Indistinguishability operators: modelling fuzzy equalities and fuzzy equivalence relations

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 firsttime. 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 metricbehaviour of indistinguishability operators and their connection with clusteranalysis 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 tothe study of fuzzy subgroups are also provided. The book ends with a chapter on finite-valued indistinguishability operators. Well organized book with veryclear mathematical reasoning Helps to better understand the world of ideas related to imprecise partitionings and the major aspects of indistinguishabilityoperators Written by a leading expert in the field INDICE: Introduction.- Granularity and Extensional Sets.- Isometries Between Indistinguishability Operators.- min-indistinguishability Operators and Hierarchical Trees.- Betweenness Relations.- Dimension and Basis.- Aggregation ofIndistinguishability Operators.- Making Proximities Transitive.- Fuzzy Functions.- Indistinguishability Operators and Approximate Reasoning.- Vague Groups.- Finitely Valued Indistinguishability Operators.

• ISBN: 978-3-642-16221-3
• Editorial: Springer
• Encuadernacion: Cartoné
• Páginas: 262
• Fecha Publicación: 30/09/2010
• Nº Volúmenes: 1
• Idioma: Inglés