Research On A Comprehensive Type-2 Fuzzy Time Series Model

Time series forecasting is an important part of prediction. With the development of society and the increase of digital information, it becomes more and more important to analyze and research time series model. Compared with the classical time series model, the fuzzy time series model can deal with the uncertainty and vagueness inherent in historical data. Therefore, it has been given more and more attention from scholars. In order to take advantage of more effective information related to factors that to be predicted, Hurang and Yu proposed a type-2 fuzzy time series model based on the concept of type-2 fuzzy sets. Building upon work of Hurang and Yu, this paper proposes improved methods from the three aspects which include the division of fuzzy intervals, the operations of fuzzy relations and the prediction of fuzzy inference, and finally put forward a comprehensive type-2 fuzzy time model.In the universe of discourse partition stage, particle swarm optimization (PSO) algorithm is used to adjust the lengths of intervals. This method overcomes the shortcomings of domain division with equal interval and helps improving the accuracy of the data fuzzification. Considering the different importance of each fuzzy language variables in the fuzzy relational operation stage, this paper proposes a new method to calculate the weight matrix based on the frequency number and priorities of each fuzzy set which makes the results of fuzzy relational operation more accurate.In the stage of fuzzy reasoning, this paper adopts support vector machine (SVM) mode to forecast the index of the fuzzy set of the predicted time, based on the one-to-one corresponding relations between the actual value of type-1 observation and the results of fuzzy relational operation. At last, an modified adaptive model is applied to adjust the forecasting values which helps effectively improve the prediction accuracy. At the same time, through conducting experiments on several groups of data, the effectiveness of the proposed methods is verified respectively.In order to further improve the prediction accuracy, a comprehensive type-2 fuzzy time model is presented by combining the modified algorithms of each stage together. And then the high-order form of the comprehensive model is established by constructing the high-order fuzzy logical relationships. The results of computer simulation experiments indicate that the proposed comprehensive model and its form of high order can effectively improve the prediction accuracy.