Implement multi-step-ahead forecasting with multi-point association fuzzy logical relationship for time series

In the existing high-order fuzzy logical relationship (FLR) based forecasting model, each FLR is used to describe the association between multiple premise observations and a consequent observation. Therefore, these FLRs concentrate on the one-step-ahead forecasting. In real applications, there exist another kind of association: the association between multiple premise observations and multiple consequent observations. For such association, the existing FLRs can’t express and ignored. To depict it, the high-order multi-point association FLR is raised in this study. The antecedent and consequent of a high-order multi-point association FLR are consisted of multiple observations. Thus, the proposed FLR reflects the influence of multiple premise observations on the multiple consequent observations, and can be applied for multi-step-ahead forecasting with no cumulative errors. On the basis of high-order multi-point association FLR, the high-order multi-point trend association FLR is constructed, it describes the trend association in time series. By using these two new kinds of FLRs, a fuzzy time series based multi-step-ahead forecasting model is established. In this model, the multi-point (trend) association FLRs effective in capturing the associations of time series and improving forecasting accuracy. The benefits of the proposed FLRs and the superior performance of the established forecasting model are demonstrated through the experimental analysis.

Fuzzy First-Order Transition-Rules-Trained Hybrid Forecasting System for Short-Term Wind Speed Forecasts

Due to the ever-increasing environmental pollution becoming progressively more serious, wind power has been widely used around the world in recent years. However, because of their randomness and intermittence, the accurate prediction of wind speeds is difficult. To address this problem, this article proposes a hybrid system for short-wind-speed prediction. The system combines the autoregressive differential moving average (ARIMA) model with a three-layer feedforward neural network. An ARIMA model was employed to predict linear patterns in series, while a feedforward neural network was used to predict the nonlinear patterns in series. To improve accuracy of the predictions, the neural network models were trained by using two methods: first-order transition rules and fuzzy first-order transition rules. The Levenberg–Marquardt (LM) algorithm was applied to update the weight and deviation of each layer of neural network. The dominance matrix method was employed to calculate the weight of the hybrid system, which was used to establish the linear hybrid system. To evaluate the performance, three statistical indices were used: the mean square error (MSE), the root mean square error (RMSE) and the mean absolute percentage error (MAPE). A set of Lorenz-63 simulated values and two datasets collected from different wind fields in Qilian County, Qinghai Province, China, were utilized as to perform a comparative study. The results show the following: (a) compared with the neural network trained by first-order transition rules, the prediction accuracy of the neural network trained by the fuzzy first-order transition rules was higher; (b) the proposed hybrid system attains superior performance compared with a single model; and (c) the proposed hybrid system balances the forecast accuracy and convergence speed simultaneously during forecasting. Therefore, it was feasible to apply the hybrid model to the prediction of real time-series.