# Risk Assessment for the Development of Emergency Scenarios for Tram Driver Training
## 3 Methodology
The risk of training scenarios for tram drivers was assessed based on the following:  
* Probability of scenario occurrence (PSO);
* Consequences of scenario occurrence (CSO). The boundaries and shape of the membership functions used in the model were developed based on interviews with 30 experts, among whom were driving instructors, safety specialists, training and development specialists, and experienced tram drivers (experience of more than ten years). The limits of the membership function were statistically estimated using the parameters mean, standard deviation, and median minimum and maximum. The probability of scenario occurrence (PSO) membership function is based on a five-element scale: rare, unlikely, possible, very likely, and inevitable. A description of the linguistic variables for the PSO variable is presented in Table 3. The boundaries and shape of the PSO variable's membership function are presented in Figure 6.  
The membership function of consequences of scenario occurrence (CSO) is based on a five-element scale: negligible, minor, moderate, high, and catastrophic. A description of the linguistic variables for the CSO variable is presented in Table 4. The boundaries and shape of the membership function of the CSO variable are presented in Figure 7.  
The inference block of the risk assessment model for motorist training scenarios is based on 25 IF-THEN rules. The evaluation model uses Mamdani implications and is based on MIN and MAX operators. The rule base of the assessment model is presented in Table 5. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Variable** & **Symbol** & **Description** & **Fuzzy Value** \\ \hline Negligible & C1 & No or negligible impact on the transport process & \((0,\ 0,\ 1.5,\ 2.5)\) \\ Minor & C2 & Minor disruption to the transport process resulting in a few & \((1.5,\ 2.5,\ 3.5,\ 4.5)\) \\  & & minutes delay of the tram & \((3.5,\ 4.5,\ 5.5,\ 6.5)\) \\ Moderate & C3 & Temporary suspension of transport or risk to passengers’ & \((3.5,\ 4.5,\ 5.5,\ 6.5)\) \\ High & C4 & Temporary out-of-service of a vehicle, loss of health of & \((5.5,\ 6.5,\ 7.5,\ 8.5)\) \\ Catastrophic & C5 & Prolonged out-of-service or cancellation of the vehicle, & \((7.5,\ 8.5,\ 10,\ 10)\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Description of the linguistic variables—consequences of scenario occurrence. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**No.** & **PSO** & **CSO** & **RL** \\ \hline
1 & P1 & C1 & Low \\
2 & P2 & C1 & Low \\
3 & P3 & C1 & Minor \\
4 & P4 & C1 & Medium \\
5 & P5 & C1 & Medium \\
6 & P1 & C2 & Low \\
7 & P2 & C2 & Minor \\
8 & P3 & C2 & Minor \\
9 & P4 & C2 & Medium \\
10 & P5 & C2 & Intermediate \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Description of the linguistic variables—consequences of scenario occurrence. Figure 7: Input variable—consequences of scenario occurrence. The risk level (_RL_) membership function is based on a five-element scale: low, minor, medium, intermediate, and high. A description of the linguistic variables for the RL variable is presented in Table 6. The boundaries and shape of the RL variable's membership function are presented in Figure 8.  
The sharpening block of the risk assessment model for driver training scenarios uses the center of gravity method. The output value is determined from the formula [38]:  
\[y=\frac{\int\mu_{A}\Big{(}\widetilde{y}\Big{)}\times d\widetilde{y}}{\int\mu_{A} \Big{(}\widetilde{y}\Big{)}d\widetilde{y}} \tag{1}\]  
where \(y\)--defuzzified output; \(\mu_{A}\Big{(}\widetilde{y}\Big{)}\)--the aggregated output MF; and \(\widetilde{y}\)--the universe of discourse.