## 7 Conclusions  
Effective, accurate, and reliable forecast of wind speed is a crucial component of wind-farm management, and also a significant part of the economic development of a nation. However, previous studies only focused on one type of accuracy or stability. Due to this reason, former models cannot achieve satisfying results that obtain high accuracy and strong stability. Wind-speed forecast is also a multicriteria problem; considering only one criterion (accuracy or stability) cannot achieve satisfying results. Thus, it is difficult to select one objective function from multiple-objective functions, and arduous to ensure that the selected function can obtain low MAPE and strong stability. In this paper, a combined forecasting model based on data preprocessing and MOP theory, which could simultaneously improve the accuracy and stability of wind-speed forecasting and four models (two hybrid nonlinear models and two linear models), is proposed and was successfully applied to wind-speed forecasting, not only overcoming the issue of forecasting accuracy, but also solving the difficulty of forecasting stability. Then, as the results show, our proposed combined model with three objective functions achieved lower MAPE and STMAPE than the other models. From the results of our research, our proposed combined model improved the MAPE range from 0.007% to 2.31%, and the STDMAPE range from 0.0044 to 0.3497. Moreover, according to our study, the combined model could be used in large wind farms to forecast wind speed, evaluate wind-energy resources, and save operation costs and wind energy. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & **CS-BPNN** & **DE-OSELM** & **ARIMA** & **HW** & **CM \({}^{*}\)** & **CM \({}^{**}\)** & **CM \({}^{***}\)** & **CM** \\ \hline \multirow{2}{*}{Mon} & 1-order & 0.9110 & 0.9143 & 0.8432 & 0.8851 & 0.9284 & 0.9291 & 0.9249 & 0.9456 \\  & 2-order & 0.8311 & 0.8343 & 0.7715 & 0.8121 & 0.8611 & 0.8621 & 0.8562 & 0.8973 \\ \hline \multirow{2}{*}{Tue} & 1-order & 0.9453 & 0.9456 & 0.9116 & 0.9302 & 0.9520 & 0.9525 & 0.9521 & 0.9605 \\  & 2-order & 0.9023 & 0.9030 & 0.8709 & 0.8825 & 0.9154 & 0.9162 & 0.9141 & 0.9259 \\ \hline \multirow{2}{*}{Wed} & 1-order & 0.9390 & 0.9398 & 0.9135 & 0.9399 & 0.9481 & 0.9486 & 0.9464 & 0.9616 \\  & 2-order & 0.8973 & 0.8987 & 0.8817 & 0.9018 & 0.9112 & 0.9117 & 0.9098 & 0.9313 \\ \hline \multirow{2}{*}{Thu} & 1-order & 0.8985 & 0.9018 & 0.8831 & 0.9276 & 0.9230 & 0.9228 & 0.9166 & 0.9471 \\  & 2-order & 0.7773 & 0.7776 & 0.7836 & 0.8693 & 0.8281 & 0.8281 & 0.8134 & 0.8816 \\ \hline \multirow{2}{*}{FRI} & 1-order & 0.9269 & 0.9279 & 0.8812 & 0.9212 & 0.9351 & 0.9356 & 0.9351 & 0.9423 \\  & 2-order & 0.8623 & 0.8642 & 0.8325 & 0.8614 & 0.8784 & 0.8791 & 0.8775 & 0.8862 \\ \hline \multirow{2}{*}{Sat} & 1-order & 0.9262 & 0.9262 & 0.8750 & 0.9174 & 0.9348 & 0.9357 & 0.9342 & 0.9446 \\  & 2-order & 0.8657 & 0.8655 & 0.8269 & 0.8675 & 0.8817 & 0.8826 & 0.8812 & 0.8935 \\ \hline \multirow{2}{*}{Sun} & 1-order & 0.9468 & 0.9466 & 0.9110 & 0.9473 & 0.9513 & 0.9518 & 0.9515 & 0.9624 \\  & 2-order & 0.9041 & 0.9036 & 0.8831 & 0.9106 & 0.9127 & 0.9135 & 0.9131 & 0.9317 \\ \hline \hline \end{tabular}  
* Combined Model with the objective functions: TIC (\(\hat{\mathbf{Y}},\ \mathbf{Y}\)) and RMSE (\(\hat{\mathbf{Y}},\ \mathbf{Y}\)). \({}^{**}\) Combined Model with the objective functions: TIC (\(\hat{\mathbf{Y}},\ \mathbf{Y}\)) and MAPE (\(\hat{\mathbf{Y}},\ \mathbf{Y}\)). \({}^{***}\) Combined Model with the objective functions: RMSE (\(\hat{\mathbf{Y}},\ \mathbf{Y}\)) and MAPE (\(\hat{\mathbf{Y}},\ \mathbf{Y}\)).  
\end{table} 
Table 10: Results for the forecasting effectiveness.