## 4 Experimental Results
### Cross-Validation Experiments
\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) & 85.6 (0.6) & 95.5 (0.9) & 83.8 (1.3) & 86.3 (1.1) & 20.7 (0.4) & 3.2 (0.1) \\ DIMLP (50) & **85.8** (0.6) & 95.5 (1.0) & **84.4** (1.1) & **86.8** (0.9) & 20.4 (0.5) & 3.2 (0.0) \\ DIMLP (100) & 85.7 (0.5) & 95.7 (1.0) & 83.9 (0.6) & 86.4 (0.6) & 20.1 (0.4) & 3.2 (0.0) \\ DIMLP (150) & 85.7 (0.5) & 95.8 (1.0) & 83.5 (0.9) & 86.1 (0.7) & 20.0 (0.5) & 3.2 (0.0) \\ \hline RF (25) & 81.9 (2.1) & 93.8 (1.6) & 81.0 (1.8) & 83.6 (1.6) & 39.0 (0.9) & 4.0 (0.0) \\ RF (50) & 82.3 (1.7) & 93.1 (2.0) & 80.5 (1.5) & 83.7 (1.1) & 40.0 (0.6) & 4.1 (0.0) \\ RF (100) & 82.7 (1.6) & 93.2 (1.7) & 81.4 (1.6) & 84.4 (1.1) & 39.7 (1.1) & 4.1 (0.0) \\ RF (150) & 83.3 (1.5) & 94.7 (1.3) & 81.9 (1.5) & 84.5 (0.9) & 39.8 (1.1) & 4.1 (0.0) \\ \hline RF-3 (25) & 83.7 (1.3) & 95.9 (1.2) & 82.0 (1.4) & 84.2 (1.4) & 18.8 (0.6) & 3.1 (0.0) \\ RF-3 (50) & 83.7 (1.3) & 95.6 (1.3) & 82.8 (1.3) & 84.9 (1.1) & 17.6 (0.6) & 3.1 (0.0) \\ RF-3 (100) & 83.7 (0.8) & 96.0 (0.9) & 82.4 (1.1) & 84.5 (0.7) & 18.0 (0.5) & 3.1 (0.0) \\ RF-3 (150) & 84.7 (1.1) & 96.1 (1.3) & 82.8 (1.9) & 85.1 (1.1) & 18.1 (0.5) & 3.1 (0.0) \\ \hline GB (1,25) & 84.7 (0.8) & **99.0** (0.6) & 84.0 (0.7) & 84.7 (0.8) & **11.0** (0.3) & **2.6** (0.0) \\ GB (1,50) & 84.9 (1.1) & 98.1 (0.8) & 84.3 (1.0) & 85.2 (0.9) & 15.2 (0.5) & 2.8 (0.0) \\ GB (1,100) & 84.0 (1.3) & 95.5 (1.6) & 82.0 (1.0) & 84.5 (1.3) & 20.9 (0.7) & 3.2 (0.0) \\ GB (1,150) & 83.2 (1.2) & 95.1 (1.0) & 81.7 (0.9) & 84.1 (1.0) & 21.9 (0.5) & 3.2 (0.0) \\ \hline GB (2,25) & 81.3 (1.1) & 96.0 (1.1) & 81.3 (1.4) & 82.6 (1.0) & 17.0 (0.7) & 3.0 (0.0) \\ GB (2,50) & 81.6 (1.1) & 95.3 (1.3) & 80.6 (1.6) & 82.7 (1.1) & 22.7 (0.8) & 3.3 (0.1) \\ GB (2,100) & 81.6 (1.1) & 95.1 (1.6) & 79.9 (1.7) & 82.3 (1.3) & 27.5 (0.6) & 3.6 (0.0) \\ GB (2,150) & 80.8 (1.2) & 95.1 (1.6) & 80.0 (1.3) & 82.0 (1.0) & 30.8 (0.7) & 3.7 (0.0) \\ \hline GB (3,25) & 80.8 (1.3) & 95.5 (1.4) & 80.3 (1.1) & 82.1 (1.4) & 22.8 (0.6) & 3.4 (0.0) \\ GB (3,50) & 80.4 (1.5) & 94.1 (0.9) & 80.0 (1.4) & 82.2 (1.3) & 28.4 (0.5) & 3.6 (0.0) \\ GB (3,100) & 79.9 (1.9) & 94.1 (1.5) & 79.7 (1.9) & 81.7 (2.1) & 34.8 (0.7) & 3.8 (0.0) \\ GB (3,150) & 79.8 (1.4) & 94.2 (1.8) & 78.8 (2.3) & 81.1 (1.8) & 37.3 (1.2) & 3.8 (0.0) \\ \hline SR (25) & — & — & 77.1 (1.4) & — & 23.2 (0.9) & 3.0 (0.0) \\ SR (50) & — & — & 75.2 (2.1) & — & 36.3 (1.7) & 3.0 (0.0) \\ SR (100) & — & — & 71.4 (0.7) & — & 54.9 (2.0) & 3.0 (0.0) \\ SR (150) & — & — & 69.6 (1.4) & — & 69.5 (2.9) & 3.0 (0.0) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Average results obtained on the “Heart Disease” 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. With the \"Ionosphere\" dataset, the results illustrated in Table 6 show that the highest average predictive accuracy was obtained by both the DIMLP ensembles and RFs (93.4%). Moreover, the same models provided the highest average predictive accuracy of the rules when ensembles and rulesets agreed (94.5%). However, rulesets generated from DIMLPs were less complex than those extracted from RFs, on average (18.3 versus 32.6). The highest average fidelity was attained by GB (99.6%), with the least complex rulesets (6.5 rules with 1.9 antecedents). Table 7 depicts the results for the \"Mammographic\" classification problem. The highest average predictive accuracies were achieved by the DIMLPs for both ensembles and their generated rulesets. Moreover, the lowest predictive accuracy averages were provided by RF. The reason could be that the RFs were overtrained in this particular case. Indeed, for the average predictive accuracy, the difference from the DIMLPs was greater than five points, with almost eight times more rules generated.