## 3 Material and Methods
### Formal Formulation of the Evaluation Problem
They associate the values of the input data \((\Delta_{1},\Delta_{2},\ldots,\Delta_{6},\delta)\) with one possible assessment of the level of practical knowledge \(D\):  
IF \(Z_{1}=\Delta_{i1}\) (with weight \(\alpha_{1}\)) and \(Z_{2}=\Delta_{i2}\) (with weight \(\alpha_{2}\)) \(\ldots\) and \(Z_{6}=\Delta_{i6}\) (with weight \(\alpha_{6}\)) and \(E=\delta_{i}(E)\)(with weight \(\alpha_{7}\)) THEN \(Y=D_{i}\) ELSE \(\ldots\)  
\(i\) is a student ATCo based on which the level of practical knowledge is determined, \(i=\overline{1,m}\). \(\alpha_{1},\alpha_{2},\ldots,\alpha_{7}\) are the synaptic weights of the neuro-fuzzy model. Synaptic weights are obtained in the process of learning a neuro-fuzzy network. The derivation of levels of practical knowledge can be illustrated in the form of a four-layer neuro-fuzzy network (Figure 2). Where the following notations are used, the input is data on student \(P\), for which an assessment is made on 6 tasks \(\{Z_{1};Z_{2};\ldots;Z_{6}\}\) in exercises, which characterizes the number of repetitions \(E\). Next is the calculation in terms of four layers: First layer: \(\{\Delta_{1},\ \Delta_{2},\ \ldots,\ \Delta_{6}\}\) is normalized assessments of the performance of the corresponding tasks \(\{Z_{1};Z_{2};\ldots;Z_{6}\}\); \(\delta(E)\) is the repetition coefficient of the exercise within the limits of data fuzzification testing. Second layer: \(W_{1},W_{2},\ldots,W_{7}\) is the value of the excitation level of neurons that form input signals with synaptic weights. Third layer: \(Q_{1},\ Q_{2},\ldots,\ Q_{7}\) is the postsynaptic potential of neurons of the third layer. Fourth layer: \(Y\) is the level of practical knowledge of the student. Below are the formalized steps performed at each layer of the neuro-fuzzy model. _First layer: Fuzzification of input data_  
In the neurons of the first layer, a data fuzzification operation is performed to obtain normalized and comparative data. Fuzzification is carried out with the help of the developed information model of data processing of student ATCo reactions in multitasking situations, \(I_{FI}\). The formalization of error data and the reaction time for the performance of the given task is carried out according to Formulas (3) and (4), after which the data are aggregated according to Formula (5), and a generalized assessment of the performance of the given task is obtained within 50 instructions, according to Formula (6). Further, Formula (7) considers the performance exercise's repetition within the testing limits. _Second layer: Combining values of activation conditions_  
At the second layer, the functions of the postsynaptic potential are aggregated according to the tasks set by the student ATCo and the repetition of the performance exercise within the testing framework. The second layer contains seven neurons, and the synaptic weights \(\alpha_{1},\alpha_{2},\ldots,\alpha_{7}\) and are obtained in the process of learning the neuro-fuzzy model. For this, the authors suggest, but are not limited to, the method of backpropagation of the error. It is said that input signals with synaptic weights form the values of the neurons'  
Figure 2: The structure of the neuro-fuzzy model. excitation level \(W_{1},W_{2},\ldots,W_{7}\). In this case, the functions of the postsynaptic potential of neurons of the second layer are determined by the following formula:  
\[\left\{ \begin{array}{l}W_{1}(p_{i})=\alpha_{1}\cdot\Delta_{1i};\\ W_{2}(p_{i})=\alpha_{2}\cdot\Delta_{2i};\\ \ldots\ldots\ldots\ldots\ldots\ldots\ldots;\\ W_{6}(p_{i})=\alpha_{6}\cdot\Delta_{i6};\\ W_{7}(p_{i})=\alpha_{7}\cdot\delta_{i}(E).\end{array} \right. \tag{8}\]  
As a result, the output neurons of the second layer \(W_{1},W_{2},\ldots,W_{7}\) are obtained, and this process is repeated separately for exercises \(E_{h}\) (\(h=\overline{1,15}\)). _Third layer: Adjustment of neurons of the second layer_  
On the third layer, the neurons of the second layer are adjusted to the importance of a given task and the repetition of the exercise.