## 5 Analysis of Examples
### Cluster Grading and Effectiveness Analysis of the Status Values of Traffic Interruptions
#### 5.2.2 Validity Analysis  
The number of clusters should be preset in FCM clustering analysis, which relies on personal experience. However, this preset number does not guarantee an optimal clustering outcome. Therefore, the optimal number of clusters is determined through alternative methods to ensure the ideal clustering effect. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Number of Clusters** & **Level** & **Clustering Center** & **Interval for the Status Values of Traffic Interruptions** \\ \hline \multirow{2}{*}{2} & Level 1 & 1.704 & [0.0014, 13.1542] \\  & Level 2 & 25.1895 & [13.5997, 61.2340] \\ \hline \multirow{4}{*}{3} & Level 1 & 1.259 & [0.0014, 6.0787] \\  & Level 2 & 11.2554 & [6.5636, 23.9298] \\  & Level 3 & 37.4272 & [24.8619, 61.2340] \\ \hline \multirow{4}{*}{4} & Level 1 & 1.0993 & [0.0014, 4.4056] \\  & Level 2 & 7.8311 & [4.4829, 14.5598] \\ \cline{1-1}  & Level 3 & 22.4148 & [15.7651, 32.4697] \\ \cline{1-1}  & Level 4 & 47.823 & [38.6265, 61.2340] \\ \hline \multirow{4}{*}{5} & Level 1 & 0.8635 & [0.0014, 2.4523] \\  & Level 2 & 4.0759 & [2.4716, 7.4245] \\ \cline{1-1}  & Level 3 & 10.7764 & [7.5325, 17.4541] \\ \cline{1-1}  & Level 4 & 24.203 & [18.0349, 32.4697] \\ \cline{1-1}  & Level 5 & 48.8477 & [38.6265, 61.2340] \\ \hline \hline \end{tabular}
\end{table} 
Table 6: FCM clustering results. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**1** & **2** & **641** & **642** \\ \hline
0.7827 & 0.9612 &... & 0.9900 & 0.9796 \\
0.2040 & 0.03540 &... & 0.0087 & 0.0177 \\
0.0020 & 0.00054 &... & 0.0002 & 0.0004 \\
0.0111 & 0.0027 &... & 0.0009 & 0.0021 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Four-level fuzzy membership matrix. When the number of clusters is changed, there is an impact on the results, and this impact can be discussed from three perspectives:  
1. Lesser number of clusters: Interruptions were categorized as \"major interruptions\" and \"minor interruptions\". While this categorization simplifies the understanding of the data, it may hide some important nuances. For example, some highways were interrupted for the same reasons, but there were significant differences in the duration and mileage of the interruptions. Take the interruptions numbered 160 to 200 on the Sichuan-Tibet and Yunnan-Tibet highways as an example: although most of these events were caused by collapse and debris flow, they were grouped into the same level when n_cluster = 2 and into different levels when n_cluster = 4 and 5. This suggests that using a smaller number of clusters may overlook these specific differences, leading to an incomplete understanding of the actual situation. Advantages: This simple categorization offers a quick decision-making tool during emergencies, allowing managers to quickly identify which events need immediate attention. Disadvantages: However, this approach overlooks significant differences between events, potentially leading to inefficient resource allocation. For example, two highways might experience interruptions due to the same cause, but the interruption duration and the affected distance may differ significantly. A smaller number of clusters may lead to underestimating the severity of certain interruptions, affecting timely and appropriate responses. Figure 16: Four-level FCM clustering results. Figure 17: Five-level FCM clustering results. 2. Moderate number of clusters: This provides a more detailed categorization, identifying levels of interruptions with similar causes of interruption. This helps to reveal which highways are more susceptible to specific conditions (e.g., severe weather or geologic hazards) and how they are affected differently. Advantages: Moderate clustering helps distinguish between various types of interruption events, enabling managers to craft more appropriate emergency response plans. For example, some highways may be more vulnerable to weather conditions, while others may experience more frequent geological hazards.