对数凸函数的Choquet积分  

Choquet Integrals of Log-convex Functions

作　　者：王洪霞[1,2] WANG Hong-xia(Statistics and Big Data College,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 [2]河南省教育统计数据分析与研究中心

出　　处：《模糊系统与数学》2019年第6期29-36,共8页Fuzzy Systems and Mathematics

基　　金：河南省高等学校重点科研项目(18A110011)

摘　　要：本文研究了对数凸函数的Choquet积分的上界和下界。首先,对于连续可微的对数凸函数,当其单调时,研究了其Choquet积分的Hadamard不等式;当其不单调时,分别在扭曲勒贝格测度和非可加测度下,研究了其Choquet积分的上界。接着,在非可加测度是凹的情形下,给出了对数E函数的Choquet积分的詹淼不等式,并举例说明其可用来估计Choquet积分的下界。In this paper,we investigate the upper bound and the lower bound of the Choquet integral for log-convex functions.Firstly,for monotone log-convex function we state the similar Hadamard inequality of the Choquet integral in the framework of distorted measure.Secondly,we estimate the upper bound of the Choquet integral for general log-convex function.Finally,we present Jensen's inequality of the Choquet integral for log-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 对数凸函数 不等式 

分 类 号：O211[理学—概率论与数理统计]