Studies in Fuzziness and Soft Computing: Modelling Fuzzy Equalities and Fuzzy Equivalence Relations

Recasens, Jordi

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.

Details

Published by: Springer

Publication Date: 2010-09-30

Format: Hardcover

ISBN-13: 9783642162213

DOI: 10.1007/978-3-642-16222-0

Dimensions: 235cm x155cm

Pages: 244