集值函数关于非可加集值测度的Choquet积分

doi:10.6040/j.issn.1671-9352.0.2014.340

山东大学学报（理学版） ›› 2015, Vol. 50 ›› Issue (08): 62-71.doi: 10.6040/j.issn.1671-9352.0.2014.340

集值函数关于非可加集值测度的Choquet积分

巩增泰, 魏朝琦

西北师范大学数学与统计学院, 甘肃兰州 730070

收稿日期:2014-07-02 出版日期:2015-08-20 发布日期:2015-07-31
作者简介:巩增泰(1966- ), 男, 博士, 教授, 研究方向为实分析、模糊分析学和粗糙集理论. E-mail:gongzt@nwnu.edu.cn
基金资助:
国家自然科学基金资助项目(61262022, 11461062)

Choquet integral of set-valued functions with respect to multisubmeasures

GONG Zeng-tai, WEI Zhao-qi

College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China

Received:2014-07-02 Online:2015-08-20 Published:2015-07-31

摘要/Abstract

摘要： 按照集值积分的经典定义方法,不可避免地涉及集值函数和集值测度两方面的选择问题.本文利用集值函数关于非可加测度的实值Choquet积分,定义和讨论了集值函数关于非可加集值测度的Choquet积分,并刻画了其原函数性质.结果表明,弱零可加性、零可加性、凸零可加性、伪度量性质以及Darboux性质在其不定积分中均可遗传到其原函数中.

关键词: 集值测度, Choquet积分, 集值函数

Abstract: It is inevitable for the problem how to deal with two aspects of selections for a set-valued function and a multisubmeasure according to the classical definition method of the set-valued integral. The Choquet integral of a set-valued function with respect to a multisubmeasure is defined and discussed by using the real-valued Choquet integral of the set-valued function with respect to the non-additive measure, and some basic properties are characterized. It shows that a lot of characters could be well kept to their primitives such as the weakly null-additive, null-additive, converse null-additive, the pseudometric property and the Darboux property, and so on.

Key words: set-valued functions, multisubmeasures, Choquet integral

中图分类号:

O175.8

巩增泰, 魏朝琦. 集值函数关于非可加集值测度的Choquet积分[J]. 山东大学学报（理学版）, 2015, 50(08): 62-71.

GONG Zeng-tai, WEI Zhao-qi. Choquet integral of set-valued functions with respect to multisubmeasures[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(08): 62-71.

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集值函数关于非可加集值测度的Choquet积分

Choquet integral of set-valued functions with respect to multisubmeasures

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