## 2 Materials and Methods
### Multi-Criteria Decision Analysis (MCDA)  
Multi-criteria decision analysis is based on a set of criteria used to evaluate a set of objects (alternatives--in this study, ships). The performance of the alternatives is compared in a structured, mathematical manner. In this article, the authors have chosen the PROMETHEE method (Preference Ranking Organization Method for Enrichment Evaluations), which is widely applied across various sectors. Other methods, such as the AHP (Analytic Hierarchy Process), are also commonly used in decision-making problems. In comparison to the AHP, the PROMETHEE method offers several advantages. It handles a larger number of alternatives more efficiently and does not require pairwise comparisons for all criteria, which significantly reduces the cognitive load on decision-makers. PROMETHEE also allows for more nuanced preference modeling through the use of preference functions, enabling better handling of imprecise or uncertain data. Additionally, it avoids the rank reversal problem often associated with the AHP. Developing a set of criteria and a method for evaluating alternatives in the maritime domain requires expert knowledge. The authors conducted a study involving a group of maritime professionals. To support this, an in-depth analysis was carried out on the risks associated with underwater infrastructure and vessel behavior in the vicinity of such critical areas. The method is a multi-criteria decision analysis technique designed to rank a finite set of alternatives based on multiple, often conflicting criteria. PROMETHEE is particularly useful when decision-makers aim to evaluate and compare objects using both qualitative and quantitative criteria, while incorporating the concept of preference intensity. The method begins by defining a set of alternatives \(A\),  
\[A=\{A_{1},A_{2},\ldots A_{n}\} \tag{1}\]  
and a set of evaluation criteria \(C\),  
\[C=\{C_{1},C_{2},\ldots C_{m}\} \tag{2}\]  
each associated with a weight \(w_{j}\), where  
\[\sum w_{j}=1 \tag{3}\]  
For each criterion \(C_{j}\), a preference function \(P_{j}\),  
\[P_{j}=(A_{i},A_{k}),\ \epsilon\;[0,1] \tag{4}\] \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Date** & **Time** & **MMSI** & **Lat** & **Lon** & **Status** & **SOG** & **COG** & **Type** & **Length** & **Drawbit** & **Class** \\ \hline
10.11.2024 & 13:39:13 & 219005477 & 56.15255 & 10.25132 & 0 & 0 & 299.3 & 50 & 14 & & 1 \\ \hline
10.11.2024 & 13:39:13 & 211548430 & 54.63187 & 8.382897 & 0 & 0 & 283 & 55 & 45 & 1.8 & 1 \\ \hline
10.11.2024 & 13:39:13 & 219016832 & 55.21227 & 11.22108 & 0 & 7.5 & 88.7 & 60 & 38 & & 1 \\ \hline
10.11.2024 & 13:39:13 & 314975000 & 54.7427 & 12.66214 & 0 & 9.7 & 231.6 & 80 & 249 & 14.2 & 1 \\ \hline
10.11.2024 & 13:39:13 & 220329000 & 57.96155 & 10.53818 & 7 & 2.5 & 160 & 30 & 18 & & 1 \\ \hline
10.11.2024 & 13:39:13 & 219012459 & 57.83916 & 10.2919 & 15 & 2.7 & 218 & 30 & 15 & & 2 \\ \hline \hline \end{tabular} Here, MMSI—Marine Mobile Service Identity; Status—current ship navigational status—here, 0 = underway using engine; SOC—speed over ground; COG—course over ground; Type—ship type—here, 70 = cargo ship, and 80 = tanker.  
\end{table} 
Table 1: _Cont._is used to express the degree to which alternative \(A_{i}\) is preferred over \(A_{k}\). The aggregated preference index \(\pi\) between any two alternatives is given by  
\[\pi(A_{i},A_{k})=\sum_{j=1}^{m}w_{j}*P_{j}(A_{i},\ A_{k}) \tag{5}\]  
Based on the aggregated preference indices, two flows are computed for each alternative: the positive flow \(\varphi^{+}(A_{i})\), indicating how much an alternative outranks others, and the negative flow \(\varphi^{-}(A_{i})\), representing how much it is outranked by others:  
\[\phi^{+}(A_{i})=\frac{1}{n-1}{\sum_{k\
eq i}\pi(A_{i},A_{k})},\phi^{-}(A_{i}) =\frac{1}{n-1}{\sum_{k\
eq i}\pi(A_{k},A_{i})} \tag{6}\]  
The net flow \(\varphi\) is then defined as  
\[f\ (A_{i})=(A_{i})=\phi^{+}(A_{i})-\phi^{-}(A_{i}) \tag{7}\]  
In the method, alternatives are fully ranked based on their net flow values.