## 3 Material and Methods
### Formal Formulation of the Evaluation Problem
After that, the data are entered into the neuro-fuzzy model to assess students' level of practical knowledge at ATCo--\(M_{NT}\) (block \"Neuro-fuzzy model--\(M_{NT}\)\"). Based on the data from student ATCo respondents, the neural network is trained to determine the synaptic weights. The knowledge gained forms the \"knowledge base\" block of the study. The acquired knowledge forms the research knowledge base. Based on the input data, a student ATCo's practical knowledge is evaluated based on their reactions in multitasking situations using the calculation of the neuro-fuzzy model \(M_{NT}\). Next, the assessment of the level of practical knowledge is derived using the knowledge base of the study. After that, the final evaluation of the DM is determined. After that, the result goes to the block \"Determination of the final assessment of the DM\". An Information Model for Processing the Data of ATCo Student Reactions in Multitasking Situations--\(I_{fi}\)  
Student ATCo P is tested using a device to measure reaction time and relative error rate in multitasking tasks. The number of mistakes made and the reaction time to perform the tasks, \(Z_{1}(e_{1},t_{1})\), \(Z_{2}(e_{2},t_{2})\ldots Z_{6}(e_{6},t_{6})\), are considered for each task. As a result, a data set is obtained for each student \(p_{i}\), \(i=\overline{1,n}\):  
\[\left  
functions of this type are described by Z-like membership functions: quadratic Z-spline, harmonic Z-spline, Z-sigmoid, and Z-linear. To construct the membership function, it is necessary to determine the parameters of the lower and upper limits. Membership functions are constructed based on accurate data from the students' training [28]. For example, a quadratic Z-spline given by the following analytical formula is proposed for the number of errors:  
\[\mu_{1}(e_{ijk})=\left\{ \begin{array}{cl}1,&e_{ijk}\leq 0;\\ 1-\frac{1}{450}\left(e_{ijk}\right)^{2},&1<e_{ijk}\leq 15;\\ \frac{1}{450}\left(29-e_{ijk}\right)^{2},&15<e_{ijk}<30,\\ 0,&e_{ijk}\geq 30.\end{array} \right. \tag{3}\]  
\(\mu_{1}(e_{ijk})\in[0;1]\), and the larger the value, the fewer errors the student makes. The quadratic Z-spline will have the form for the reaction time to perform the assigned task:  
\[\mu_{2}(t_{ijk})=\left\{ \begin{array}{cl}1,&t_{ijk}\leq 0;\\ 1-2\left(\frac{t_{ijk}}{3}\right)^{2},&0<t_{ijk}\leq 1,5;\\ 2\left(\frac{3-t_{ijk}}{3}\right)^{2},&1,5<t_{ijk}<3,\\ 0,&t_{ijk}\geq 3.\end{array} \right. \tag{4}\]  
\(\mu_{2}(e_{ijk})\in[0;1]\), and the value goes to 1 when the reaction time is the minimum possible. Thus, the obtained values \(\mu_{1}(e_{ijk})\), \(\mu_{2}(t_{ijk})\) are normalized and comparative, \(i=\overline{1,n}\); \(j=\overline{1,50}\); \(k=\overline{1,6}\). Second stepIn the second step, the aggregated level of performance of the assigned task is obtained. Aggregation of values \(\mu_{1}(e_{ijk})\), \(\mu_{2}(t_{ijk})\) is carried out within the limits of \(Z_{k}\) problems by modeling the uncertainty of the \"average value\" form based on multidimensional membership functions. For example, such modeling can be naturally performed using a cone-shaped membership function. Putting the value of the center of the base of the cone as a unit vector, the scaling according to the coordinates of the vector \((\mu_{1}(e_{ijk});\mu_{2}(t_{ijk}))\), will be \((2;2)\):  
\[\lambda_{ijk}=\left\{ \begin{array}{cl}1-g_{ijk},&\text{if }g_{ijk}<1,\\ 0,&\text{otherwise.}\end{array} \right. \tag{5}\]  
where \(g_{ijk}=\frac{1}{2}\cdot\sqrt{\left(\mu_{1}\left(e_{ijk}\right)-1\right)^{2}+ \left(\mu_{2}\left(t_{ijk}\right)-1\right)^{2}}\cdot i=\overline{1,n}\); \(j=\overline{1,50}\); \(k=\overline{1,6}\). The obtained values of \(\lambda_{ijk}\in[0;1]\) characterize the aggregated level of performance of the assigned task by the student ATCo regarding the mistakes made and the reaction time to perform the assigned task. When the value goes to 1, it means the best result, accompanied by a quick reaction and error-free task execution.