## 5 Conclusions  
To sum up, we applied a time series forecasting method for natural gas demand in three Greek cities, implementing an efficient ensemble forecasting approach through combining ANN, RCGA-FCM, SOGA-FCM, and hybrid FCM-ANN. The proposed forecasting combination approach incorporates the two most popular ensemble methods for error calculation in forecasting problems and is deployed in certain steps offering generalization capabilities. The whole framework seems to be a promising approach for ensemble time series forecasting that can easily be applied in many scientific domains. An initial comparison analysis was conducted with benchmark methods of ANN, FCM, and their different configurations. Next, further comparison analysis was conducted with new promising LSTM networks previously used for time series prediction.  
Through the experimental analysis, two error statistics (MAE, MSE) needed to be calculated in order to examine the effectiveness of the ensemble learning approach in time series prediction. The results of this study showed that the examined ensemble approach through designing an ensemble structure of various ANN, SOGA-FCM models by different learning parameters and their hybrid structures could significantly improve forecasting. Moreover, obtained results clearly demonstrated that a relatively higher forecasting accuracy was noticed when the applied ensemble approach was compared against independent forecasting approaches, such as ANN or FCM, as well as with LSTM.  
Future work is devoted to applying the advantageous forecast combination approach to a larger number of distribution points that compose the natural gas grid of Greek regions (larger and smaller cities) as well as to investigate a new forecast combination structure of efficient convolutional neural networks (CNN) and LSTM networks for time series prediction in various application domains. Furthermore, an extensive comparative analysis with various LSTM structures, as well as with other advanced machine learning and time series prediction methods, will be conducted in future work. The presented research work could also contribute to explainability, transparency, and re-traceability of artificial intelligence (AI) and machine learning systems. These systems are being applied in various fields, and the decisions being made by them are not always clear due to the use of complicated algorithms in order to achieve power, performance, and accuracy. The authors with the use of complicated, but powerful algorithms, such as neural networks and ensemble methods, tried to describe all the steps and models involved in decision-making process to attain explainability and, in future, they would further explore ways to make the best-performing methods more transparent, re-traceable, and understandable, explaining why certain decisions have been made [92].  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{2}{c}{**Best Ensemble**} & \multicolumn{2}{c}{**LSTM (Dropout = 0.2)**} \\ \hline  & **Case (A) (Individual)** & **Case (B) (Ensemble)** & **1 layer** \\ \multicolumn{1}{c}{_Valitation_} & \multicolumn{2}{c}{**ATHENS**} \\ \hline \(MAE\) & 0.0326 & 0.0337 & 0.0406 \\ \(MSE\) & 0.0032 & 0.0032 & 0.0039 \\ \(Testing\) & & & \\ \hline \(MAE\) & 0.0328 & 0.0352 & 0.0426 \\ \(MSE\) & 0.0031 & 0.0032 & 0.0041 \\ \(Valitation\) & & **THESSALONIK** & \\ \hline \(MAE\) & 0.0340 & 0.0355 & 0.0462 \\ \(MSE\) & 0.0027 & 0.0028 & 0.0043 \\ \(Testing\) & & & \\ \hline \(MAE\) & 0.0369 & 0.0381 & 0.0489 \\ \(MSE\) & 0.0031 & 0.0034 & 0.0045 \\ \(Valitation\) & & **LARISSA** & \\ \hline \hline \(MAE\) & 0.0319 & 0.0326 & 0.0373 \\ \(MSE\) & 0.0027 & 0.0026 & 0.0029 \\ \(Testing\) & & & \\ \hline \(MAE\) & 0.0417 & 0.0423 & 0.0462 \\ \(MSE\) & 0.0040 & 0.0040 & 0.0042 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Comparison results with LSTM (long short-term memory) (with best configuration parameters).