A Research For Fuzzy Time Series Based On Principal Component Analysis

Fuzzy time series model,which was proposed to solve the fuzzy problems that can't be dealt with classical time series analysis methods,is an extensive research subject in the research field of data prediction and analysis.At present,fuzzy time series is successfully applied to the stock index prediction,enrollment prediction,temperature prediction and shipping index prediction,etc.In order to further improve the prediction accuracy,scholars have proposed many different fuzzy time series models and forecasting methods.Most of the methods are improved around the division of domain and the establishment of fuzzy rules.In the actual forecasting process,there are some correlations and redundancies between the fuzzy rules.It is not conducive to simplify the forecasting process and improve the prediction accuracy.So,the urgent problem to be solved is to remove the correlations and redundancies between the fuzzy rules.To solve this problem,this paper proposes a fuzzy time series optimization algorithm based on principal component analysis.Considering the principal component analysis is only applicable to the situation when the covariance matrix is positive definite,this paper describes and validates the algorithm from two different cases respectively.When the covariance matrix is positive definite,the fuzzy relations between the data are constructed and the fuzzy rules are expressed in the form of matrix firstly.Then the fuzzy relation matrices are constructed.Secondly,the fuzzy covariance matrix of the fuzzy relation matrices is constructed by different methods.Thirdly,the principal component analysis is carried out to the fuzzy covariance matrix.The principal components are extracted to optimize the fuzzy rules.Finally,the new algorithm is applied to Amazon stock forecasting.The results show that the new algorithm is effective.When the covariance matrix is non-positive definite,the difference of algorithm is that the covariance matrix needs to be positive defined before the principal component analysis.The original covariance matrix is replaced by an approximate positive definite correlation matrix.The other steps are the same as the case when the covariance matrix is positive definite.Finally,the new algorithm is applied to the enrollment forecasting of Alabama.The results show that the new algorithm is effective.Through the above description,this paper extends the application of algorithm.It not only makes the algorithm applicable to the case when the covariance matrix is non-positive definite,but also improves the prediction accuracy.This sufficiently shows that the new algorithm is effective.