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Indistinguishability Operators

Modelling Fuzzy Equalities and Fuzzy Equivalence Relations

  • Book
  • © 2011

Overview

Authors:
  1. Jordi Recasens

    1. Department of Mathematics and Computer Sciences, ETS Arquitectura del Vallès, Sant Cugat del Vallès, Spain

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  • Well organized book with very clear mathematical reasoning
  • Helps to better understand the world of ideas related to imprecise partitionings and the major aspects of indistinguishability operators
  • Written by a leading expert in the field

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

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Table of contents (13 chapters)

  1. Front Matter

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  2. Introduction

    • Jordi Recasens
    Pages 1-12

  3. Generating Indistinguishability Operators

    • Jordi Recasens
    Pages 13-39

  4. Granularity and Extensional Sets

    • Jordi Recasens
    Pages 41-79

  5. Isometries between Indistinguishability Operators

    • Jordi Recasens
    Pages 81-95

  6. Min-indistinguishability Operators and Hierarchical Trees

    • Jordi Recasens
    Pages 97-105

  7. Betweenness Relations

    • Jordi Recasens
    Pages 107-124

  8. Dimension and Basis

    • Jordi Recasens
    Pages 125-145

  9. Aggregation of Indistinguishability Operators

    • Jordi Recasens
    Pages 147-161

  10. Making Proximities Transitive

    • Jordi Recasens
    Pages 163-176

  11. Fuzzy Functions

    • Jordi Recasens
    Pages 177-188

  12. Indistinguishability Operators and Approximate Reasoning

    • Jordi Recasens
    Pages 189-199

  13. Vague Groups

    • Jordi Recasens
    Pages 201-215

  14. Finitely Valued Indistinguishability Operators

    • Jordi Recasens
    Pages 217-231

  15. Back Matter

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Keywords

About this book

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.

Reviews

From the reviews:

“This well-written monograph is the first one which is devoted to this topic, and hence highly welcome. The author offers a … comprehensive and up to date presentation of the theory of these operators.” (Siegfried J. Gottwald, Zentralblatt MATH, Vol. 1215, 2011)

Authors and Affiliations

  • Department of Mathematics and Computer Sciences, ETS Arquitectura del Vallès, Sant Cugat del Vallès, Spain

    Jordi Recasens

Bibliographic Information

  • Book Title: Indistinguishability Operators

  • Book Subtitle: Modelling Fuzzy Equalities and Fuzzy Equivalence Relations

  • Authors: Jordi Recasens

  • Series Title: Studies in Fuzziness and Soft Computing

  • DOI: https://doi.org/10.1007/978-3-642-16222-0

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Engineering, Engineering (R0)

  • Copyright Information: Springer Berlin Heidelberg 2011

  • Hardcover ISBN: 978-3-642-16221-3Published: 30 September 2010

  • Softcover ISBN: 978-3-642-42333-8Published: 11 October 2014

  • eBook ISBN: 978-3-642-16222-0Published: 02 October 2010

  • Series ISSN: 1434-9922

  • Series E-ISSN: 1860-0808

  • Edition Number: 1

  • Number of Pages: XVII, 244

  • Topics: Computational Intelligence, Artificial Intelligence

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