Principal Component Analysis Of Fuzzy Data Based On Structure Element Theory

At present,the multivariate statistical analysis is the most common and important means of data processing,and multivariate statistical analysis has been more and more widely used.But because of the influence of the environment and human factors,such as,make the data often has the fuzziness,called fuzzy data,thus the fuzzy data used in multivariate statistical analysis,it is a very meaningful work.The principal component analysis method of fuzzy data based on fuzzy structure element theory and classical principal component analysis is studied.By using the structure of the fuzzy number linear representation,numerical characteristics of fuzzy data are given.According to the classical principal component analysis cannot be directly applied to fuzzy data in this problem,mainly through the fuzzy data matrix was divided into master data matrix and error data matrix,and put forward the use of error data of principal component of the coefficient of master data of principal component of the coefficient correction method,get the coefficient of the fuzzy data and its expression of the principal component.On the basis of the above theoretical work,the principal component analysis by using principal component analysis method of the fuzzy data in “2006 social development of China's provinces and autonomous regions the comprehensive situation of eight comprehensive evaluation index”.