Author(s)

Xiuli Yang, Xiaoqiu Song^*, Leilei Huang

College of Science, China University of Mining and Technology, Xuzhou, China.

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, …, f_n are comonotone, we also obtain the Hölder inequality, Minkowski inequality and Lyapunov inequality hold for Choquet integral.

Choquet Integral, Fuzzy Measure, Comonotone, Hölder Inequality, Minkowski Inequality, Lyapunov Inequality

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.