集值Choquet积分的性质  

On Some Properties of Set-valued Choquet Integrals

作　　者：王洪霞[1] 

机构地区：[1]河南财经政法大学统计学院,河南郑州450046

出　　处：《模糊系统与数学》2015年第2期24-33,共10页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(11171010);校重大科研基金资助项目(855006);河南省政府决策招标课题(2014139);河南省高等学校重点科研项目(15B110002)

摘　　要：集值Choquet积分,即集值随机变量关于容度的积分,可以用来描述现实生活中许多复杂的不确定现象。给出集值Choquet积分的基本性质;接着在Choquet可积有界的集值随机变量空间中,证明集值Choquet积分仍然保持单调性和次可积性;并且给出集值Choquet积分的Hausdorff距离满足的不等式。The set-valued Choquet integral, which is the integral of set-valued random variables with respect to capacities, may be used to model some complex phenomena in reality. In this note, we firstly present several basic properties of the set-valued Choquet integral. Then in the space of the Choquet integrable set-valued random variables, we prove the monotone property and subadditive property of setvalued Choquet integrals; and what＇s more, we present the inequality of the Hausdorff metric of two set- valued Choquet integrals.

关 键 词：集值Choquet积分 CHOQUET积分 集值随机变量 

分 类 号：O211[理学—概率论与数理统计]