## 4 Model Implementation
### Discussion on Calculated FPr  
This section addresses the results generated using the calculated crisp and fuzzy probabilities. CPr measure the risk level based on historical failure incident data, and FPr measure the risk frequency and impact by adjusting for uncertainty and ambiguity via expert elicitation. The risk profile can be enhanced significantly by integrating FPr and CPr through a comprehensive analysis of identified risk factors and failure modes. Table 4 shows FPr calculations for all BEs, and the corresponding CPr are in the last column. It is evident from the calculations that FPr values vary from CPr. The reasons \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Expert** & **PP** & **EdU** & **Exp** & **Age** & **Weighting Score** \\ \hline E1 & 4 & 4 & 5 & 5 & 0.4390 \\ \hline E2 & 4 & 5 & 3 & 3 & 0.3659 \\ \hline E3 & 4 & 4 & 5 & 5 & 0.4390 \\ \hline E4 & 4 & 5 & 2 & 2 & 0.3171 \\ \hline E5 & 5 & 5 & 2 & 3 & 0.3659 \\ \hline E6 & 4 & 5 & 2 & 2 & 0.3171 \\ \hline E7 & 2 & 3 & 2 & 2 & 0.2195 \\ \hline E8 & 4 & 5 & 2 & 3 & 0.3415 \\ \hline E9 & 4 & 5 & 2 & 2 & 0.3171 \\ \hline E10 & 2 & 4 & 2 & 2 & 0.2439 \\ \hline E11 & 4 & 4 & 2 & 2 & 0.2927 \\ \hline E12 & 4 & 5 & 3 & 3 & 0.3659 \\ \hline E13 & 2 & 5 & 4 & 3 & 0.3415 \\ \hline E14 & 4 & 5 & 2 & 3 & 0.3415 \\ \hline E15 & 4 & 4 & 2 & 2 & 0.2927 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The weighting scores of fifteen experts. for these variations can be explained by the fact that, because of objective and subjective uncertainties, real-world scenarios are rarely crisp and deterministic in risk analysis, and insufficient and vague data may result in an under- or overestimation of process risk. Another reason is that the RTO databases present constant failure data over time and do not reflect recent component reliability improvements. For these reasons, the results obtained using FPr for BEs were expected to differ from those obtained using CPr. It is pertinent to mention here that the calculated probabilities are intended to be dynamic in the proposed fuzzy-aggregation approach, reflecting the evolving condition of the risk factors associated with the power grid. As power grid infrastructure degrades or new environmental risks emerge (such as extreme weather), these probabilities will be periodically recalculated using updated data, including expert opinions, maintenance records, and real-time data. The updated probabilities ensure that the model remains accurate and relevant to the current state of the power grid and its vulnerabilities. Moreover, the calculated probabilities are region-specific, as we recognize that the risks faced by power grids can differ significantly depending on geographical location. Our expert survey questionnaire asked respondents to consider regional risk factors, such as wildfires in California, snowstorms in the Midwest, and flooding risks in coastal regions. This approach ensures that the probabilities are tailored to the local environmental conditions and are not generalized across different regions. The model reflects the specific risks associated with each region by incorporating region-specific inputs.