AM  Vol.6 No.14 , December 2015
Some General Inequalities for Choquet Integral
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.

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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