## 4 Application of Methodology for Satellite Images
### Verification of Methodology
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{6}{c}{**Satellite Images**} \\ \cline{2-7}  & **square\_1,** & **desert\_23,** & **beach\_19,** & **port\_19,** & **farmland\_159,** & **river\_237,** \\ \hline FCM & 4,1,3,3,3,2,1,3,3,4 & 2,2,3,2,1,2,1,1,3,2 & 5,1,5,3,5,4,5,2,2,4 & 5,2,4,5,4,3,4,5,5,5 & 2,1,5,1,4,4,3,3,4,4 & 4,2,5,5,5,5,5,5,5 \\ \hline GMM & _3,A,A,A,A_1,2,1,2,2 & 4,3,2,3,3,3,3,2,2,3 & 2,2,3,4,1,5,4,5,4,5 & 4,3,5,4,5,2,1,2,2,4 & 3,3,2,3,2,2,1,2,1 & 2,4,4,1,4,4,4,4,4 \\ \hline SFFCM & 1,3,1,1,2,4,3,4,1 & 5,4,5,4,5,4,5,4,5 & 1,5,2,5,3,2,1,3,3,2 & 2,4,2,2,2,4,3,4,3,2 & 5,5,3,4,1,1,2,1,2,1 & 1,3,1,3,2,1,3,2,1,2 \\ \hline FRPCM & 2,2,2,2,1,3,4,2,1,3 & 1,1,1,2,1,2,1,3,1 & 3,3,4,2,4,1,2,1,1,3 & 3,1,3,3,3,1,1,2,1,1,1 & 1,2,4,2,3,4,2,3,3 & 3,1,2,2,3,2,2,1,2,1 \\ \hline RSSFCA & 5,5,5,5,5,5,5,5,5,5,5 & 3,5,4,5,4,5,5,4 & 4,4,1,1,2,3,3,4,5,2 & 1,5,1,1,3,5,5,3,4,3 & 4,4,5,5,5,5,5,5,5 & 5,5,3,4,1,3,1,3,3,3 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Ten experts’ options on the ranking of segmentation algorithms. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multirow{2}{*}{**Expert Rank**} & \multirow{2}{*}{**PROMETHEE-IFS**} & \multirow{2}{*}{**Rank Difference**} & \multirow{2}{*}{
\begin{tabular}{c} **Percentage** \\ **Difference** \\ \end{tabular} } \\ \hline FCM & 3.35 & 3.8(3) & \(-\)0.48(3) & 13.4571 \\ \hline GMM & 2.9(6) & 2.50 & 0.4(6) & 17.0731 \\ \hline SFFCM & 2.8 & 2.(6) & 0.1(3) & 4.8780 \\ \hline FRPCM & 2.05 & 1.8(3) & 0.21(6) & 11.1588 \\ \hline RSSFCA & 3.88(3) & 4.1(6) & \(-\)0.28(3) & 7.0393 \\ \hline \hline \end{tabular}  
* In the following rankings, a lower numerical value indicates a higher level of algorithm performance while a higher numerical value indicates a lower performance. Therefore, a rank close to 1 represents the best result (first place), while a rank close to 5 corresponds to the worst result (last place). A repeating decimal is denoted by parentheses.  
\end{table} 
Table 8: Average expert rank comparison with average rank by the PROMETHEE-IFS method *. This analysis relies on the precision of image assessments, specifically, how the oscillations of the respondents' evaluations affect the selection of segmentation algorithms. Two new groups, consisting of students and experienced users, evaluated the image content according to the given criteria. The image \"square_1\" was taken for sensitivity analysis. After the content was evaluated, two new sets of rankings were compared. The impact of rank sensitivity analysis is presented in Table 9, and its visualization is shown in Figure 15. A robust method should handle small variations in ranking data without significantly altering the overall decision outcome. The assessments presented in Figure 15 lead to the conclusion that for the square_1 image, both the experts and experienced users regarded the FCM algorithm (preserved more details) as the best choice, while students preferred the FR  
Figure 15: Rating of the five segmentation algorithms based on the different evaluation of the image content by three evaluator groups. PROMETHEE-IFS was used for the experiment with image “square_1 in Figure 9” (\(A_{1}\)-FCM, \(A_{2}\)—GMM, \(A_{3}\)—SFFCM, \(A_{4}\)—FRFCM, \(A_{5}\)—RSSFCA). \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Features of Images (Criteria)**} & \multirow{2}{*}{**Optimum**} & \multicolumn{3}{c}{**Evaluator Groups**} \\ \cline{3-5}  & & **Students** & **Experienced Users** & **Experts** \\ \hline Contrast, \(C_{1}\) & max & **7** & **8** & **7** \\ \hline Roughness, \(C_{2}\) & min & **5** & **5** & **5** \\ \hline Regions of very small size, \(C_{3}\) & min & **5** & **4** & **5** \\ \hline Distortions of regions (holes, shadows etc.), \(C_{4}\) & min & **7** & **7** & **5** \\ \hline Smoothness (continuity) of region edges, \(C_{5}\) & max & **4** & **5** & **5** \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Opinions of the evaluator groups in the evaluation of the image “square_1”.