# Energy Performance Forecasting of Residential Buildings Using Fuzzy Approaches
## 4 Results and Discussion  
### Fuzzy Approaches Results and Discussion  
The RMSE and MAE obtained by ANFIS and FIR models, for both HL and CL output variables, are summarized in the last two rows of Table 2. To demonstrate the performance of the developed fuzzy models, we compare the results with those obtained using 13 other techniques, namely IRLS, RF, SVR, GLR, CHAID, CART, SVM, RBFNN, BFNN, MARS, GSGP, GSGP-LS, GSGP-LS-LIN [17; 19; 20; 21]. All these machine-learning methodologies have in common that they generate individual predictive  
Figure 8: FIR mask obtained for heating load (HL) and cooling load (CL) models. Figure 7: Example of uniform (upper plot) and non-uniform (lower plot) membership functions distribution. models and are not an ensemble of models. The full results obtained for all the machine-learning approaches are also shown in Table 2.  
IRLS is a linear regression algorithm that adjusts weights in the coefficients of the classical regression scheme. RF is a method that builds a set of classification and regression trees using the Bagging algorithm. SVR is a support vector machine that solves regression problems. While other linear regression models try to minimize the error between the predicted and the actual value, SVR tries to fit the best line within a predefined or threshold error value. GLR, general linear regression, is a more flexible version of standard linear regression that assumes that data points have an arbitrary distribution pattern. CHAID, Chi-squared automatic interaction detector, is a decision tree classification technique that uses the Chi-square as test of independence. The CART is a decision binary tree method of constructing a classification or regression tree according to its dependent variable. The split is chosen using a greedy algorithm to minimize a cost function. The support vector machines, SVM, construct a hyperplane or a set of hyperplanes in a high or infinite dimensional space, which can be used for classification or other tasks like outliers detection. A radial basis function network, RBFNN, is an artificial neural network that uses radial basis functions as activation functions. BPNN is a back-propagation neural network. These networks can be trained with a training dataset propagating the error back to input until the minimal mean square error is achieved. MARS, multivariate adaptive regression splines, fits a basis function (term) to distinct independent variable intervals. The next three techniques, i.e., GSGP, GSGP-LS and GSGP-LS-LIN, are genetic programming approaches based on evolutionary computation. All of them use geometric semantic operators to produce new candidate solutions. GSGP-LS includes a local search strategy within mutation operator. GSGP-LS-LIN modifies the fitness function including linear scaling. For knowing the parameter settings of these methodologies for the problem at hand refer to [17; 19; 20; 21]. The best prediction performances are highlighted in Table 2. The best results for CL and HL are obtained when the SVR algorithm is used. The second and third best results are obtained by the fuzzy approaches. FIR obtains a slightly better synthesis index (SI) than ANFIS when modelling the HL, whereas for CL it is ANFIS that obtains a slightly better index. Following SVR, FIR and ANFIS performances (with SI lower than 0.1), the next-based alternative is the MARS algorithm. MARS is able