Indistinguishability Operators
Modelling Fuzzy Equalities and Fuzzy Equivalence Relations
(Sprache: Englisch)
This book examines various aspects of indistinguishability operators. It is intended to be useful to people involved in either theory and applications who are interested in systems dealing with uncertainty and soft computing in general.
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This book examines various aspects of indistinguishability operators. It is intended to be useful to people involved in either theory and applications who are interested in systems dealing with uncertainty and soft computing in general.
Klappentext zu „Indistinguishability Operators “
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.
Inhaltsverzeichnis zu „Indistinguishability Operators “
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.
Bibliographische Angaben
- Autor: Jordi Recasens
- 2014, 2011, XVII, 244 Seiten, Maße: 15,5 x 23,5 cm, Kartoniert (TB), Englisch
- Verlag: Springer, Berlin
- ISBN-10: 3642423337
- ISBN-13: 9783642423338
Sprache:
Englisch
Pressezitat
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)
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