Markov type inequalities for fuzzy integrals
type: Item
instance of: scholarly article
title: Markov type inequalities for fuzzy integrals
zbMATH Open document ID: 1178.28029
author: A. Flores-Franulič
author: Heriberto E. Román-Flores
author: Yurilev Chalco-Cano
published in: Applied Mathematics and Computation
publication date: 2009-03-02T00:00:00Z
review text: Given a fuzzy measure space \((X,\Sigma,\mu)\) and a \(\mu\)-measurable nonnegative function \(f:X\to[0,\infty)\), a typical result from the paper is the following inequality: For \(0<c\leq1\), \[ \mu\{x\in A:f(x)\geq c\}\leq\frac{1}{c} \fint_A f(t)dt, \] where \(-\!\!\!\!\!\int\) stands dor the Sugeno fuzzy integral defined by \[ \fint_A f(t)dt := \sup_{\alpha\geq 0}\min\big(\alpha,\mu\{x\in A:f(x)\geq\alpha\}\big). \] This inequality can be regarded as the analogue of Markov's inequality for the Sugeno integral setting. The paper also contains various generalizations of the above inequality and fundamental properties of the Sugeno integral are established.
reviewed by: Zsolt Páles
Mathematics Subject Classification ID: 28E10
Mathematics Subject Classification ID: 26E50
zbMATH DE Number: 5522209
zbMATH Keywords: Markov's inequality
zbMATH Keywords: Sugeno's fuzzy integral
MaRDI profile type: Publication
full work available at URL: j.amc.2008.10.029
OpenAlex ID: W2007283741
cites work: SUGENO INTEGRAL AND GEOMETRIC INEQUALITIES
cites work: The fuzzy integral for monotone functions
cites work: A Jensen type inequality for fuzzy integrals
cites work: A Chebyshev type inequality for fuzzy integrals
cites work: A convolution type inequality for fuzzy integrals
cites work: A note on fuzzy integral inequality of Stolarsky type
cites work: Q4271955
cites work: Probability and Computing
cites work: The fuzzy integral
DOI: 10.1016/J.AMC.2008.10.029
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description: scientific article; zbMATH DE number 5522209