**Exploring an Ensemble of Methods that Combines Fuzzy Cognitive Maps and Neural Networks in Solving the Time Series Prediction Problem of Gas Consumption in Greece**

**Konstantinos I. Papageorgiou 1,\*, Katarzyna Poczeta 2, Elpiniki Papageorgiou 3, Vassilis C. Gerogiannis 3,\* and George Stamoulis 1**


Received: 30 September 2019; Accepted: 31 October 2019; Published: 6 November 2019

**Abstract:** This paper introduced a new ensemble learning approach, based on evolutionary fuzzy cognitive maps (FCMs), artificial neural networks (ANNs), and their hybrid structure (FCM-ANN), for time series prediction. The main aim of time series forecasting is to obtain reasonably accurate forecasts of future data from analyzing records of data. In the paper, we proposed an ensemble-based forecast combination methodology as an alternative approach to forecasting methods for time series prediction. The ensemble learning technique combines various learning algorithms, including SOGA (structure optimization genetic algorithm)-based FCMs, RCGA (real coded genetic algorithm)-based FCMs, efficient and adaptive ANNs architectures, and a hybrid structure of FCM-ANN, recently proposed for time series forecasting. All ensemble algorithms execute according to the one-step prediction regime. The particular forecast combination approach was specifically selected due to the advanced features of each ensemble component, where the findings of this work evinced the effectiveness of this approach, in terms of prediction accuracy, when compared against other well-known, independent forecasting approaches, such as ANNs or FCMs, and the long short-term memory (LSTM) algorithm as well. The suggested ensemble learning approach was applied to three distribution points that compose the natural gas grid of a Greek region. For the evaluation of the proposed approach, a real-time series dataset for natural gas prediction was used. We also provided a detailed discussion on the performance of the individual predictors, the ensemble predictors, and their combination through two well-known ensemble methods (the average and the error-based) that are characterized in the literature as particularly accurate and effective. The prediction results showed the efficacy of the proposed ensemble learning approach, and the comparative analysis demonstrated enough evidence that the approach could be used effectively to conduct forecasting based on multivariate time series.

**Keywords:** fuzzy cognitive maps; neural networks; time series forecasting; ensemble learning; prediction; machine learning; natural gas
