## 3 Results and Discussions
### Anfs-Ga  
In this research study, ANFIS-GA and standalone ANFIS models were developed to predict the traffic flow of non-autonomous vehicles at signalized road intersections using the South Africa Road transportation systems as a case study. The above-mentioned models were trained and tested using traffic data from the signalized road intersections. The traffic data were divided according to the data collected from these road intersections.  
Based on the results obtained when we compared the ANFIS-GA and ANFIS models results showed that the performance of the predictive models was dependent on the lowest root mean square error (RMSE). According to Figures 13 and 14, the ANFIS-GA results show that the performance of the training and testing was based on the size of population (\(n=100\)), the number of iterations (\(n=500\)), the percentage of crossovers, the rate of mutation, and the selection function. Figures 15 and 16 show the ANFIS-GA model's corresponding performance on the traffic volume of vehicles at the four signalized road intersections. It is significant to note that although the ANFIS model sometimes produced the best \(R^{2}\) performance, the results of this study have shown that ANFIS-GA provided the best model performance for any of the four signalized road intersections from which the traffic data is collected. This is illustrated by the \(R^{2}\) values in the testing of the ANFIS-GA model in Figure 16, which shows 0.9980 as compared to the testing of the ANFIS model, which shows \(R^{2}=0.9790\) in Figure 20.  
Figure 12: Road intersection 4.  
Figure 14: ANFIS-GA model testing with the traffic datasets.  
Figure 13: Training of the ANFIS-GA model with the traffic datasets.  
The 850 traffic datasets obtained from the four congested signalized road intersections on the South African road network were divided into 595 and 255 for the training and testing of the ANFIS-GA and ANFIS models, respectively. The division of the traffic data for each of the four intersections is shown in tabulated form in Table 4. A trial-and-error method was used to achieve the optimum performance of the ANFIS and ANFIS-GA models. This method was used during the ANFIS and ANFIS-GA model training and testing to determine the optimal parameter for the number of populations and iterations. The best optimal parameters for the ANFIS-GA and ANFIS performance training and testing are shown in Figures 15-18. It is interesting to note that in all four signalized road  
Figure 16: ANFIS-GA model testing.  
Figure 15: ANFIS-GA model training.  
intersections, the ANFIS-GA and ANFIS models' parameters significantly impacted the predictive performance of the models.  
The fuzzy rule viewer representation used in this research uses a continuous discretization of the inputs triangular mf to evaluate the cuts by alpha technique to create the fuzzy inference inputs (Figure 17).  
Figure 17: ANFIS model rule viewer.  
Figure 18: 3D image of the ANFIS model. (Input 1= time, input 2 = speed of vehicles, output = traffic volume).  
Figure 18 shows the three-dimensional surface views of the inputs and output using the ANFIS rule viewer.  
To determine the ANFIS model training accuracy, we compared the observed and predicted output of the traffic volume of vehicles in Figure 19, with the training of the ANFIS model accuracy being 0.9709.  
The observed and predicted output of the traffic volume of vehicles at the road intersections were compared in Figure 20 to determine the accuracy of the testing of the ANFIS model with the testing accuracy being 0.9790.  
Figure 19: ANFIS model training accuracy.  
Figure 20: ANFIS model testing accuracy.