## 3 Materials and Methods
### The Modified DE Algorithm
``` Input:\(BRB_{initial}\), \(D_{train}=\{X_{train},Y_{train}\}\) Output:\(BRB_{trained}\)  encode the initial BRB to a solution vector as shown in Figure 1;  initialize the population of first generation as \(P^{1}=\{I_{1}^{1},I_{2}^{1},\ldots I_{NP}^{1}\}\); for\(g\gets 1\)to\(Generation_{max}\)do for\(i\gets 1\)to\(NP\)do  randomly select three distinct individuals \(I_{p}\), \(I_{q}\), \(I_{r}\) from \(NP\) solutions other than \(I_{i}\); Mutation:\(V_{i}^{g+1}=I_{p}^{g}+F*(I_{q}^{g}-I_{r}^{g})\); Crossover:\(V_{i,j}^{g+1}= \begin{cases}I_{i,j}^{g},\,if\,random(0,1)>CR\\ V_{i,j}^{g+1},\,otherwise\end{cases} \) \(j=1,\ldots,N\); Correction:\(V_{i,j}^{g+1}= \begin{cases}V_{i,j}^{g+1};&if\,lb_{j}\leq V_{i,j}^{g}\leq ub _{j}\\ \frac{V_{i,j}^{g+1}+F*(ub_{j})+lb_{j}}{2F+1};&\text{otherwise}\end{cases} \); \(j=1,\ldots,N\); Fitness calculation: for\(l\gets 1\)to\(length(\{X_{train},Y_{train}\})\)do  Rules activation: Formulas (7) and (8); Rules aggregation: Formulas (5) and (6); Classification:\(Prediction_{train}(l)=arg\underset{i=1,\ldots,N}{max}\{\beta_{i}\}\); if\(Prediction_{train}(l)==Y_{train}(l)\)then \(Error_{train}(l)=0\); else \(Error_{train}(l)=1\);  end if  end for \(MSE_{train}=\frac{1}{t}\sum_{t=1}^{T}Error_{train}(t)\); Selection:\(I_{i}^{g+1}=\begin{cases}V_{i}^{g+1}\

## 4 Experiments

### Dataset

The dataset used in this study was collected by the authors of [19] from Tongji Hospital located in the region of Wuhan, China. The dataset includes the epidemiological, demographic, clinical, laboratory, and mortality outcome information collected from the medical records of 485 patients. In this study, to develop the predictive model, we consider three laboratory information: lactic dehydrogenase (LDH), lymphocytes, and high-sensitivity C-reactive protein (h-CRP) of a patient as features. Among the patients, those who are transferred to ICU are considered critical patients and the rest of the patients are considered normal in this study. Therefore, the dataset consists of 110 positive instances (critical) and 375 negative(normal) samples. ### Experimental Settings

The real patient data described in Section 4.1 are used to performs different set of experiments to validate the proposed method and to compare its performance with others state-of-art methods. Fivefold cross-validation technique is performed to train and test all the predictive models to avoid the effect of the data imbalance as well as to avoid overfitting and underfitting. The dataset was split into five folds where each fold contains roughly the same proportion of the two types of outcome. A single fold out of five folds is kept to test the model while the remaining four folds are used to train the model The performance of the proposed method is evaluated in terms of three criteria--accuracy, specificity, and sensitivity. These are widely used performance measure matrices for classification problem. The metrics are calculated based on the confusion matrix shown in the Table 3.

Accuracy is defined as the ratio of total number of prediction that are correct [36]. \[Accuracy=\frac{TP+TN}{TP+FP+TN+FN} \tag{24}\]

Sensitivity is the proportion of positive observed values (critical patient) correctly predicted as positive (critical) [36]. \[Sensitivity=\frac{TP}{TP+FN} \tag{25}\]

Specificity is the proportion of negative tuples (non-severe patients) are correctly identified [36]. \[Specificity=\frac{TN}{FP+TN} \tag{26}\]

Besides, the ROC curve is used for comprehensive and visual comparison of different classifiers' performance [37]. In the ROC curve, the area under the curve (AUC) is calculated to estimate the accuracy of the classifier where a larger AUC value indicates higher accuracy [38]. Python programming language [39] (version 3.6.1) is used for implementation of Conjunctive and Disjunctive BRB. The first experiment was perform to compare the prediction performance of Conjunctive and Disjunctive to select the best BRB model.