Conditions for Choquet integral representation of the comonotonically additive and monotone functional.
type: Item
instance of: scholarly article
title: Conditions for Choquet integral representation of the comonotonically additive and monotone functional.
zbMATH Open document ID: 1045.28015
DOI: 10.1016/S0022-247X(03)00139-2
author: Yasuo Narukawa
author: Toshiaki Murofushi
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-07-30T00:00:00Z
review text: In the paper a locally compact space \(X\) is considered. Two real functions \(f\), \(g\) are comonotonic \((f\sim g)\) if \(f(x)< f(x')\) implies \(g(x)\leq g(x')\). A functional \(I\) is comonotonically additive, if \(f\sim g\) implies \(I(f+ g)= I(f)+ I(g)\) and \(f\leq g\) implies \(I(f)\leq I(g)\). There are given some conditions for the possibility to represent a comonotonically additive functional as a Choquet integral. The results are based on the paper by \textit{Y. Narukawa}, \textit{T. Murofushi} and \textit{M. Sugeno} [Fuzzy Sets Syst. 112, No. 2, 177--186 (2000; Zbl 0954.28007)].
reviewed by: Beloslav Riečan
Mathematics Subject Classification ID: 28E10
zbMATH DE Number: 1956911
zbMATH Keywords: nonadditive measure
zbMATH Keywords: fuzzy measure
zbMATH Keywords: cooperative game
zbMATH Keywords: Choquet integral
zbMATH Keywords: comonotonic additivity
MaRDI profile type: Publication
Wikidata QID: Q62609320
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description: scientific article; zbMATH DE number 1956911