*1.1. Related Literature*

In recent years, the natural gas market has progressed greatly in terms of fast development and, thus, it has become a very competitive area. Undoubtedly, natural gas is among primary energy sources and has a significant environmental role considering its valuable environmental benefits, such as low-level emissions of greenhouse gases in comparison with other non-renewable energy sources [38,39]. Natural gas demand seems to increase considerably due to several socio-economic and political reasons, while the price and environmental concerns are significant regulatory factors a ffecting natural gas demand. Therefore, the prediction of natural gas consumption, as a time series forecasting problem, is becoming important in contemporary energy systems, allowing energy policymakers to apply e ffective strategies to guarantee su fficient natural gas supplies.

So far, many research papers have tried to give a clear insight regarding natural gas forecasting by suggesting models for predicting the consumption of this non-renewable energy source. A summary of natural gas consumption forecasting regarding prediction methods, input variables used for modeling, as well as prediction area, can be found in many review papers in the relevant literature. Particularly, there is a thorough literature survey of published papers [38–40] that classifies various models and techniques that have been recently applied in the field of natural gas forecasting, with respect to the paradigm that each model/technique is based on, while there has been also an attempt by researchers to classify all models applied in this area according to their performance characteristics, as well as to o ffer some future research directions. The models presented were developed by researchers to predict natural gas consumption on an hourly, daily, weekly, monthly, or yearly basis, in an attempt to predict natural gas consumption with an acceptable degree of accuracy. Accurate forecasting of natural gas consumption can be particularly important for project planning, engineering design, pipeline operation, gas imports, tari ff design, and optimal scheduling of a natural gas supply system [41].

Due to the need for distribution planning, especially in residential areas, the increasing demand for natural gas, and the restricted natural gas network in many countries, the forecasting of consumption on a daily and weekly basis seems to be of high importance. In the relevant literature, many suggestions apply various ANN topologies and methods to support day-ahead natural gas demand prediction [42–50]. For example, [42] used ANN, while [45] used a combination of ANN forecasters for predicting gas consumption at a citywide distribution level. For the same distribution level (citywide), a strategy was proposed in [51] to estimate the forecasting risk by using hourly consumption data. Having as aim to find the best solution for natural gas consumption, the researchers in [52] used linear regression with the sliding window technique, while in [53], a univariate artificial bee colony-based artificial neural network (ANN-ABC) was applied to minimize error in the case of forecasting day-ahead demand. The researchers in [54] also considered various methods for the prediction of daily gas consumption, such as the seasonal autoregressive integrated moving average model with exogenous inputs (SARIMAX), multi-layer perceptron ANN (ANN-MLP), ANN with radial basis functions (ANN-RBF), and multivariate ordinary least squares (OLS).

In the relevant literature, there are also some research works on neuro-fuzzy methods and genetic algorithms applied in natural gas demand, as in [41,55–58]. Specifically, a novel hybrid model that combines the wavelet transform (WT), genetic algorithm (GA), adaptive neuro-fuzzy inference system (ANFIS), and feed-forward neural network (FFNN) was recently examined in [41] and applied to the Greek natural gas grid. Moreover, evolutionary fuzzy cognitive maps (FCMs) were recently used for time series problems modeling and forecasting. FCMs can be understood as recurrent neural networks inheriting many features from them, such as learning capabilities, which elevate the performance of FCMs in modeling and prediction and further helped FCMs to gain momentum over recent years [59,60]. The researchers in [61,62] were the first to examine the application of FCMs to time series modeling, proposing nodes selection criteria in an FCM, which was used to model univariate time series. Further techniques for simplifying FCMs by removing nodes and weights were investigated, while a dynamic optimization of the FCM structure was studied in [63] for univariate time series forecasting. Concerning multivariate interval-valued time series, an evolutionary algorithm for learning fuzzy grey cognitive maps was developed as a nonlinear predictive model [64]. Taking one step further, the researchers in [65] and [66] enhanced the evolutionary FCMs with the structure optimization genetic algorithm (SOGA). These approaches can be used to automatically construct an FCM model after selecting the crucial concepts and defining the relationships between them by taking into consideration any available historical data. An example regarding rented bikes' count prediction was examined, where SOGA-FCM was compared with the multi-step gradient method (MGM) [67] and the real-coded genetic algorithm (RCGA) [68]. A two-stage prediction model for multivariate time series prediction, based

on the e fficient capabilities of evolutionary fuzzy cognitive maps (FCMs) and enhanced by structure optimization algorithms and artificial neural networks (ANNs), was introduced in [69]. Furthermore, the researchers in [21,60] recently conducted a preliminary study on implementing FCMs with NNs for natural gas prediction.

### *1.2. Research Aim and Approach*

The purpose of this paper was to propose a new forecast combination approach resulting from FCMs, ANNs, and hybrid models. This ensemble forecasting method, including the two most popular ensemble methods, the Average and the Error-based, is based on ANNs, FCMs with learning capabilities, as well as on a hybrid FCM-ANN model with di fferent configurations, to produce an accurate non-linear time series model for the prediction of natural gas consumption. A real case study problem of natural gas consumption in Greece was performed to show the applicability of the proposed approach. Furthermore, in order to validate the proposed forecasting combination approach, a comparison analysis between the ensemble methods and an innovative machine learning technique, the long short-term memory (LSTM) algorithm (which is devoted to time series forecasting), was conducted, and the results demonstrated enough evidence that the proposed approach could be used e ffectively to conduct forecasting based on multivariate time series. The LSTM algorithm, as an advanced recurrent NN method, was previously used for short-term natural gas demand forecasting in Greece [70]. In that research paper, LSTM was applied in one day-ahead natural gas consumption, forecasting for the same three Greek cities, which were also examined in the case study presented in the current paper. Many similar works can be found in the literature that examine various forecast combinations in terms of accuracy and error variability but, in the present work, an innovative approach that combines FCMs, ANNS, and hybrid FCM-ANN models, producing a non-linear time series model for the prediction of natural gas consumption, was studied exclusively, contributing to the novelty of the current study. The results demonstrated in a clear way that the proposed approach had attained better accuracies than other individual models. This study justified the superiority of the selective ensemble method over combining the important features and capabilities of the models that consist of the overall approach, making it a useful tool for future work.

The outline of the paper is as follows. Section 2 describes the material and methods of our research study; Section 2.1 describes the case study problem and refers to the datasets of natural gas demand that are used, whereas Section 2.2 presents the analyzed approaches for time series forecasting based on ANNs, FCMs with evolutionary learning algorithms, and their hybrid combinations. The most widely used ensemble methods for forecasting problems (i.e., the error-based and the simple average method) are also presented in Section 2.2. In Section 3, the proposed forecasting combination approach is described. The same Section presents the evaluation criteria, which we have used to analyze the performance of the analyzed approaches for natural gas prediction. Section 4 presents the results of simulation analysis for three di fferent Greek cities, as well as the conducted comparative analysis of the proposed approach with other intelligent techniques. A discussion of the results highlights the main findings of the proposed ensemble forecasts approach. Section 5 summarizes the main conclusions of the paper with further discussion and suggestions about future research expansion.

### **2. Materials and Methods**
