# Fuzzy Logic in Selection of Maritime Search and Rescue Units
## 4 Case Study
### Stage 3: The computational test and the results  
Multi-criteria decision analysis can be done by different methods. The expert group chose the Promethee II method for the simulation. This method has many advantages. It quantitatively measures the distances between alternative solutions. It allows for one-person selection (lower number of decision makers). It has detailed preferences, but uses an uncomplicated preference model. It allows to conduct selection on a small group of alternatives and allows results to be obtained in graphical form. Does not require much computational effort. Calculations were performed using Visual Promethee software. First, vessel (alternatives) data and coordinator preferences were entered into the software dialog window (Figure 5). The columns represent the criteria. The first row contains the units in which the (quantitative) criteria are expressed. Qualitative criteria are expressed on a scale. The following rows contain the preferences of the decision-maker (direction of preferences, preference function and thresholds, if applicable). The sign n/a indicates \"not applicable\" and has been inserted where the threshold value is not specified. The next section presents the statistics of the results. The values of the individual vessel scores are entered in the \begin{table}
\begin{tabular}{l c c c c c} \hline \hline  & **Vessel 1** & **Vessel 2** & **Vessel 3** & **Vessel 4** & **Vessel 5** \\ \hline \(\omega^{*}\) & 42.5 & 76.5 & 51.96 & 61.95 & 79.05 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Results for defuzzification. Figure 5: Dialog window of the Visual Promethee software. lower section. The best values for the criterion are marked in green, the worst in red. Black is used for intermediate values. Then the calculations were carried out. The results were presented in the form of a net flow table and network (Figure 6). The table shows the outcomes in the form of a ranking of the alternatives. Vessels are ranked in order of decreasing potential search and rescue performance (net flow value). In Figure 6 (Case 1), we can see that Vessel 5 (Phi = 0.1252) comes first and Vessel 4 (Phi = \(-01191\)) comes last. The numerical result also makes it possible to assess whether the vessels can be treated equally. Vessel 3 and Vessel 1 achieved a similar score. The table also includes data on entering and leaving flow (partial rankings). These values influence the horizontal arrangement of alternatives in the network (lower part of the Figure 6). Alternatives closer to the right edge of the network have higher negatives values. It means they have been assessed lower in the single-criterion assessment than those located to the left. Vessel 5 is a military ship with very good medical equipment. Although it is not fast and the observation height is medium, in the overall assessment it meets the coordinator's requirements to the greatest degree. If the coordinator needs one vessel for action then this will potentially be the most useful. The coordinator may also consider the cooperation of two units (e.g., Vessel 5 and Vessel 2). The second vessel is a passenger ship with a high superstructure and high speed. Instead of Vessel 2 the coordinator may choose to pair Vessel 3 if he/she feels that the risk of Vessel 2 is too high (this is due to the poorer rating of the vessel type criterion). Vessel 2 is located to the right of Vessel 3 on the network. Both forms of presentation of results are a great help to the coordinator. He/she can decide to choose the first vessel or select the group of vessels with the highest potential (upper left corner of the network). Such a complete assessment (including all necessary criteria) was only possible by supplementing the data with the quality criterion (which is based on observation altitude and medical equipment). To compare the results of the analysis without taking these parameters into account, Case 2 was developed. Figure 6: Results of the analysis (table and network). Left: Case 1, Right: Case 2.