基于r-凸函数的Choquet积分不等式  

Choquet Integral Inequalities Based on r-convex Functions

作　　者：王洪霞[1,2] WANG Hong-xia(Department of Statistics,Henan University of Economics and Law,Zhengzhou 450046,China;Analysis and Research Center on Education and Statistic Data of Henan Province,Zhengzhou 450046.China)

机构地区：[1]河南财经政法大学统计与大数据学院,河南郑州450046 [2]河南省教育统计数据分析与研究中心,河南郑州450046

出　　处：《模糊系统与数学》2020年第4期57-65,共9页Fuzzy Systems and Mathematics

基　　金：河南省高等学校重点科研项目(18A110011);河南省哲学社会科学规划项目(2019BJJ011)。

摘　　要：本文研究了r-凸函数的Choquet积分的Hadamard不等式和詹森不等式。首先,针对单调r-凸函数,研究了其Choquet积分的类似Hadamard型不等式;接着,分别在扭曲勒贝格测度和非可加测度下,估计了r-凸函数的Choquet积分的上界;最后,在非可加测度是凹的情形下,给出了两个r-凸函数的Choquet积分的詹森不等式,其可用来估计Choquet积分的下界。另外,在扭曲勒贝格测度下,对文中所有结果进行了例证。In this paper we investigate the Hadamard inequality and Jensen’s inequality of Choquet integral for r-convex functions. Firstly, for monotone r-convex function we state the similar Hadamard inequality of the Choquet integral. Secondly, we estimate the upper bound of Choquet integral for general r-convex function, respectively, in the ditorted Lebesgue measure and in the non-additive measure. Finally, we present two Jensen’s inequalities of Choquet integral for r-convex functions, which can be used to estimate the lower bound of this kind, when the non-additive measure is concave. We provide some examples in the framework of the distorted Lebesgue measure to illustrate all the results.

关 键 词：CHOQUET积分 R-凸函数 不等式 

分 类 号：O211[理学—概率论与数理统计]