Topological and Algebraic Structures in Fuzzy Sets

A Handbook of Recent Developments in the Mathematics of Fuzzy Sets

  • Stephen Ernest Rodabaugh
  • Erich Peter Klement

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

Table of contents

  1. Front Matter
    Pages i-xi
  2. Introduction

    1. Stephen Ernest Rodabaugh, Erich Peter Klement
      Pages 1-16
  3. Topological Structures in Fuzzy Sets

    1. Front Matter
      Pages 17-17
    2. B. Banaschewski
      Pages 19-56
    3. W. Gähler
      Pages 57-79
    4. J. Gutiérrez García, M. A. de Prada Vicente, A. P. Šostak
      Pages 81-114
    5. U. Höhle, S. E. Rodabaugh
      Pages 189-197
    6. L. N. Stout
      Pages 235-253
  4. Algebraic Structures in Fuzzy Sets

    1. Front Matter
      Pages 255-255
    2. M. Gehrke, C. Walker, E. Walker
      Pages 257-276
    3. S. Jenei
      Pages 277-308
    4. C. J. Mulvey
      Pages 309-336
  5. Related Topics in Topological and Algebraic Structures

    1. Front Matter
      Pages 373-373
    2. Bernard De Baets, Radko Mesiar
      Pages 389-400

About this book

Introduction

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.

Keywords

Algebraic structure Lattice Volume algebra logic

Editors and affiliations

  • Stephen Ernest Rodabaugh
    • 1
  • Erich Peter Klement
    • 2
  1. 1.Department of Mathematics and StatisticsYoungstown State UniversityYoungstownUSA
  2. 2.Institut für Algebra, Stochastik und wissensbasierte mathematische SystemeJohannes Kepler UniversitätLinzAustria

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-017-0231-7
  • Copyright Information Springer Science+Business Media B.V. 2003
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-6378-6
  • Online ISBN 978-94-017-0231-7
  • Series Print ISSN 1572-6126
  • Series Online ISSN 2212-7313
  • About this book
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