Principal Component Analysis And Application Of Two Types Of Fuzzy Random Variables

Principal component analysis(PCA)is a statistical analysis method widely used in data compression.In order to introduce PCA into fuzzy random variables,this paper gives the correlation coefficient formula of trapezoidal fuzzy random variables and the correlation coefficient formula of intuitive fuzzy random variables.Based on the trapezoidal fuzzy random variable correlation coefficient formula and intuitive fuzzy random variable correlation coefficient formula,the influencing factors of satisfaction and personality of Jinan Forest Park are studied,and then the principal component analysis is carried out.The main content is divided into two parts.In this paper,the formulas of correlation coefficient and correlation degree are proposed for trapezoidal fuzzy random variables,and the properties of the proposed correlation coefficient and correlation degree are proved.Trapezoidal fuzzy random variable correlation coefficient is based on ?-cut set.This makes the correlation coefficients of trapezoidal fuzzy random variables become nonfuzzy.The simulation analysis of the proposed formula shows that the correlation degree can represent the correlation degree between trapezoidal fuzzy random variables.Compared with the correlation coefficient of trapezoidal fuzzy random variables,the correlation degree is more convenient to solve.In addition,the principal component analysis method is applied to the investigation of the influencing factors of satisfaction of Jinan forest park.Through the analysis,it can be obtained that the correlation coefficient and correlation degree can represent the correlation degree between two trapezoidal fuzzy random variables,and when people are satisfied with the green space coverage and plant diversity of the park.When the satisfaction of entertainment facilities and artificial lake increases,people's overall satisfaction with the park will also increase.In this paper,a correlation coefficient formula for intuitionistic fuzzy random variables is proposed,and the properties of the proposed correlation coefficient are proved.The correlation coefficient is proposed based on cross entropy.Cross entropy is not only a correlation index,but also an information index.Compared with Pearson correlation coefficient,it can provide more data information.Using the correlation coefficient of intuitionistic fuzzy random variables,this paper makes a principal component analysis on the factors affecting personality,and compares it with the existing principal component analysis methods of intuitionistic fuzzy random variables.Through the comparison,it can be seen that the correlation coefficient of intuitionistic fuzzy random variables proposed in this paper is feasible.