Overview
- 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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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.
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Keywords
Table of contents (13 chapters)
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Front Matter
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Back Matter
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
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