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Indistinguishability Operators

Modelling Fuzzy Equalities and Fuzzy Equivalence Relations

By: Jordi Recasens

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Indistinguishability Operators

Modelling Fuzzy Equalities and Fuzzy Equivalence Relations

By: Jordi Recasens

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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Page Count

250

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642162215

ISBN 13

9783642162213

Indistinguishability Operators

Modelling Fuzzy Equalities and Fuzzy Equivalence Relations

By: Jordi Recasens

Write a review Read reviews Take a Quiz Solve Book Puzzle

Indistinguishability Operators

Modelling Fuzzy Equalities and Fuzzy Equivalence Relations

By: Jordi Recasens

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.

Average ratings

N/A

5

0%

4

0%

3

0%

2

0%

1

0%

Solve jigsaw puzzle

Age

Page Count

250

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642162215

ISBN 13

9783642162213