## 2 Materials and Methods  
### Material-Dataset  
In the considered case study, three different prediction datasets of natural gas demand, derived from different districts in Greece, were analyzed from the records of the Hellenic Gas Transmission System Operator S.A. (www.desfa.gr, DESFA). DESFA company is responsible for the operation, management, exploitation, and development of the Greek Natural Gas System and its interconnections in a technically sound and economically viable way. From 2008, DESFA provides historical data of transmission system operation and natural gas deliveries/off-takes. In this research work, historical data with the values of gas consumption for a period of five years, from 2013 to 2017, were used as initial data to accomplish forecasting. These data were split into training and testing data, where usually the training data came from the first four years and were used for learning models, whereas the data of the last year were used for testing the applied artificial intelligence models.  
It is crucial for an efficient forecast to properly select the number and types of inputs. Thus, we emphasized on defining proper input candidates. Six different inputs for time series prediction were considered. The first three inputs were devoted to month indicator, day indicator, and mean temperature. Specifically, concerning the calendar indicators, we used one input for months and one input for days coding. Let \(m=1,\ 2,\ \ldots,12\) be the number of months. We considered the following matching: January/1, February/2,..., December/12. Let \(l=1,\ 2,\ \ldots,\ 7\) be the number of days. The day type matching was as follows: Monday/1, Tuesday/2,..., Sunday/7. The temperature data were obtained by the nearest to the distribution gas point station. The rest three inputs were the previously measured values of natural gas demand, for one-day before, two-day before, and the current day. These six variables were used to form the input pattern of the FCM. The output referred to the total daily demand for the specific distribution point.  
The features that were gathered and used in our study to form the FCM model were enough and properly selected according to the relevant literature. From a recent literature review regarding the prediction of natural gas consumption [40], it can be seen that past gas consumption combined with meteorological data (especially temperature) are the most commonly used input variables for the prediction of natural gas consumption. A recent study [41] used past consumption, temperature, months, and days of the week, while in [55], day of week and demand of the same day in the previous year were used as input variables for natural gas forecasting. Considering the above practices described in the literature, it can be concluded that the features used in the current work were enough to predict the consumption of natural gas for the selected areas.  
The Greek cities of Thessaloniki, Athens, and Larissa were selected for the conducted simulation analysis and comparison of the best performing algorithms. These different natural gas consumption datasets may offer insight into whether the analyzed algorithms perform equally in different locations, where the energy demand could be completely different for the same days.