独立不同分布不确定变量中心极限定理证明及其应用

doi:10.16183/j.cnki.jsjtu.2019.10.013

上海交通大学学报 ›› 2019, Vol. 53 ›› Issue (10): 1230-1237.doi: 10.16183/j.cnki.jsjtu.2019.10.013

独立不同分布不确定变量中心极限定理证明及其应用

孟祥飞，王瑛，李超，亓尧，孙贇

空军工程大学装备管理与无人机工程学院，西安 710051

出版日期:2019-10-28 发布日期:2019-11-01
通讯作者: 王瑛,女,教授,博士生导师, 电话（Tel.）：18133962570; E-mail：yingwangkgd@163.com.
作者简介:孟祥飞（1989-），男，河北省邢台市人,博士生，主要研究方向为不确定多目标规划模型求解及应用.
基金资助:
国家自然科学基金（71571190,71601183）资助项目

Central Limit Theorems Proving for Independent and Non-Identically Distributed Uncertain Variables and Its Application

MENG Xiangfei,WANG Ying,LI Chao,QI Yao,SUN Yun

Equipment Management and Unmanned Aerial Vehicle Engineering College, Air Force Engineering University, Xi’an 710051, China

Online:2019-10-28 Published:2019-11-01

摘要/Abstract

摘要： 针对不确定变量分布函数的问题，提出了两个不确定中心极限定理.定义了不确定变量的特征函数并基于期望计算法则提出了特征函数的计算方法.分析了不确定变量特征函数的性质.将随机理论中的正态分布引入到不确定理论中，证实了该分布在形式上为一种正则不确定分布.通过新型坦克射击测试的案例验证了所提定理的可行性和有效性.

关键词: 不确定理论；独立不同分布变量；中心极限定理；特征函数

Abstract: In order to determine the distribution of uncertain variables, two central limit theorems for independent and identical variables are proposed. Firstly, the characteristic function of uncertain variables is defined and its calculation formula is given based on the expected value of uncertain variables. Secondly, the properties of the characteristic function are analyzed and the normal distribution in probability theory is introduced into uncertainty theory. It is proved that the distribution can also be regarded as an uncertain one. Finally, an example of shooting accuracy of a new kind of tanks moving at a high speed is given to verify the feasibility and effectiveness of the proposed theorems.

Key words: uncertainty theory; independent and non-identically distributed uncertain variables; central limit theorem; characteristic functions

中图分类号:

O 212

孟祥飞，王瑛，李超，亓尧，孙贇. 独立不同分布不确定变量中心极限定理证明及其应用[J]. 上海交通大学学报, 2019, 53(10): 1230-1237.

MENG Xiangfei,WANG Ying,LI Chao,QI Yao,SUN Yun. Central Limit Theorems Proving for Independent and Non-Identically Distributed Uncertain Variables and Its Application[J]. Journal of Shanghai Jiaotong University, 2019, 53(10): 1230-1237.

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独立不同分布不确定变量中心极限定理证明及其应用

Central Limit Theorems Proving for Independent and Non-Identically Distributed Uncertain Variables and Its Application

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