## 3 Materials and Methods
### Formal Formulation of the Evaluation Problem
The equation is as follows:  
\[\gamma we_{\delta F}(\chi)=a_{\text{ave}_{\delta F}}+b_{\text{ave}_{\delta F}} \cdot\chi.\;\big{(}\delta=\overline{1,5};F=\{F_{1};\;F_{2};\;F_{3}\}\big{)}. \tag{4}\]  
Using the least squares method, the coefficients \(\overline{a},\overline{b}\) are calculated as follows:  
\[\overline{b_{\text{ave}_{\delta F}}}=\frac{l\cdot\sum_{u=1}^{l}t_{u}\cdot we _{\delta F}(t_{u})-\sum_{u=1}^{l}t_{u}\cdot\sum_{u=1}^{l}we_{\delta F}(t_{u}) }{l\cdot\sum_{u=1}^{l}(t_{u})^{2}-\Big{(}\sum_{u=1}^{l}t_{u}\Big{)}^{2}}, \tag{5}\]  
\[\overline{a_{\text{ave}_{\delta F}}}=\frac{1}{l}\sum_{u=1}^{l}we_{\delta F}(t _{u})-\overline{b_{\text{ave}_{\delta F}}}\cdot\frac{1}{l}\sum_{u=1}^{l}t_{u}. \tag{6}\]  
After that, by substituting the value of the future period \(t_{l+1}\) into Equation (4), a predicted estimate of the individual psychophysiological load of a flight instructor is obtained for a certain indicator \(we_{\delta F}\) of the working environment \((we_{\delta F})_{p}=\gamma we_{\delta F}(l+1)\in[0;1]\). It is noted that pairwise linear regression is often chosen for forecasting due to its simplicity and clarity. More complex machine learning algorithms, while capable of accounting for nonlinear dependencies, may require more computing power, be prone to overfitting, or be difficult to interpret. The obtained predicted estimate of the individual psychophysiological workload of the flight instructor indicates a complex trend dependent on the defined indicator. Processing such information enables the detection of trends and anomalies, which may indicate increased workload or stress. Thus, in the process of forecasting input data for the flight instructor, normalized estimates of psychophysiological workload factors, particularly regarding noise levels, are formed. To obtain a single aggregated predicted estimate of the individual psychophysiological workload of the flight instructor in the working environment, it is proposed to apply the knowledge intelligence analysis approach and multidimensional membership functions. Since there is modeling of uncertainties of the \"mean value\" type within the estimates [0; 1], a conical membership function is used. The result approaches 1 when the values approach their maximum values:  
\[\overline{we_{F}}(C)=\left\{ \begin{array}{ll}1-\zeta,\;if\;\zeta<1,\\ 0,\;otherwise.\end{array} \right. \tag{7}\]  
where \(\zeta=\frac{1}{5}\cdot\sqrt{\left(\left(we_{F}\right)_{p}-1\right)^{2}+\ldots +\left(\left(we_{F}\right)_{p}-1\right)^{2}}\), the center of the basis is a unit vector, \(F=\left\{F_{1};F_{2};F_{3}\right\}\). For aggregation in multidimensional membership functions, as many arguments as there are defined indicators of the working environment are considered. The use of multidimensional membership functions for forecasting the individual psychophysiological workload of the flight instructor allows consideration of multiple factors in the working environment that affect the instructor's condition. This ensures accurate aggregation of data, enabling the detection of trends and anomalies in psychophysiological workload, as well as forecasting potential dangers or stressful situations. The application of this approach enables effective control and adjustment of the flight instructor's working conditions in real time. Aggregated predicted estimates of the individual psychophysiological load on a flight instructor in the work environment are normalized: \(\left\{\overline{we_{F_{1}}}(C);\overline{we_{F_{2}}}(C);\overline{we_{F_{3} }}(C)\right\}\in[0;1]\). Moreover, when \(\overline{we_{F}}(C)\rightarrow\)1, we can say that the flight instructor has an unfavorable predicted estimate in terms of individual psychophysiological load in their work environment. The smaller the value, the smaller the psychophysiological load on the flight instructor. Next, based on the obtained value, it is necessary to change the direction of the goals.