## 3 Fuzzy Set Theory-Based Risk Assessment System for Navigational Obstacles
### Collision Risk Assessment Model
#### 3.3.1 Selection of Simulation Waters and Analysis of Ship Traffic
Grid-space traffic pattern analysis was performed as follows: to extract maritime traffic patterns, the dynamic data of the vessels, including the latitude, longitude, and COGs, were clustered within a four-level grid space using Density-Based Spatial Clustering of Applications with Noise (DBSCAN) [33; 34]. In addition, polygon objects reflecting the grid space and traffic separation schemes for the target waters were created. New variables were assigned by determining whether the traffic separation schemes were applied to the waters. This was to ensure the application of \"Proximity to Navigation Zones and Routes\" (#8) and \"Ship Navigation Methods\" (#10) in Table 2. Figure 5 shows the results of the grid-space variable assignment and visualization, where the ship traffic in the transit zone is represented by the blue area. Figure 4: Visualization results of the vessel occupancy area in the gridded space. (**a**) Area for simulation 1 and (**b**) area for simulation 2. Figure 3: Study area for simulation. (**a**) Entire study area, (**b**) Area for simulation 1, and (**c**) Area for simulation 2. Table 3 presents the results of the analysis of ship passage patterns in the four-stage grid space. The metrics include the average number of ships per separated cell, the average number of ships per clustered cell, and the average number of ships per cell of another type. In this paper, separated cells refer to grid cells with low vessel traffic density, where ships are sparsely distributed without forming any noticeable clusters. In contrast, clustered cells are grid cells characterized by high vessel traffic density, where ships are concentrated in close proximity, indicating areas of heavy maritime activity. Other types of cells represent grid cells that do not fall strictly into either the separated or clustered cell categories, often exhibiting transitional or mixed traffic patterns that reflect variable vessel distributions. The term normalized traffic volume refers to the vessel traffic volume that has been adjusted through statistical normalization techniques. This process ensures comparability across  
Figure 5: Results of the grid-space variable assignment and visualization. (**a**) Area for simulation 1 and (**b**) Area for simulation 2. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Results of Ship Traffic Pattern Analysis** & **Area 1** & **Area 2** \\ \hline Number of separated cells & 16 & 22 \\ Number of ships in separated cells & 590 & 672 \\ Avg. number of ships per & 36.88 & 30.55 \\ separated cell & 61 & 105 \\ Number of ships in clustered cells & 994 & 1712 \\ Traffic volume & Avg. number of ships per & 16.30 & 16.39 \\ clustered cell & 146 & 673 \\ Number of ships in other types & 855 & 2234 \\ of cells & Avg. number of ships per other type & 5.86 & 3.32 \\ of cell & & \\ \hline Normalized number of ships per & 6 & 9 \\ Normalized traffic volume & Normalized number of ships per & 3 & 5 \\ Normalized number of ships per & 1 & 1 \\ other type of cell & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results of ship traffic pattern analysis in the 4 th-level grid space. different grid areas by eliminating the influence of scale differences, thus allowing for a standardized evaluation of the traffic patterns. In this study, the normalized traffic volume was six normalized ships per separated cell, three normalized ships per clustered cell, and one normalized ship per other type of cell in Area 1. In Area 2, the traffic volume was nine normalized ships per separated cell, five normalized ships per clustered cell, and one normalized ship per other type of cell.