## 5 Discussion  
The goal of this research is to propose a methodology by extending the PROMETHEE MCDM method through IFS and applying it to the selection of optimal segmentation methods for satellite images. The selection of the optimal algorithm depends on the subjective visual characteristics of the satellite images being analyzed. Different segmentation methods may excel in different scenarios based on the desired outcome, application, or characteristics of the data set [57]. In the segmentation of satellite images, the objective is often to accurately identify and separate various regions by specific criteria, as described in Section 3.2. These five criteria related to satellite image content were selected and used for content evaluation. The segmentation algorithms were evaluated according to the same criteria. Table 8 shows a correlation between subjective (expert ranks) and objective ranks produced by PROMETHEE-IFS. In all cases, the rank difference is less than one rank. The visual ranking of segmentation results revolved around balancing under-segmentation and over-segmentation. The results in Table 2 indicate that \(C_{1}\) (contrast) is the most important criterion, while \(C_{5}\) (smoothness) is the least important criterion in the list. This outcome can be attributed to the fact that human visual perception can tolerate certain types of distortions while being very sensitive to others. For example, humans can tolerate border holes to some extent, which is known as human visual tolerance [27]. This could explain the difference in obtained SWARA weightings for \(C_{1}\) and \(C_{5}\) criteria. The test results in Table 6 show that even classic segmentation methods (GMM and FCM) may achieve better results than modernized versions depending on the content. In addition, some segmentation algorithms may be tuned against over-segmentation, so images with small objects may not have a clear separation (under-segmentation). For example, the RSSFCA is tuned against over-segmentation and obtained the worst expert and PROMETHEE-IFS ranks, as it often unnecessarily merged regions, such as dunes in desert_23 or did not preserve finer details (smaller lakes in river_237). On the other hand, RSSFCA yielded better results in the case of the beach_19 image dominated by three large clusters, suggesting its suitability for less complex content. Compared to another classical method like the GMM, the FCM fails to correctly separate between blue coastal water and green fields in port_19, which is possibly due to several contributing factors. In a given dataset, the GMM treats the input data points as being generated from a mixture of several Gaussian distributions. This modeling approach is often more suitable for capturing the distribution of colors and their variations. Overall, the GMM outperformed FCM (Table 8) due to being more robust to noise than FCM. The GMM can provide a more flexible representation of the data density in the feature space. This can be especially beneficial when dealing with regions with smooth color transitions. Moreover, light green and cyan are relatively close to each other in the RGB color space, so an algorithm like FCM that relies on the default Euclidean distance in the RGB color space might fail to distinguish between shallow water and grass. Small expert and PROMETHEE-IFS rank differences, such as for SFFCM, can be interpreted as a stable segmentation solution in relation to other methods. In this case, the SFFCM method produced consistent results (2-3 places) in all segmentation scenarios. Conducting a comprehensive comparison with existing research results is challenging. However, we can refer to the articles in which our selected algorithms are evaluated. For example, the rankings provided by PROMETHEE-IFS align with the findings presented by the FRFCM authors [40], particularly in scenarios involving noise (see Tables 3 and 4 from the original article). Our proposed method also selects FRFCM over FCM in the cases of more noisy desert_23 and river_237 images.