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Erschienen in:
Toward a Restriction-Centered Theory of Truth and Meaning (RCT) Kapitel lesen Erstes Kapitel lesen

2015 | OriginalPaper | Buchkapitel

Fuzzy Measures and Integrals: Recent Developments

verfasst von : Michel Grabisch

Erschienen in: Fifty Years of Fuzzy Logic and its Applications

Verlag: Springer International Publishing

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Abstract

This paper surveys the basic notions and most important results around fuzzy measures and integrals, as proposed independently by Choquet and Sugeno, as well as recent developments. The latter includes bases and transforms on set functions, fuzzy measures on set systems, the notion of horizontal additivity, basic Choquet calculus on the nonnegative real line introduced by Sugeno, the extension of the Choquet integral for nonmeasurable functions, and the notion of universal integral.

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Vorheriges Kapitel Incremental Granular Fuzzy Modeling Using Imprecise Data Streams
Nächstes Kapitel Important New Terms and Classifications in Uncertainty and Fuzzy Logic
Fußnoten
1
A chain from \(\varnothing \) to \(X\) is a sequence \(\varnothing =A_0,A_1,\ldots , A_q=X\) of sets in \({\mathcal F}\) such that \(A_0\subset A_1\subset \cdots \subset A_q\). Its length is \(q\), and the chain is maximal if no other chain from \(\varnothing \) to \(X\) contains it.
 
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Metadaten
Titel
Fuzzy Measures and Integrals: Recent Developments
verfasst von
Michel Grabisch
Copyright-Jahr
2015
Buch
Fifty Years of Fuzzy Logic and its Applications

Print ISBN: 978-3-319-19682-4

Electronic ISBN: 978-3-319-19683-1

Copyright-Jahr: 2015

DOI
https://doi.org/10.1007/978-3-319-19683-1_8