Optimization Algorithm Of Fuzzy Time Series Based On Principal Component Analysis

The fuzzy time series is used in many fields with the development of the society,so it is very important that construct the time series model.The division of domains and the establishment of fuzzy rules have always been the focus of many scholars.But little attention has been paid to the nonlinearity of time series.As we all know,the objects of time series are stationary processes,but most of the time series in life are non-stationary,especially in natural disasters,engineering control,economics and finance.Analysis will lead to poor effect because of the nonlinearity of non-stationary time series.In order to improve the accuracy and guarantee the validity of the prediction,the time series was stabilized by transform the data in the front.In view of that,this paper proposed stabilization algorithm of fuzzy time series model based on principal component analysis.Test the stationary of fuzzy time series analysis,and reduce the correlation between fuzzy rules through PCA.For non-stationary time series,pre-process the data and the new stationary series will be the object to analysis.Prediction based on the framework of fuzzy time series analysis.Firstly,definite and divide the domain.Secondly,set the fuzzy sets and build the generalized covariance matrix.Then calculate characteristic value and the characteristic vector of the matrix based on PCA.The fuzzy rules are optimized according to the accumulative contribution rate of principal component that extracted.Finally,forecast with the new rules and defuzzification.In order to improve the accuracy further,this paper also optimizes the domain ivision.The fuzzy time series model,which divides the domain equally,is not enough to reflect the distribution characteristics of the data,and the human interference is larger in the past.Therefore,the method of FCM is used to divide the domain into non-equal division.Test the stability of data and stationary,and obtain the clustering center and non equal interval division after FCM.Using the new rules to predict that principal components through PCA.Finally,through the forecast of enrollment the University of Alabama and TAIFEX,verify the effectiveness of the algorithm.