## 4 Experimental Results
### Cross-Validation Experiments
The average highest fidelity was reached by the decision stumps (99.0%). For this model, the average predictive accuracy attained by the rules was equal to 96.7%, and the complexity of the rules was less than half that obtained by RF (11.2 versus 24.3). Finally, the average predictive accuracy obtained by SR decreased as the number of trees in an ensemble increased. Moreover, with SR, the rules were, on average, the most complex. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Model** & **Acc.** & **Fid.** & **Acc. R. (a)** & **Acc. R. (b)** & **Nb. R.** & **Nb. Ant.** \\ \hline GB (1,25) & 85.6 (0.2) & **100.0** (0.0) & 85.6 (0.2) & 85.6 (0.2) & **2.0** (0.0) & **1.0** (0.0) \\ GB (1,50) & 85.6 (0.2) & **100.0** (0.0) & 85.6 (0.2) & 85.6 (0.2) & 2.1 (0.3) & **1.0** (0.1) \\ GB (1,100) & 87.1 (0.4) & 99.3 (0.3) & **86.6** (0.5) & 87.2 (0.4) & 13.2 (0.7) & 2.8 (0.1) \\ GB (1,150) & 86.9 (0.5) & 98.8 (0.3) & 86.5 (0.4) & 87.2 (0.5) & 20.7 (0.7) & 3.3 (0.1) \\ \hline GB (2,25) & 85.8 (0.4) & 99.8 (0.1) & 85.7 (0.4) & 85.8 (0.4) & 7.3 (0.4) & 2.2 (0.0) \\ GB (2,50) & 86.6 (0.3) & 99.2 (0.5) & 86.4 (0.5) & 86.8 (0.4) & 22.3 (0.8) & 3.3 (0.1) \\ GB (2,100) & 86.9 (0.5) & 97.7 (0.5) & 86.2 (0.6) & 87.4 (0.6) & 34.1 (0.8) & 3.9 (0.0) \\ GB (2,150) & 86.7 (0.5) & 97.3 (0.7) & 86.1 (0.5) & 87.4 (0.5) & 40.1 (0.7) & 4.1 (0.0) \\ \hline GB (3,25) & 85.9 (0.5) & 99.0 (0.4) & 85.4 (0.5) & 86.0 (0.5) & 21.9 (0.4) & 3.4 (0.0) \\ GB (3,50) & 86.7 (0.3) & 97.9 (0.4) & 85.9 (0.6) & 87.1 (0.5) & 35.3 (1.1) & 4.0 (0.0) \\ GB (3,100) & 86.8 (0.5) & 96.6 (0.9) & 86.1 (0.8) & 87.8 (0.6) & 48.6 (0.5) & 4.2 (0.0) \\ GB (3,150) & 86.7 (0.8) & 96.4 (0.9) & 86.0 (0.7) & 87.7 (1.0) & 57.2 (0.7) & 4.3 (0.0) \\ \hline SR (25) & — & — & 85.4 (0.2) & — & 13.2 (0.8) & 3.0 (0.0) \\ SR (50) & — & — & 85.5 (0.3) & — & 19.3 (0.8) & 3.0 (0.0) \\ SR (100) & — & — & 85.2 (0.5) & — & 28.3 (1.4) & 3.0 (0.0) \\ SR (150) & — & — & 85.5 (0.4) & — & 35.3 (1.3) & 3.0 (0.0) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._ \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Model** & **Acc.** & **Fid.** & **Acc. R. (a)** & **Acc. R. (b)** & **Nb. R.** & **Nb. Ant.** \\ \hline DIMLP (25) & 97.0 (0.2) & 98.7 (0.2) & 96.4 (0.4) & 97.3 (0.2) & 12.4 (0.6) & 2.7 (0.1) \\ DIMLP (50) & 97.2 (0.2) & 98.6 (0.4) & 96.3 (0.4) & 97.4 (0.2) & 12.5 (0.7) & 2.6 (0.1) \\ DIMLP (100) & 97.1 (0.1) & 98.8 (0.4) & 96.4 (0.4) & 97.3 (0.2) & 12.7 (0.3) & 2.7 (0.1) \\ DIMLP (150) & 97.2 (0.2) & 98.8 (0.4) & 96.4 (0.4) & 97.3 (0.3) & 12.7 (0.2) & 2.7 (0.1) \\ \hline RF (25) & 97.0 (0.3) & 98.5 (0.4) & 96.7 (0.6) & 97.6 (0.3) & 24.6 (0.7) & 3.4 (0.1) \\ RF (50) & 97.1 (0.3) & 98.5 (0.4) & 96.7 (0.3) & 97.6 (0.3) & 24.3 (0.5) & 3.4 (0.0) \\ RF (100) & 97.2 (0.2) & 98.4 (0.5) & 96.6 (0.5) & 97.7 (0.2) & 24.2 (0.5) & 3.4 (0.0) \\ RF (150) & **97.4** (0.1) & 98.5 (0.2) & **96.9** (0.2) & **97.9** (0.2) & 24.3 (0.5) & 3.3 (0.0) \\ \hline RF-3 (25) & 97.0 (0.4) & 98.9 (0.4) & 96.3 (0.4) & 97.1 (0.4) & 10.9 (0.7) & 2.6 (0.1) \\ RF-3 (50) & 97.1 (0.4) & 98.7 (0.5) & 96.4 (0.4) & 97.4 (0.3) & 11.0 (0.4) & 2.6 (0.0) \\ RF-3 (100) & 97.3 (0.2) & 98.7 (0.5) & 96.5 (0.3) & 97.5 (0.3) & 11.2 (0.4) & 2.6 (0.1) \\ RF-3 (150) & 97.3 (0.2) & 98.8 (0.3) & 96.5 (0.4) & 97.5 (0.2) & 11.1 (0.6) & 2.6 (0.0) \\ \hline GB (1,25) & 97.3 (0.2) & **99.0** (0.3) & 96.7 (0.3) & 97.4 (0.2) & 11.2 (0.4) & 2.6 (0.0) \\ GB (1,50) & 96.8 (0.2) & 98.7 (0.2) & 96.1 (0.4) & 97.1 (0.3) & 11.8 (0.4) & 2.7 (0.0) \\ GB (1,100) & 96.7 (0.2) & 98.9 (0.5) & 96.3 (0.4) & 97.0 (0.3) & 12.0 (0.3) & 2.7 (0.1) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Average results obtained on the “Breast Cancer” dataset. For each column, the highest average accuracy or average fidelity is represented in bold, along with the lowest average number of rules or average number of antecedents. Table 4 depicts the results for the \"Divorce\" dataset. The highest predictive accuracy was obtained by the DIMLP ensembles (98.1%) with 5.5 rules, on average. GB provided the highest fidelity with 99.5% and 3.8 rules, on average.