# Reliability Evaluation of the Factors That Influenced COVID-19 Patients' Condition
## 3 Method of the Structure Function Building
Decision tree and FDT are powerful tools used for visualisation and explicit description of the decision-making process in decision analysis. The following are the advantages of the FDT classifiers: (a) simple to understand and interpret; (b) different possible scenarios of decision making can be analysed by this tool; (c) easy transformation to a decision table and collection of if-then decision rules; and (d) simple implementation into decision-making support systems and expert systems. The use of FDT for the structure function construction aids the definition of the correlation of terminologies of the reliability engineering and classifier induction. The system state is interpreted as the class attribute and the component states are considered as the input attributes: the component \(x_{i}\) corresponds to the input attribute \(A_{i}\). Each attribute \(\Lambda_{i}\) (\(1\leq i\leq n\)) is measured by two values of the attribute that correspond to the values of the \(i\)-th component states: \(\{A_{i,0},A_{i,1}\}\). The class attribute (the system state defined by the structure function value \(\phi(\mathbf{x})\)) B has two values, B\({}_{0}\) and B\({}_{1}\). For example, the initial data of the laparoscopic surgery procedure consist of input attributes \(\{A_{1}\), A\({}_{2}\), A\({}_{3}\), A\({}_{4}\}\) and class attribute B. In this case, the attributes \(\{A_{1}\), A\({}_{2}\), A\({}_{3}\), A\({}_{4}\}\) correspond to the components \(x_{1}\), \(x_{2}\), \(x_{3}\), \(x_{4}\). The values of these attributes are values of the component states, which are in Table 3. The class attribute B agrees with the system states and its values are values of the structure function in Table 3. All values of the input attributes and class attribute are interpreted as fuzzy values for the induction of the classifier. The fuzzy classifier for the structure function construction can be inducted according to the different approaches. In this paper, we propose to use FDT. FDT can be inducted based on cumulative information estimates, which is considered in detail in [33]. The concept of this method is based on the selection of the input attribute with maximal influence on the result and its association with the non-terminal node. The influence is evaluated by the cumulative information estimations. Two parameters are calculated and associated with every node: frequency f of this node and the confidences of values of the class attribute for this node. Two thresholds \(\alpha\) and \(\beta\) are introduced for FDT induction. The values of \(\alpha\) and \(\beta\) can be defined from 0 to 1. A tree's branch is stopped by the leaf if (a) its frequency \(f\) is less than the indicated value of \(\alpha\) or the confidence of one of the values of class attribute is greater than \(\beta\). The \(\alpha\) and \(\beta\) values in FDT induction are the key parameters needed to transform the node into a leaf. Decreasing the threshold \(\alpha\) and increasing the threshold \(\beta\) allows us to build large FDTs. Large FDTs describe datasets in more detail. However, these FDTs are more sensitive to noise in the data. The values of thresholds \(\alpha\) and \(\beta\) are selected empirically and evaluated at the training step of the FDT induction. The initial data are divided for the training and controlled sets. FDT is inducted based on the training set for the fixed values of \(\alpha\) and \(\beta\). The controlled set allows the evaluating accuracy and sensitivity of the inducted FDT. If the accuracy and sensitivity are not sufficient, another FDT is inducted for other values of the thresholds \(\alpha\) and \(\beta\). For example, for the simplified laparoscopic surgery procedure, the values of these thresholds were selected as \(\alpha\) = 0.15 and \(\beta\) = 0.70. The FDT inducted based on the dataset in Table 2, according to these thresholds, is shown in Figure 3. The FDT in Figure 3 has non-terminal nodes that are indicated by the associated attributes.