## 3 Materials and Methods
### The Modified DE Algorithm
In order to further testify the effectiveness of the proposed BRBES in identifying severe and non-severe COVID-19, it is compared with five state-of-the-art machine learning algorithms including logistic regression (LR), support vector machine (SVM), neural network (NN), and decision tree (DT). The comparison results are shown in Table 11. The comparison results of proposed BRBES with traditional machine learning algorithms are graphically shown in Figure 5. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **P-CBRB** & **T-CBRB** & **P-DBRB** & **T-DBRB** \\ \hline Accuracy & 0.845 & 0.954 & 0.791 & 0.927 \\ \hline Sensitivity & 0.615 & 0.923 & 0.538 & 0.769 \\ \hline Specificity & 0.876 & 0.959 & 0.825 & 0.948 \\ \hline No of Parameter & 378 & & 18 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Comparision among different BRB models. Figure 4: Comparison of Accuracy, Sensitivity and Specificity for P-CBRB, T-CBRB, P-DBRB, and T-DBRB. According to the result presented in Table 11, the BRBES perform better in classification than all the aforementioned machine learning algorithms. The accuracy of BRBES is approximately 11%, 9%, 7%, and 3% higher than LR, SVM, NN, and DT, respectively. The other two matrices (i.e., sensitivity and specificity) of BRBES are also better than other methods to a large margin. All these aforementioned results prove that BRBES outperforms the traditional machine learning algorithms in early prediction of COVID-19 clinical severity. Finally, the ROC curves and AUC values for the classifiers mentioned above--BRBES, SVM, LR, NN, and DR--are shown in Figure 6 to clearly compare their performance. The AUC values for BRBES, DT, ANN, SVM, and LR are 0.9885, 0.9558, 0.9422, 0.9153, and 0.9230, respectively. It is evident that our proposed BRBES achieved better performance in both ROC curves and AUC values than all the traditional machine learning algorithms compared in this study. Moreover, the standard deviation of BRBES is the lowest among all the methods which demonstrate that our proposed method is more stable than traditional machine learning algorithms. This is because unlike BRBES, the machine learning algorithms are data-driven; they rely just on data to predict the outcome, whereas BRBES is both a data-driven and knowledge-driven approach. The experts knowledge about the domain can be integrate in the BRBES in the form of belief rule base which can be later fine-tuned using different optimization techniques utilizing historical data to imitate the real situation. Thus, BRBES predicts the outcome base on both expert knowledge and data. Moreover, BRBES can address different types of uncertainty like incompleteness, ignorance, vagueness, imprecision, and ambiguity, which is not true for traditional machine learning algorithms. Therefore, we can conclude that the ability to take into account the expert knowledge in the inference process and handling different type of uncertainty in data are the secrete behind the superior performance of BRBES. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **BRBES** & **LR** & **SVM** & **NN** & **DT** \\ \hline Accuracy & 0.954 & 0.855 & 0.873 & 0.891 & 0.918 \\ \hline Sensitivity & 0.923 & 0.615 & 0.692 & 0.769 & 0.846 \\ \hline Specificity & 0.959 & 0.887 & 0.897 & 0.907 & 0.928 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Comparison among different machine learning algorithms. Figure 5: Comparison of accuracy, sensitivity, and specificity for BRBES (T-CBRB), LR, SVM, NN, and DT. ## 6 Conclusions

This paper proposed a COVID-19 severity prediction method based on the belief rule-based expert system. The proposed method can integrate the advantages of knowledge-based plus data-driven approaches in a single framework that is more suitable for COVID-19 severity identification. The initial belief rule base is established by expert knowledge which is further optimized by COVID-19 patients' data using a modified differential evolution algorithm.