一类梯形模糊随机变量的主成分分析  

Principal component analysis of a kind of trapezoidal fuzzy random variable

作　　者：李肖南 曲智林[1] LI Xiao-nan;QU Zhi-lin(School of Science,Northeast Forestry University,Harbin 150040,China)

机构地区：[1]东北林业大学理学院,150040

出　　处：《哈尔滨商业大学学报（自然科学版）》2021年第1期97-101,共5页Journal of Harbin University of Commerce：Natural Sciences Edition

基　　金：林业公益性行业科研专项资助(201404402)。

摘　　要：对模糊随机变量的主成分分析方向进行研究,其中相关矩阵是研究主成分分析的一个重要指标,而模糊随机变量与随机变量本质不同,所以不能直接用随机变量的相关矩阵进行使用.研究改进了随机变量的相关矩阵,将其推广到模糊随机变量中,通过给出两个模糊随机变量的α-贴近度概念构造了α-贴近度矩阵,利用α-贴近度矩阵作为模糊随机变量的相关矩阵研究了一类梯形模糊随机变量的主成分分析问题,通过实例分析表明,本文给出的方法用来研究模糊随机样本的主成分分析问题是可行的.This paper studied on fuzzy random variables,and from the main points of fuzzy random variables.The research was carried out in the direction of component analysis,in which the correlation matrix was an important indicator of principal component analysis,and fuzzy random variables were essentially different from random variables,so the correlation matrix of random variables cannot be used directly.This paper studied and improved theα-correlation matrix of random variables and extends it to fuzzy random variables.This paper constructed theα-closeness matrix by giving theα-closeness concept of two fuzzy random variables,and uses theα-closeness matrix as the fuzzy random variable The correlation matrix studied the principal component analysis of a class of trapezoidal fuzzy random variables.The analysis of examples showed that the method given in this paper was feasible to study the principal component analysis of fuzzy random samples.

关 键 词：不确定性理论 梯形 模糊随机变量 相关矩阵 α-贴近度矩阵 主成分分析 

分 类 号：O159[理学—基础数学]