# A Convex Combination Approach for Artificial Neural Network of Interval Data
## 3 The Proposed Method Artificial Neural Network with Convex Combination (ANN-CC)
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**One Hidden Node** & **Weight Parameter** & \multicolumn{2}{c}{**MAE**} & \multicolumn{2}{c}{**MSE**} & \multicolumn{2}{c}{**RMSE**} \\ \hline PTT & w1 & w2 & out & in & out & in & out & in \\ \hline tanh & 0.648521 & 0.999000 & 0.014094 & 0.013565 & 0.000315 & 0.000298 & 0.017751 & 0.017265 \\ sigmoid & 0.608577 & 0.962942 & 0.011501 & 0.011931 & 0.000249 & 0.000237 & 0.015792 & 0.015362 \\ linear & 0.611678 & 0.999000 & 0.013707 & 0.013696 & 0.000303 & 0.000301 & 0.017401 & 0.017378 \\ exp & 0.607746 & 0.999000 & **0.010572** & **0.010023** & **0.000221** & **0.000209** & **0.014862** & **0.014465** \\ \hline SCC & w1 & w2 & out & in & out & in & out & In \\ \hline tanh & 0.510112 & 0.927919 & 0.011382 & 0.011377 & 0.000218 & 0.000211 & 0.014768 & 0.014533 \\ sigmoid & 0.513121 & 0.910014 & **0.010506** & **0.011060** & **0.000190** & **0.000160** & **0.013781** & **0.012658** \\ linear & 0.519982 & 0.920239 & 0.011793 & 0.011423 & 0.000235 & 0.000232 & 0.015343 & 0.015238 \\ exp & 0.509987 & 0.930019 & 0.010734 & 0.011065 & 0.000193 & 0.000168 & 0.013897 & 0.012970 \\ \hline CPALL & w1 & w2 & out & in & out & in & out & In \\ \hline tanh & 0.412312 & 0.481917 & 0.013848 & 0.013835 & 0.000391 & 0.000384 & 0.019765 & 0.019588 \\ sigmoid & 0.461660 & 0.500013 & **0.012627** & **0.012231** & **0.000235** & **0.000191** & **0.015343** & **0.013832** \\ linear & 0.386464 & 0.342022 & 0.013619 & 0.012975 & 0.000353 & 0.0002277 & 0.018756 & 0.016650 \\ exp & 0.461668 & 0.500101 & 0.013608 & 0.012891 & 0.000342 & 0.000269 & 0.018489 & 0.016413 \\ \hline
**Two Hidden Nodes** & **Weight Parameter** & \multicolumn{2}{c}{**MAE**} & \multicolumn{2}{c}{**MSE**} & \multicolumn{2}{c}{**RMSE**} \\ \hline PTT & w1 & w2 & out & in & out & in & out & In \\ \hline tanh & 0.398420 & 0.398420 & 0.014168 & 0.013570 & 0.000328 & 0.000294 & 0.018121 & 0.017151 \\ sigmoid & 0.409278 & 0.409278 & 0.010203 & 0.009748 & 0.000167 & 0.000157 & 0.012934 & 0.012535 \\ linear & 0.421373 & 0.421373 & 0.013431 & 0.013755 & 0.000315 & 0.000298 & 0.017763 & 0.017269 \\ exp & 0.389728 & 0.389728 & **0.009030** & **0.009085** & **0.000151** & **0.000145** & **0.012275** & **0.012040** \\ \hline SCC & w1 & w2 & out & in & out & in & out & In \\ \hline tanh & 0.358503 & 0.358503 & 0.012146 & 0.011344 & 0.000242 & 0.000201 & 0.0155543 & 0.014181 \\ sigmoid & 0.387659 & 0.387659 & 0.010360 & 0.010467 & 0.000162 & 0.000168 & 0.012736 & 0.012977 \\ linear & 0.359730 & 0.359730 & 0.010858 & 0.010981 & 0.000172 & 0.000190 & 0.013121 & 0.013779 \\ exp & 0.351820 & 0.351820 & **0.010011** & **0.010006** & **0.000156** & **0.000155** & **0.012494** & **0.012469** \\ \hline CPALL & w1 & w2 & out & in & out & in & out & In \\ \hline tanh & 0.423709 & 0.423709 & 0.014073 & 0.013789 & 0.000318 & 0.000319 & 0.017836 & 0.017856 \\ sigmoid & 0.376741 & 0.376741 & 0.012700 & 0.012163 & 0.000255 & 0.000262 & 0.015960 & 0.016191 \\ linear & 0.431735 & 0.431735 & 0.015190 & 0.013474 & 0.000393 & 0.000301 & 0.019825 & 0.017356 \\ exp & 0.427827 & 0.427827 & **0.011830** & **0.011123** & **0.000212** & **0.000201** & **0.014567** & **0.014183** \\ \hline
**Three Hidden Nodes** & **Weight Parameter** & \multicolumn{2}{c}{**MAE**} & \multicolumn{2}{c}{**MSE**} & \multicolumn{2}{c}{**RMSE**} \\ \hline PTT & w1 & w2 & out & in & out & in & out & In \\ \hline tanh & 0.394010 & 0.394010 & 0.012486 & 0.011650 & 0.000279 & 0.000215 & 0.016751 & 0.014672 \\ sigmoid & 0.387755 & 0.387755 & 0.010510 & 0.009682 & 0.000192 & 0.000151 & 0.013866 & 0.012291 \\ linear & 0.425890 & 0.425890 & 0.012102 & 0.0115



Furthermore, we also compared the performance of the ANN-CC models with the traditional ANN models, ANN-Center (Table 5) and RANN-LU (Table 6). Tables 5 and 6 also provide the MAE, MSE, and RMSE of ANN-Center and RANN-LU, respectively. We note that four activations and a different number of hidden neurons were compared, and we also found that the exponential activation function provided higher performance in most cases.