# Rough Set Theory and Soft Computing Methods for Building Explainable and Interpretable AI/ML Models
## 4 Methodology
### Classification
#### 4.2.2 MLSpecialReduct
* **Exang (Exercise-Induced Angina)**: Indicates presence of angina (1 = Yes, 0 = No). * **Oldpeak (ST Depression Induced by Exercise)**: ST depression relative to rest. * 0 = Upsloping;
- 1 = Flat;
- 2 = Downsloping. * **CA (Number of Major Vessels Colored by Fluoroscopy)**: Ranges from 0 to 3. * 1 = Normal; \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Method** & **Time Complexity** & **Max Features (1 h)** \\ \hline MLRduct & \(O(2^{n})\) & 20 \\ \hline MLSpecialReduct & \(O(n^{2})\) & 100+ \\ \hline PCA & \(O(n^{3})\) & 10,000+ \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Computational complexity comparison. * 2 = Fixed defect;
* 3 = Reversible defect. * **Target**: Indicates presence of cardiovascular disease (1 = Yes, 0 = No). #### 5.1.3 Sample Data

Table 4 presents a sample of the dataset. This dataset was used to analyze correlations between medical attributes and cardiovascular risk factors. The classification models aim to predict the likelihood of cardiovascular disease based on these attributes. #### 5.1.4 Dataset Characteristics

Table 5 compares the specifications of our private dataset with the UCI Heart Disease dataset. **Data Collection**: Our private cardiovascular dataset was prospectively collected over 3 years (2020-2023) from partner hospitals. It contains the following:

* **A total of 14 Clinically Validated Features**:
* 6 continuous (age, BP, cholesterol, etc. );
* 5 ordinal (chest pain type, ECG results);
* 3 nominal (gender, thalassemia, etc.). * **Strict Inclusion Criteria**:
* Adults (29-77 years) with complete labwork;
* Confirmed diagnosis via angiography (gold standard). **Preprocessing Pipeline**: * Table 6 summarizes the preprocessing steps applied to the clinical data, along with their medical rationale. \begin{table}
\begin{tabular}{l l l l l l l l l l l l l l} \hline \hline
**Patient** & **Age** & **Sex** & **CP** & **BP** & **Chol** & **FBS** & **ECG** & **Thalach** & **Ex** & **OldPk** & **Slp** & **CA** & **Thl** & **Tgt** \\ \hline Patient 1 & 63 & 1 & 3 & 145 & 233 & 1 & 0 & 150 & 0 & 2.3 & 0 & 0 & 1 & 1 \\ \hline Patient 2 & 37 & 1 & 2 & 130 & 250 & 0 & 1 & 187 & 0 & 3.5 & 0 & 0 & 2 & 1 \\ \hline Patient 3 & 61 & 0 & 0 & 130 & 330 & 0 & 0 & 169 & 0 & 0 & 2 & 0 & 2 & 0 \\ \hline Patient 4 & 58 & 1 & 2 & 112 & 230 & 0 & 0 & 165 & 0 & 2.5 & 1 & 1 & 3 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Sample of the dataset used in this study. \begin{table}
\begin{tabular}{l c c} \hline \hline
**Characteristic** & **Our Dataset** & **UCI Heart** \\ \hline Samples & 1000 & 303 \\ Features & 14 & 13 \\ \hline Demographics & & \\ Age Range (years) & 29–77 & 29–77 \\ Male/Female Ratio & 55\%/45\% & 68\%/32\% \\ \hline Clinical Targets & & \\ CVD Prevalence & 50\% & 44\% \\ Positive/Negative Balance & 1:1 & 1.27:1 \\ \hline Data Quality & & \\ Missing Values & 0.1\% & 0.3\% \\ Outlier Fraction & 2.7\% & 3.1\% \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparative dataset specifications. **Reproducibility Measures**:
* Identical preprocessing applied to both datasets;
* Publicly available UCI dataset used for benchmarking;
* Full preprocessing code available upon request from the corresponding author (see Data Availability Statement). ### Experimental Protocol

To ensure statistical rigor and reproducibility, we implemented the following evaluation framework:

* **Ten-fold stratified cross-validation**:
* Fixed random seed (42) for reproducible splits;
* Stratification by both class labels and key demographics (age, gender);
* 9:1 training/validation ratio maintained across all folds. * **L2 regularization*
* Applied consistently across all classifiers (SVM, Neural Net, etc. );
* Penalty strength selected via grid search on validation folds;
* Regularization terms normalized by feature counts. * **Held-out validation set**:
* 20% of data (n = 200) reserved for final evaluation;
* Balanced for class distribution (50% CVD positive/negative);
* Never used during model development or hyperparameter tuning.