## 3 Computational Results
### Experimental Results  
The predicted job cycle times and the observed job cycle times for different numbers of clusters and different membership threshold values are presented in Figure 8. It shows that the predicted job cycle time follows similar patterns to those of the observed data. The proposed approach is quite effective in predicting the job cycle time, and computational results show that the observed and predicted job cycle times are matched well when the number of clusters goes from 16 to 20. Note that the membership threshold value may indeed affect the accuracy of the job cycle time prediction. As the number of clusters increases from 20 to 24, the job cycle time prediction performance fluctuates more under different membership threshold values. Next, we discuss the job cycle time prediction accuracy in terms of the MAE (hours), MAPE (%), and RMSE (hours). To investigate how the number of clusters affects the prediction accuracy, we experimented using six different numbers of clusters, namely 14, 16, 18, 20, 22, and 24. The MAE, MAPE, and RMSE are used to evaluate the effects of the number of clusters overall testing data for the identical threshold value and the identical number of neurons in the BPN hidden layer, in Figures 9-11, respectively. These figures show similar trends in the MAE, MAPE, and RMSE values against different numbers of clusters, indicating that there might be the need to study optimal numbers of clusters appropriate to datasets but beyond the scope of this study. The curves of MAE, MAPE, and RMSE show that the job cycle time prediction accuracy is strongly correlated with the number of clusters. The job cycle time prediction performance varies with the number of clusters and is poor with too many or too few clusters, meaning that increasing or decreasing the number of clusters does not provide better job cycle time predictions. In Figure 9, we generally obtain better job cycle time prediction performance (MAE) with the threshold values \(\delta=0.05\) or \(0.08\). These threshold values provide good data classification that improves the job cycle time prediction accuracy in the BPN predictor. Similar trends are obtained for the MAPE and RMSE values in Figures 10 and 11, respectively. To investigate the effect of different numbers of neurons in the BPN hidden layer, we test the job cycle time prediction performance with the identical numbers of clusters (18, 20, and 22) by taking the average MAE, MAPE, and RMSE values for five runs and four threshold values, as shown in Figure 12. The job cycle time prediction performance is clearly not strongly correlated with the number of neurons in the hidden layer of the BPN predictor: increasing the number of neurons \(\xi\), improves the prediction accuracy only marginally. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Fuzziness exponent (\(m\)) & 2 \\ FCM termination tolerance (\(\phi\)) & \(10^{-4}\) \\ Number of clusters (\(G\)) & 14, 16, 18, 20, 22, and 24 \\ Population size (\(PS\)) & 40 \\ Number of generations (\(GN\)) & 1000 \\ Mutation probability (\(P_{m}\)) & 0.2 \\ Crossover probability (\(P_{c}\)) & 0.1 \\ Membership threshold value (\(\delta\)) & 0.01, 0.05, 0.08, and 0.1 \\ Fitness variance value (\(\epsilon\)) & \(10^{-4}\) \\ Learning rate (\(\pi\)) & 0.99 \\ Number of neurons in the input layer (\(\varphi\)) & 6 \\ Number of neurons in the hidden layer (\(k\)) & 7, 9, 11, 13, and 15 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters used in the proposed approach. Figure 8: Predicted and observed job cycle times (unit: hour) for different numbers of clusters; 14 (**a**), 16 (**b**), 18 (**c**), 20 (**d**), 22 (**e**), and 24 (**f**). Figure 10: Mean absolute percentage error (MAPE, unit: %)) against the number of clusters for different numbers of neurons \(\xi\) for different thereshold values \(\delta\); \(\delta=0.01\) (**a**), \(\delta=0.05\) (**b**) \(\delta=0.08\), (**c**), and \(\delta=0.1\) (**d**).