On the closure of families of fuzzy measures under eventwise aggregations
type: Item
instance of: scholarly article
title: On the closure of families of fuzzy measures under eventwise aggregations
zbMATH Open document ID: 1068.28012
published in: Fuzzy Sets and Systems
publication date: 2005-06-13T00:00:00Z
review text: The paper discusses several special families of fuzzy measures, especially their closedness under distortion and under aggregation. A special attention is paid to the coherent lower probabilities, \(k\)-monotone fuzzy measures and belief measures (compare also [\textit{L. Valášková} and \textit{P. Struk}, Kybernetika 41, No.~2, 205--212 (2005)]. For example, an aggregation \(A(m_1,\dots,m_n)\) of belief measures \(m_1,\dots,m_n\) is a belief measure independent of the underlying measurable space and incoming belief measures if and only if \(A\) is totally monotone, i.e., if all partial derivatives of any order exist and are non-negative. Observe that by duality, the corresponding results for the dual fuzzy measures can be obtained (e.g., for the coherent upper probabilities or for plausibility measures). Multilinear extensions of fuzzy measures to aggregation operators are also discussed.
reviewed by: Radko Mesiar
Mathematics Subject Classification ID: 28E10
zbMATH DE Number: 2175513
zbMATH Keywords: aggregation operator
zbMATH Keywords: fuzzy measure
zbMATH Keywords: coherent lower probability
zbMATH Keywords: \(k\)-monotonicity
zbMATH Keywords: multilinear extension
zbMATH Keywords: distortion function
author: Andrey G. Bronevich
MaRDI profile type: Publication
full work available at URL: j.fss.2004.12.005
OpenAlex ID: W2087590862
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DOI: 10.1016/J.FSS.2004.12.005
description: scientific article; zbMATH DE number 2175513