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Recasens, Jordi

Indistinguishability Operators Modelling Fuzzy Equalities and Fuzzy Equivalence Relations (Gebundene Ausgabe)

Reihe: Studies in Fuzziness and Soft Computing 260

Springer-Verlag GmbH, November 2010

244 S. - Sprache: Englisch - 244x167x23 mm

ISBN: 3642162215 EAN: 9783642162213

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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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


Introduction.- Granularity and Extensional Sets.- Isometries Between Indistinguishability Operators.- min-indistinguishability Operators and Hierarchical Trees.- Betweenness Relations.- Dimension and Basis.- Aggregation of Indistinguishability Operators.- Making Proximities Transitive.- Fuzzy Functions.- Indistinguishability Operators and Approximate Reasoning.- Vague Groups.- Finitely Valued Indistinguishability Operators.


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)

ISBN 3-642-16221-5

ISBN 978-3-642-16221-3

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