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Titlebook: Indistinguishability Operators; Modelling Fuzzy Equa Jordi Recasens Book 2011 Springer Berlin Heidelberg 2011 Fuzziness.Indistinguishabilit

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发表于 2025-3-21 19:06:32 | 显示全部楼层 |阅读模式
书目名称Indistinguishability Operators
副标题Modelling Fuzzy Equa
编辑Jordi Recasens
视频video
概述Well organized book with very clear mathematical reasoning.Helps to better understand the world of ideas related to imprecise partitionings and the major aspects of indistinguishability operators.Writ
丛书名称Studies in Fuzziness and Soft Computing
图书封面Titlebook: Indistinguishability Operators; Modelling Fuzzy Equa Jordi Recasens Book 2011 Springer Berlin Heidelberg 2011 Fuzziness.Indistinguishabilit
描述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.
出版日期Book 2011
关键词Fuzziness; Indistinguishability Operators; Modelling Fuzzy Equalities; Modelling Fuzzy Equivalence Rela
版次1
doihttps://doi.org/10.1007/978-3-642-16222-0
isbn_softcover978-3-642-42333-8
isbn_ebook978-3-642-16222-0Series ISSN 1434-9922 Series E-ISSN 1860-0808
issn_series 1434-9922
copyrightSpringer Berlin Heidelberg 2011
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Generating Indistinguishability Operators, and the use we want to make of them. The four most common ways are:.In many situations, data come packed as a reflexive and symmetric fuzzy matrix or relation ., also known as a proximity or tolerance relation. When, for coherence, transitivity is also required, the relation . must be replaced by a
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Min-indistinguishability Operators and Hierarchical Trees,uishability operator on a set . and . ∈ [0,1], the .-cuts of . are partitions of . and if . ≥ ., then the .-cut is a refinement of the partition corresponding to the .-cut. Therefore, . generates an indexed hierarchical tree. Reciprocally, from an indexed hierarchical tree a min -indistinguishabilit
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Aggregation of Indistinguishability Operators, suppose, for example that we have a set of instances defined by some features. We can generate an indistinguishability operator or a fuzzy preorder from each feature. Also, we can have some prototypes, and again we can define a relation from each of them in our universe. In these cases we may need
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