Indistinguishability Operators

Modelling Fuzzy Equalities and Fuzzy Equivalence Relations

  • Jordi Recasens

Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 260)

Table of contents

  1. Front Matter
  2. Jordi Recasens
    Pages 1-12
  3. Jordi Recasens
    Pages 13-39
  4. Jordi Recasens
    Pages 41-79
  5. Jordi Recasens
    Pages 107-124
  6. Jordi Recasens
    Pages 125-145
  7. Jordi Recasens
    Pages 147-161
  8. Jordi Recasens
    Pages 163-176
  9. Jordi Recasens
    Pages 177-188
  10. Jordi Recasens
    Pages 201-215
  11. Jordi Recasens
    Pages 217-231
  12. Back Matter

About this book

Introduction

Indistinguishability operators are essential tools in fuzzy logic since they fuzzify the concepts of equivalence relation and crisp equality. This book collects all the main aspects of these operators in a single volume for the first time. The stress is put on the study of their structure and the monograph starts presenting the different ways in which indistinguishability operators can be generated and represented. Special attention is paid to the Representation Theorem and the Sup-T product. Extensionality of fuzzy subsets is studied in detail and is related to their observability and to the granularity. The metric behaviour of indistinguishability operators and their connection with cluster analysis and hierarchical trees is established. Different ways to aggregate such operators are given as well as a number of methods to obtain transitive approximations of a fuzzy relation. Applications to approximate reasoning and to the study of fuzzy subgroups are also provided. The book ends with a chapter on finite-valued indistinguishability operators.

Keywords

Fuzziness Indistinguishability Operators Modelling Fuzzy Equalities Modelling Fuzzy Equivalence Relations

Authors and affiliations

  • Jordi Recasens
    • 1
  1. 1.Department of Mathematics and Computer SciencesETS Arquitectura del VallèsSant Cugat del VallèsSpain

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-16222-0
  • Copyright Information Springer Berlin Heidelberg 2011
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Engineering
  • Print ISBN 978-3-642-16221-3
  • Online ISBN 978-3-642-16222-0
  • Series Print ISSN 1434-9922
  • Series Online ISSN 1860-0808
  • About this book
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