Inner and outer representation by Choquet integral
type: Item
instance of: scholarly article
title: Inner and outer representation by Choquet integral
zbMATH Open document ID: 1143.28008
author: Yasuo Narukawa
published in: Fuzzy Sets and Systems
publication date: 2007-05-04T00:00:00Z
review text: A non-additive measure \(\mu\) is \(i\)-regular, if its values at a compact set \(C\) can be aproximated by values \(\mu (O)\), where \(O\) is an open set, \(C \subseteq O\). In a similar way an \(o\)-regular non-additive measure is defined, where its values at an open set \(O\) can be aproximated by values \(\mu (C)\), where \(C\) is as above. Representation theorems of a comonotone additive and monotone function by a Choquet integral are shown using \(o\)-regular and \(i\)-regular non-additive measures. Also the representation of a comonotone additive monotone functional is shown.
reviewed by: Vladimír Janiš
Mathematics Subject Classification ID: 28E10
zbMATH DE Number: 5149450
zbMATH Keywords: fuzzy measure, non-additive measure
zbMATH Keywords: Choquet integral
Wikidata QID: Q62609316
MaRDI profile type: Publication
full work available at URL: j.fss.2006.12.005
OpenAlex ID: W2056251380
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DBLP publication ID: journals/fss/Narukawa07
DOI: 10.1016/J.FSS.2006.12.005
description: scientific article; zbMATH DE number 5149450