ENGLISH

Indistinguishability Operators: Modelling Fuzzy Equalities and Fuzzy Equivalence Relations

By Jordi Recasens (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
2011
ISBN
3642162215, 9783642162213
DOI
10.1007/978-3-642-16222-0
Language
english
Format
PDF
Filesize
4 MB (4413130 bytes)
Series
Studies in Fuzziness and Soft Computing 260
Edition
1
Pages
244\262
Topic
Education
Time added
2011-06-04 13:46:07
Computational Intelligence; Artificial Intelligenc

Description

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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