Rodabaugh, Erich Peter Klement
      Pages 1-16

  3. Topological Structures in Fuzzy Sets

    1. Front Matter

      Pages 17-17
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    2. Uniform Completion In Pointfree Topology

      • B. Banaschewski
      Pages 19-56

    3. Monadic Convergence Structures

      • W. Gähler
      Pages 57-79

    4. A Unified Approach To The Concept Of Fuzzy L-Uniform Space

      • J. Gutiérrez García, M. A. de Prada Vicente, A. P. Šostak
      Pages 81-114

    5. Many Valued Topologies And Borel Probability Measures

      • U. Höhle
      Pages 115-135

    6. Fuzzy Reals: Topological Results Surveyed, Brouwer Fixed Point Theorem, Open Questions

      • T. Kubiak
      Pages 137-151

    7. Lattice-Valued Frames, Functor Categories, And Classes Of Sober Spaces

      • A. Pultr, S. E. Rodabaugh
      Pages 153-187

    8. Weakening The Requirement That L Be A Complete Chain

      • U. Höhle, S. E. Rodabaugh
      Pages 189-197

    9. Axiomatic Foundations For Uniform Operator Quasi-Uniformities

      • S. E. Rodabaugh
      Pages 199-233

    10. Fully Fuzzy Topology

      • L. N. Stout
      Pages 235-253

  4. Algebraic Structures in Fuzzy Sets

    1. Front Matter

      Pages 255-255
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    2. Fuzzy Logics Arising From Strict De Morgan Systems

      • M. Gehrke, C. Walker, E. Walker
      Pages 257-276

    3. Structure Of Girard Monoids On [0,1]

      • S. Jenei
      Pages 277-308

    4. On The Geometry Of Choice

      • C. J. Mulvey
      Pages 309-336

  5. Related Topics in Topological and Algebraic Structures

    1. Front Matter

      Pages 373-373
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    2. On Some Fuzzy Categories Related To Category L-TOP Of L-Topological Spaces

      • A. P. Šostak
      Pages 337-371

    3. Fuzzy Compactness Via Categorical Closure Operators

      • I. W. Alderton
      Pages 375-387

    4. Discrete Triangular Norms

      • Bernard De Baets, Radko Mesiar
      Pages 389-400
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Keywords

About this book

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.

Editors and Affiliations

  • Department of Mathematics and Statistics, Youngstown State University, Youngstown, USA

    Stephen Ernest Rodabaugh

  • Institut für Algebra, Stochastik und wissensbasierte mathematische Systeme, Johannes Kepler Universität, Linz, Austria

    Erich Peter Klement

Bibliographic Information

  • Book Title: Topological and Algebraic Structures in Fuzzy Sets

  • Book Subtitle: A Handbook of Recent Developments in the Mathematics of Fuzzy Sets

  • Editors: Stephen Ernest Rodabaugh, Erich Peter Klement

  • Series Title: Trends in Logic

  • DOI: https://doi.org/10.1007/978-94-017-0231-7

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media B.V. 2003

  • Hardcover ISBN: 978-1-4020-1515-1Published: 30 September 2003

  • Softcover ISBN: 978-90-481-6378-6Published: 04 December 2010

  • eBook ISBN: 978-94-017-0231-7Published: 14 March 2013

  • Series ISSN: 1572-6126

  • Series E-ISSN: 2212-7313

  • Edition Number: 1

  • Number of Pages: XI, 470

  • Topics: Mathematical Logic and Foundations, Geometry, Order, Lattices, Ordered Algebraic Structures, Group Theory and Generalizations, Logic

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