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Applications of Category Theory to Fuzzy Subsets

  • Book
  • © 1992

Overview

Editors:
  1. Stephen Ernest Rodabaugh

    1. Department of Mathematical and Computer Sciences, Youngstown State University, Youngstown, USA

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  2. Erich Peter Klement

    1. Institut für Mathematik, Johannes Kepler Universität, Linz, Austria

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    You can also search for this editor in PubMed   Google Scholar

  3. Ulrich Höhle

    1. Fachbereich Mathematik, Bergische Universität, Wuppertal, Germany

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Theory and Decision Library B (TDLB, volume 14)

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Table of contents (14 chapters)

  1. Front Matter

    Pages i-ix
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  2. Introduction

    1. Introduction

      • Stephen Ernest Rodabaugh, Erich Peter Klement, Ulrich Höhle
      Pages 3-5

  3. Topos-like and Model-Theoretic Approaches

    1. Front Matter

      Pages 7-7
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    2. Classification of Extremal Subobjects of Algebras Over SM-SET

      • J. Coulon, J.-L Coulon, U. Höhle
      Pages 9-31

    3. M-valued Sets and Sheaves over Integral Commutative CL-Monoids

      • U. Höhle
      Pages 33-72

    4. The Logic of Unbalanced Subobjects in a Category with Two Closed Structures

      • L. N. Stout
      Pages 73-105

  4. Categorical Methods in Topology

    1. Front Matter

      Pages 107-107
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    2. Fuzzy Filter Functions and Convergence

      • P. Eklund, W. Gähler
      Pages 109-136

    3. Convenient Topological Constructs

      • H. Herrlich
      Pages 137-151

    4. A Topological Universe Extension of FTS

      • E. Lowen, R. Lowen
      Pages 153-176

    5. Categorical Frameworks for Stone Representation Theories

      • S. E. Rodabaugh
      Pages 177-231

  5. Applications and Related Topics in Logic and Topology

    1. Front Matter

      Pages 233-233
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    2. Pointless Metric Spaces and Fuzzy Spaces

      • G. Gerla
      Pages 235-244

    3. Fuzzy Unit Interval and Fuzzy Paths

      • F. Klawonn
      Pages 245-256

    4. Lattice Morphisms, Sobriety, and Urysohn Lemmas

      • W. Kotzé
      Pages 257-274

    5. The Topological Modification of the L-fuzzy Unit Interval

      • T. Kubiák
      Pages 275-305

    6. A Categorical Approach to Fuzzy Relational Database Theory

      • W. A. MacCaull
      Pages 307-324

    7. Fuzzy Points and Membership

      • M. W. Warner
      Pages 325-334

  6. Back Matter

    Pages 335-399
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Keywords

About this book

This book has a fundamental relationship to the International Seminar on Fuzzy Set Theory held each September in Linz, Austria. First, this volume is an extended account of the eleventh Seminar of 1989. Second, and more importantly, it is the culmination of the tradition of the preceding ten Seminars. The purpose of the Linz Seminar, since its inception, was and is to foster the development of the mathematical aspects of fuzzy sets. In the earlier years, this was accomplished by bringing together for a week small grou ps of mathematicians in various fields in an intimate, focused environment which promoted much informal, critical discussion in addition to formal presentations. Beginning with the tenth Seminar, the intimate setting was retained, but each Seminar narrowed in theme; and participation was broadened to include both younger scholars within, and established mathematicians outside, the mathematical mainstream of fuzzy sets theory. Most of the material of this book was developed over the years in close association with the Seminar or influenced by what transpired at Linz. For much of the content, it played a crucial role in either stimulating this material or in providing feedback and the necessary screening of ideas. Thus we may fairly say that the book, and the eleventh Seminar to which it is directly related, are in many respects a culmination of the previous Seminars.

Editors and Affiliations

  • Department of Mathematical and Computer Sciences, Youngstown State University, Youngstown, USA

    Stephen Ernest Rodabaugh

  • Institut für Mathematik, Johannes Kepler Universität, Linz, Austria

    Erich Peter Klement

  • Fachbereich Mathematik, Bergische Universität, Wuppertal, Germany

    Ulrich Höhle

Bibliographic Information

  • Book Title: Applications of Category Theory to Fuzzy Subsets

  • Editors: Stephen Ernest Rodabaugh, Erich Peter Klement, Ulrich Höhle

  • Series Title: Theory and Decision Library B

  • DOI: https://doi.org/10.1007/978-94-011-2616-8

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: Kluwer Academic Publishers 1992

  • Hardcover ISBN: 978-0-7923-1511-7Published: 30 November 1991

  • Softcover ISBN: 978-94-010-5156-9Published: 21 October 2012

  • eBook ISBN: 978-94-011-2616-8Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: IX, 398

  • Topics: Category Theory, Homological Algebra, Mathematical Logic and Foundations, Geometry

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