# Rough Set Theory and Soft Computing Methods for Building Explainable and Interpretable AI/ML Models
## 4 Methodology
### Classification
#### 4.2.2 MLSpecialReduct
\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Models** & **Precision** & **Recall** & **F1-Score** \\ \hline Gaussian Process & 0.77 & 0.77 & 0.77 \\ \hline Random Forest & 0.77 & 0.77 & 0.77 \\ \hline Nearest Neighbors & 0.74 & 0.74 & 0.74 \\ \hline Linear SVM & 0.77 & 0.77 & 0.77 \\ \hline Neural Net & 0.73 & 0.72 & 0.72 \\ \hline Naive Bayes & 0.77 & 0.77 & 0.77 \\ \hline Decision Tree & 0.72 & 0.72 & 0.72 \\ \hline AdaBoost & 0.74 & 0.72 & 0.72 \\ \hline QDA & 0.74 & 0.72 & 0.72 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Performance of classifier models with MLVarianceThreshold. \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Models** & **Precision** & **Recall** & **F1-Score** \\ \hline Gaussian Process & 0.74 & 0.74 & 0.74 \\ \hline Random Forest & 0.79 & 0.79 & 0.78 \\ \hline Nearest Neighbors & 0.74 & 0.74 & 0.74 \\ \hline Linear SVM & 0.74 & 0.74 & 0.74 \\ \hline RBF SVM & 0.74 & 0.74 & 0.74 \\ \hline Neural Net & 0.75 & 0.74 & 0.74 \\ \hline Naive Bayes & 0.83 & 0.83 & 0.83 \\ \hline Decision Tree & 0.64 & 0.64 & 0.64 \\ \hline AdaBoost & 0.73 & 0.74 & 0.73 \\ \hline QDA & 0.74 & 0.74 & 0.74 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Comparison classifier models with MLFuzzyRoughSet. ### Computational Efficiency Analysis

Table 12 quantifies the resource-accuracy trade-offs across methods, while Figure 8 visualizes the non-linear relationships. Our analysis reveals the following:

* MLSpecialReduct achieves 45% faster training than MLRduct (68 s vs. 142 s) with higher accuracy (0.99 vs. 0.87);
* Memory usage scales linearly with method complexity (Figure 8, right);
* The accuracy-time curve (Figure 8, left) suggests diminishing returns beyond 70 s.

### Public Dataset Validation

To ensure generalizability, we replicated our analysis on two benchmark datasets (Table 13): \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**UCI Heart Disease**} & \multicolumn{2}{c}{**Our Dataset**} \\
**Method** & **Acc.** & **F1** & **Acc.** & **F1** \\ \hline MLSpecialReduct & 0.97 & 0.96 & 0.99 & 0.98 \\ \hline MLRduct & 0.85 & 0.84 & 0.87 & 0.86 \\ \hline MLVarianceThreshold & 0.76 & 0.75 & 0.77 & 0.76 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Performance comparison across datasets. Figure 8: Resource–accuracy trade-offs: (**left**) Accuracy plateaus with increased training time, with MLSpecialReduct (the star) achieving optimal balance. (**right**) Memory–accuracy relationship shows diminishing returns beyond 200 MB. Figure 9 illustrates the performance comparison across datasets with error bars showing the standard deviation. **Key Observations**:

* **Ranking Consistency**: All methods maintained identical performance rankings across datasets (Kendall's \(\tau=1.0\), \(p<0.01\)). * **Performance Gap**:

* Absolute accuracy drop: 2% (UCI) vs. private dataset. * Relative F1-score stability: \(\Delta\leq 1.5\%\) across all methods. * **Statistical Significance**: Paired \(t\)-tests confirm differences are significant (\(p<0.05\)) for all method pairs. ### Statistical Validation

**Statistical Analysis:**

The cross-validation results (Table 14) and distribution (Figure 10) reveal three key insights:

1. **Performance Superiority**:

* MLSpecialReduct achieved significantly higher accuracy than MLReduct (12% improvement, \(p=2.3\times 10^{-6}\)) and MLVarianceThreshold (22% improvement, \(p=9.1\times 10^{-9}\)) based on paired \(t\)-tests. * The narrow IQR (0.98-1.00) in Figure 10 shows 75% of folds achieved \(\geq\)0.98 accuracy. 2. **Robustness**:

* Minimal standard deviations (\(\leq\)0.01) indicate consistent performance regardless of data partitioning. * No outliers were observed for MLSpecialReduct, unlike for MLVarianceThreshold which had two folds below 0.76 accuracy. 3. **Statistical Significance**:

* Effect sizes (Cohen's d) were large: 6.2 vs. MLReduct and 9.8 vs. MLVarianceThreshold. Figure 9: Performance comparison across datasets.