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Studies in Fuzziness and Soft Computing

Indistinguishability Operators

Modelling Fuzzy Equalities and Fuzzy Equivalence Relations

Authors: Recasens, Jordi

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  • Features well-organized coverage with very clear mathematical reasoning
  • Helps readers to better understand the world of ideas related to imprecise partitionings and the major aspects of indistinguishability operators
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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)

Table of contents (13 chapters)

Table of contents (13 chapters)

Buy this book

eBook $119.00
price for USA in USD
  • ISBN 978-3-642-16222-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $199.99
price for USA in USD
  • ISBN 978-3-642-16221-3
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually ready to be dispatched within 3 to 5 business days.
Softcover $159.99
price for USA in USD
  • ISBN 978-3-642-42333-8
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually ready to be dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Indistinguishability Operators
Book Subtitle
Modelling Fuzzy Equalities and Fuzzy Equivalence Relations
Authors
Series Title
Studies in Fuzziness and Soft Computing
Series Volume
260
Copyright
2011
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer Berlin Heidelberg
eBook ISBN
978-3-642-16222-0
DOI
10.1007/978-3-642-16222-0
Hardcover ISBN
978-3-642-16221-3
Softcover ISBN
978-3-642-42333-8
Series ISSN
1434-9922
Edition Number
1
Number of Pages
XVII, 244
Topics

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