# Fuzzy Comprehensive Evaluation of Pilot Cadets' Flight Performance Based on G1 Method
## 3 Method
### Multi-Level Fuzzy Comprehensive Evaluation
#### 3.2.2 Membership Function  
The fuzzy membership degrees of each factor are determined using membership functions. Figure 3 shows a graphical representation of the triangular fuzzy membership function Figure 3a and the trapezoidal fuzzy membership function Figure 3b. As shown in Table 4, the deviation value thresholds corresponding to the different levels of the 19 criteria can be categorized into two scenarios. In the first scenario, the thresholds have a center-symmetric distribution around zero. In the second scenario, the thresholds are spread over a range and spread in both directions. In this context, if the deviation value of flight data falls to the left of the threshold of the Excellent level or to the right of the threshold of the Bad level, it can also be considered Excellent or Bad, with a membership degree of 1. If the deviation value of flight data falls between the thresholds of two levels, this study postulates that the value is a membership with the level to the left \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Evaluation Indicator**} & **Standard** & \multicolumn{4}{c}{**Deviation Value**} \\ \cline{2-6}  & **Value** & **Excellent** & **Good** & **Medium** & **Bad** \\ \hline Altitude deviation in crosswind & 800 & 0 & \(-\)40 & \(-\)90 & \(-\)150 \\   turn (\(u_{1}\))/ft & & & & & \\ Altitude deviation in downwind & 1100 & 0 & \(\pm\)40 & \(\pm\)90 & \(\pm\)150 \\  (\(u_{2}\))/ft & & & & & \\ Altitude deviation in runway & 50 & \(\pm\)10 & \(\pm\)20 & \(\pm\)35 & \(\pm\)50 \\   threshold (\(u_{3}\))/ft & & & & & \\ Rotation speed (\(u_{4}\))/kt & & & & & \\ Maximum climb rate in upwind & 500 & 0 & +40 & +90 & +150 \\  (\(u_{5}\))/(ft/min) & & & & & \\ Maximum descent rate in approach & 500 & 0 & +40 & +90 & +150 \\  (\(u_{6}\))/(ft/min) & & & & & \\ Touchdown rate (\(u_{7}\))/(ft/min) & & & & & \\ Touchdown overload (\(u_{8}\))/G & 1.20 & 0 & +0.15 & +0.3 & +0.5 \\ Maximum flight overload (\(u_{9}\))/G & 1.5 & 0 & +0.3 & +0.6 & +0.9 \\ Maximum bank in crosswind turn & & & & & \\ (\(u_{10}\))/(\({}^{\circ}\)) & & & & & \\ Maximum bank in downwind turn & & & & & \\ (\(u_{11}\))/(\({}^{\circ}\)) & & & & & \\ Maximum bank in turning base & & & & & \\ (\(u_{12}\))/(\({}^{\circ}\)) & & & & & \\ Maximum bank in turning final & & & & & \\ (\(u_{13}\))/(\({}^{\circ}\)) & & & & & \\ Track deviation in upwind (\(u_{14}\))/(\({}^{\circ}\)) & & & & & \\ Track deviation in crosswind & & & & & \\ (\(u_{15}\))/(\({}^{\circ}\)) & & & & & \\ Track deviation in downwind & & & & & \\ (\(u_{16}\))/(\({}^{\circ}\)) & & & & & \\ Track deviation in approach & & & & & \\ (\(u_{17}\))/(\({}^{\circ}\)) & & & & & \\ Touchdown deviation (\(u_{18}\))/m & & & & & \\ Taxing deviation (\(u_{19}\))/m & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Flight performance evaluation threshold standards. and simultaneously with the level to the right. Furthermore, when the deviation value is exactly at the threshold of a particular level threshold, this research assumes that the value has the highest degree of membership with that particular level, with a membership degree of 1. Therefore, the trapezoidal membership function is used to deal with the boundary thresholds and the triangular membership functions for the intermediate levels. By using a combination of triangular fuzzy membership function and trapezoidal fuzzy membership function, a hybrid membership function is established to evaluate the flight performance of pilot cadets in the traffic pattern flight. The hybrid membership function is shown in Equation (5):  
\[A(x)=\left\{ \begin{aligned} & 1&& x\leq a\\ &\frac{b-x}{b-a}&& a\leq x\leq b\\ & 0&& b\leq x\end{aligned} \right\} \tag{5}\]  
\[A(x)=\left\{ \begin{aligned} &\frac{x-a}{b-a}&& a\leq x\leq b\\ &\frac{c-x}{c-b}&& b\leq x\leq c\\ & 0&& x\leq a\quad\text{or}\quad c\leq x\end{aligned} \right\}\]  
\[A(x)=\left\{ \begin{aligned} & 0&& x\leq a\\ &\frac{x-a}{b-a}&& a\leq x\leq b\\ & 1&& b\leq x\end{aligned}