## 3 Materials and Methods
### The Modified DE Algorithm
The BRB model is depicted in Figure 3 where lactic dehydrogenase (LDH), lymphocytes, and high-sensitivity C-reactive protein (hs-CRP) are antecedent attributes while the clinical severity of COVID-19 was considered as the consequent attribute. The ref \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Predicted Critical** & **Predicted Non-Critical** \\ \hline Actual Critical & TP & FN \\ Actual non-critical & FP & TN \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Confusion matrix for COVID-19 severity prediction. erential points and their initial numerical values for all antecedent attributes are shown in Tables 4-6. The referential points and corresponding numerical values for both the antecedent and consequent attributes are determined based on the suggestions of a group of physicians who have practical experience in COVID-19 patient treatment. Eventually, the initial conjunctive belief rule base (CBRB) consisting of 125 rules and disjunctive belief rule base (DBRB) consisting of five rules are shown in Tables 7 and 8. According to the physicians, all the belief rules are not equally important for COVID-19 clinical severity prediction. Some rules are most significant while others are less significant. Therefore, different weights are assigned to the rules of initial BRBs to quantify the rule's importance. \begin{table}
\begin{tabular}{c c c c c} \hline
**Referential Points** & **Very Low (VL)** & **Low (L)** & **Medium (M)** & **High (H)** & **Very High (VH)** \\ \hline Numerical Values & 0 & 79.5 & 159 & 238.5 & 318 \\ \hline \end{tabular}
\end{table} 
Table 6: The referential points and corresponding numerical values of antecedent high-sensitivity C-reactive protein (hs-CRP). \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Rule Weight**} & \multicolumn{2}{c}{**Antecedent Attributes**} & \multicolumn{2}{c}{**COVID-19 Clinical Severity**} \\ \cline{2-5}  & **A1** & **A2** & **A3** & **Normal** & **Critical** \\ \hline
0.9 & VH & VH & VH & 0.0 & 1.0 \\
0.9 & VH & VH & H & 0.1 & 0.9 \\... &... &... &... &... &... \\
1.0 & M & M & M & 0.5 & 0.5 \\... &... &... &... &... &... \\
0.9 & VL & VL & M & 0.9 & 0.1 \\
1.0 & VL & VL & VL & 1.0 & 0.0 \\ \hline \end{tabular}
\end{table} 
Table 7: Initial conjunctive belief rule base. Figure 3: BRB model for clinical severity of COVID-19. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Referential Points** & **Very Low (VL)** & **Low (L)** & **Medium (M)** & **High (H)** & **Very High (VH)** \\ \hline Numerical Values & 122 & 558.25 & 994.5 & 1430.75 & 1867 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The referential points and corresponding numerical values of antecedent lacide dehydrogenase (LDH). The weights of all the antecedent attributes lactic dehydrogenase (LDH), lymphocytes, and high-sensitivity C-reactive protein (hs-CRP) are set to 1 for both CBRB and DBRB as all of them are equally important for predicting clinical severity of COVID-19. Initial numerical values of referential points, rule weight, attributes weight, and consequent belief degrees in CBRB and DBRB are optimized according to the optimization model shown in Equations (11)-(18) using the DE algorithm. For each BRB model, DE was run for 2000 generations with 100 individuals in each generation. In both case, the crossover probability (R) and mutation factor (F) are set to 0.5 and 0.9, respectively. The second experiment was design to compare the performance of proposed method with four traditional machine learning techniques namely, decision tree (DT), support vector machine (SVM), logistic regression (LR), and artificial neural network. All the traditional machine-learning algorithms are implemented using _Scikit-learn_ package in Python [40]. The neural network (NN) architecture consists of two hidden layers with 10 and 5 neurons, respectively. The number of hidden layers and neurons in each layer are determined empirically. Each neuron of two hidden layers uses the _sigmoid_ activation to address nonlinearity of data.