PROCESSING OF SATELLITE IMAGES USING THE APPARATUS OF FUZZY SET THEORY - Alpert, S. I. (Systems and Technologies, 2025)
Fuzzy set theory is a branch of applied mathematics devoted to methods of analysis and processing of vague and inac- curate data. Main concept of this theory is membership function. Membership function defines the degree to which a certain element or object belongs to a fuzzy set. Fuzzy set theory accurately describes mathematical models of complex natural objects and processes, it is widely applied in various fields, such as: computer science, artificial intelligence, pattern recognition, and others. This theory is used to model, analyze and study various complex systems with uncertain data. Fuzzy Set Theory is a considerable mathematical tool in remote sensing. The concept of «fuzzy set» is used in classification tasks when common clas- sification methods give inaccurate results. This theory describes the classes of land cover with the degrees of belonging of object to each of these classes. This mathematical approach is useful when dealing with imprecise and ambiguous boundaries between classes. The use of fuzzy sets makes it possible to build more realistic models for solving remote sensing problems. It was noted that the proposed theory plays a serious role in the processing of satellite images for solution of remote sensing tasks, because this technique allows to accurately describe the structure of the satellite image. Some logical operations with fuzzy numbers applying the alpha-cut method were described. These logical operations with fuzzy numbers were considered using numerical examples. Fuzzy clustering using the C-means method was analyzed in detail. It was noted that this approach is widely applied for unsupervised classification of satellite images. It allows, that pixels belong to multiple classes with different degrees of mem- bership, unlike other known clustering methods. Fuzzy C-Means clustering is useful for processing, analyzing and classification mixed pixels. Apparatus of Fuzzy Set Theory can be applied for solution of such actual and important remote sensing tasks, such as: agricultural tasks, water resources monitoring, vegetation classification, various ecological and geological problems.