## 3 Materials and Methods
### The Modified DE Algorithm
The hidden layers are followed by an output layer consisting of a single neuron with _sigmoid_ activation functions to predict the category. The network is trained for 100 iterations using _Adam_ algorithm to optimize binary cross entropy loss function with a learning rate of 0.001. For SVM, since our dataset is small, we used a linear kernel to avoid overfitting. Besides, we empirically selected the value of C as 1.25 which optimizes the margin of the hyperplane and thereby minimizes misclassification on training data. The logistic regression is implemented using binary cross-entropy as the loss function with l2 penalization. We used the lbfgs optimizer with a learning rate of 0.001 to minimize the binary cross-entropy loss. For the Decision Tree (DT), we used the Gini-index as the splitting criteria and maximum depth was set to 3 so that the model can avoid overfitting. Other parameters for all the models are kept default as in the scikit learn. A summary of the hyperparameters settings of different machine learning models used in this study for comparison is shown in the Table 9. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Rule Weight**} & \multicolumn{3}{c}{**Antecedent Attributes**} & \multicolumn{3}{c}{**COVID-19 Clinical Severity**} \\ \cline{2-6}  & **A1** & **A2** & **A3** & **Normal** & **Critical** \\ \hline
0.8 & VH & VH & VH & 0.0 & 1.0 \\
0.9 & H & H & H & 0.3 & 0.7 \\
0.8 & M & M & M & 0.5 & 0.5 \\
0.9 & L & L & L & 0.7 & 0.3 \\
0.7 & VL & VL & VL & 1.0 & 0.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Initial disjunctive belief rule base. \begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{1}{c}{**Model**} & \multicolumn{1}{c}{**Settings**} \\ \hline Logistic Regression (LR) & Loss: binary cross-entropy; penalty: l2 \\  & Optimizer: lbfgs; learning rate: 0.001 \\ \hline Support Vector Machine (SVM) & Kernel: linear; C: 1.25 \\ \hline Decision Tree (DT) & Splitting Criteria: Gini-index; Maximum Depth: 3 \\ \hline \multirow{4}{*}{Neural Network (NN)} & First hidden layer—units: 10; activation: relu \\  & Second hidden layer—units: 5; activation: relu \\ \cline{1-1}  & Output layer—unit: 1; activation: sigmoid \\ \cline{1-1}  & Loss: binary cross-entropy ; optimizer: adam; learning rate: 0.001 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Hyperparameters settings of different machine learning models. ## 5 Result and Discussion

Four indices including accuracy, specificity and sensitivity for pre-trained CBRB, pretrained DBRB, trained CBRB and trained DBRB which are labelled as P-CBRB, P-DBRB, T-CBRB, and T-DBRB, respectively, are shown in Table 10. These results are shown graphically in Figure 4.

As shown in Table 10, all the evaluation indices are higher for CBRB than DBRB before and after training. This is because CBRB has large number of knowledge representation parameters compared to DBRB. Therefore, more expert knowledge can be modeled through CBRB which can better map the nonlinear casual relationship between the antecedents and consequent. Table 10 also shows that accuracy of T-CBRBES and T-DBRBES is 0.954 and 0.927, respectively, which is greatly higher than P-CBRBES and P-DBRBES (0.845 and 0.791, respectively). The other two indices--sensitivity and specificity--show a similar pattern. This demonstrates the effectiveness of the DE base optimization technique for both types of the BRBES; it also indicates that the initial BRBs provided by domain experts significantly deviated from the reality and further reveals that DE can fine tuned the initial knowledge base provided by domain expert using a historical data set such a way that can reflect the real situation more accurately. Above all, the trained CBRB performs better than all other BRB models and is utilized in the rest of the experiments.