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Some General Inequalities for Choquet Integral

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DOI: 10.4236/am.2015.614201    2,408 Downloads   3,017 Views   Citations

ABSTRACT

With the development of fuzzy measure theory, the integral inequalities based on Sugeno integral are extensively investigated. We concern on the inequalities of Choquuet integral. The main purpose of this paper is to prove the H?lder inequality for any arbitrary fuzzy measure-based Choquet integral whenever any two of these integrated functions f, g and h are comonotone, and there are three weights. Then we prove Minkowski inequality and Lyapunov inequality for Choquet integral. Moreover, when any two of these integrated functions f1, f2, , fn are comonotone, we also obtain the Hölder inequality, Minkowski inequality and Lyapunov inequality hold for Choquet integral.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Yang, X. , Song, X. and Huang, L. (2015) Some General Inequalities for Choquet Integral. Applied Mathematics, 6, 2292-2299. doi: 10.4236/am.2015.614201.

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