Jensen-type inequalities for Sugeno integral

In this paper, the classical Jensen inequalities for concave function φ, i.e.,φ(∫f(x)dμ)⩾∫φ(f)dμandφ(∑i=1nλixi)⩾∑i=1nλiφ(xi),are adapted for the Sugeno integral using the notion of the supergradient. Moreover, we give some modifications of previous results of Román-Flores et al. concerning Jensen-ty...

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Published inInformation sciences Vol. 376; pp. 148 - 157
Main Authors Abbaszadeh, Sadegh, Gordji, Madjid Eshaghi, Pap, Endre, Szakál, Anikó
Format Journal Article
LanguageEnglish
Published Elsevier Inc 10.01.2017
Subjects
Concave function
Inequalities
Integrals
Sugeno integral
Superdifferential
Supergradient
The Jensen inequality
Concave function
The Jensen inequality
Sugeno integral
Supergradient
Superdifferential
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Summary:In this paper, the classical Jensen inequalities for concave function φ, i.e.,φ(∫f(x)dμ)⩾∫φ(f)dμandφ(∑i=1nλixi)⩾∑i=1nλiφ(xi),are adapted for the Sugeno integral using the notion of the supergradient. Moreover, we give some modifications of previous results of Román-Flores et al. concerning Jensen-type inequalities for Sugeno integral. Some examples in the framework of the Lebesgue measure and counting measure to illustrate the results are presented.
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ISSN:0020-0255
1872-6291
DOI:10.1016/j.ins.2016.10.006