## 2 The Procedures of Forecasting Strategy
### Adaptive Neuro-Fuzzy Inference System (ANFIS)  
The ANFIS model is a combination of a fuzzy inference system (FIS) and an ANN, which captures the benefits of both models in a single model. The ANN possesses the ability to learn knowledge but deals with deficiency to obtain the output from the decision-making method. Moreover, the FIS method is capable of producing the output from the fuzzy logic decision but does not have any self-operating learning ability [29]. Hence, the benefits of both methods are combined in a single model in order to give a small memorization error which will enhance the performance of the ANFIS model [30]. The design of the ANFIS model consists of two parts, constructing and training. At the construction part, the number and type of membership function are defined. Besides, this construction part includes the division of the input or output data into a number of fuzzy rules which can be achieved by using various methods, such as the grid partitioning method, subtractive clustering method and fuzzy C-means (FCM) clustering method [31]. A large number of fuzzy rules will lead to a complex structure of the ANFIS model. Hence, this paper applies the FCM clustering method to divide the input data in order to obtain a small number of fuzzy rules. FCM is a data clustering method that assigns each data point to a cluster with a degree that has been specified by a membership grade. In this work, each data point of the panel temperature variable, tiled radiation variable and global radiation variation has been divided into two clusters which are illustrated in Figure 5. \(x_{1}\) denotes the panel temperature variable, \(x_{2}\) signifies the tilted radiation variable and \(x_{3}\) shows the data in global radiation variable. In the training process, the training data pairs are generated to train the ANFIS model. The data pairs comprise of input variables and the corresponding output of the ANFIS model. To the best of the author's knowledge, there is no standard rule to decide the optimum size of datasets for the training and testing processes. Thus, it is decided that the data in this study is divided into 80% of training data and 20% of testing data. This means that 4020 samples of observations obtained are divided into 3216 of training samples and 804 of testing samples. The training samples in the ANFIS model will pass through several processes which are explained as follows:  
Figure 5: Configuration of the adaptive neuro-fuzzy inference system (ANFIS) [32]. **Layer 1**: After the partitioning of training data points into the clusters, each node in Layer 1 is assigned with membership grades of the selected membership function. The assignation of membership function to a node in the first layer is known as the fuzzification process. For FCM clustering, each node in Layer 1 is assigned with the Gaussian membership function which can be shown in Equation (2):  
\[\mathrm{O_{1,j}}=\mathrm{\mu_{A_{i}}(x)}=\mathrm{exp}(-\frac{1}{2}{(\frac{x_{1 }-c_{i}}{\sigma_{i}})}^{2}) \tag{2}\]  
where \(\mathrm{O_{k,j}}\) represents the output of a \(\mathrm{j^{th}}\) node at the \(\mathrm{k^{th}}\) layer while \(\mathrm{\mu_{Ai}}\) denotes the membership function of \(\mathrm{i^{th}}\) rule \(\mathrm{A_{i}}\). The grades of this membership function consist of standard deviation (\(\sigma_{i}\)) and mean (\(c_{i}\)) of \(\mathrm{i^{th}}\) rule \(\mathrm{A_{i}}\) where they are known as premise parameters. **Layer 2**: The output of the \(\mathrm{j^{th}}\) node at the second layer is identified as the firing strength (\(w_{j}\)) and it is shown in Equation (3). This layer produces an output by multiplying the membership function of \(\mathrm{i^{th}}\) rules.