Fuzzy Time Series Forecasting Based On BP Neural Network

Time series is a sequence of datum which is collected to reflect the object or phenomena varying with time at different times. We can find the rules hidden in the data by researching the time series, then we can build time series model to solve problems in related area". Time series forecasting is to forecast the future based on the observed data, which can enable decision-maker to see further and make better decisions, this make time series forecasting important in practical application.Fuzzy time series is obtained by fuzzifying the time series, it uses the concept of fuzzy and clusters the datum into category which has semantic representation, then we can build model about the categories to forecast. The general process of fuzzy time series forecasting concludes four steps, first, we partition the universe of discourse into unequal-length intervals; then, we fuzzify the data on the basis of fuzzy sets; next, we build second-order fuzzy logical relationships; finally, we build model to forecast and defuzzify the output. We do some research about the method of universe of discourse partitioning, and propose two methods of partitioning which are based on fuzzy C-means clustering method and based on information granule method, then combine the methods with BP neural network respectively, so we obtain two combined forecasting models.In the first forecasting model, we propose the universe of discourse partitioning method based on fuzzy C-means clustering algorithm, which optimizes the objective function to obtain the prototypes, then we calculate the midpoint of adjacent prototypes and make them be the boundary of intervals, next we give the intervals fuzzy meaning to form fuzzy sets and fuzzify the observed data, so we get the fuzzy time series. We extract second-order fuzzy logical relationships on the fuzzy observations and use them to train a BP neural network which enable the network to classify, so we can obtain the prediction, at last, we defuzzify the output to get the forecasted value. The Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) is used to verify the effectiveness of the proposed model. The results compared with the existed models show that the proposed model performs better according to root mean-square error (RMSE).In the second forecasting model, we use information granule to improve the method of universe of discourse partitioning. Information granule can present data on different dimensions, so the rules hidden in the data can be found easily. Inspired by the idea, we propose the universe of discourse partitioning method based on information granule. In the first step we obtain the prototypes by using fuzzy C-means clustering; in the second step, we build the subsets based on the midpoint of the adjacent prototypes; in the third step, we construct the applicable information granule on the subsets, finally, we partition the universe of discourse based on the information granule. After that, we adopt the same modeling progress with the last model, and the accuracy of forecasting is higher than most of the existing model which verify the effectiveness of the novel model.