Song, Y.Z., Song, X.Q., et al. (2015) Berwald Type Inequality for Extremal Universal Integrals Based on (α,m)-Concave Function. Journal of Mathematical Inequalities, 1, 1-15.
http://dx.doi.org/10.7153/jmi-09-01

has been cited by the following article:

• TITLE: Some General Inequalities for Choquet Integral

  AUTHORS: Xiuli Yang, Xiaoqiu Song, Leilei Huang

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

  JOURNAL NAME: Applied Mathematics, Vol.6 No.14, December 30, 2015

  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.