Decision making based on satellite images: optimal fuzzy clustering approach

In many real-life decision-making situations, in particular, in processing satellite images, we have an enormous amount of information to process. To speed up the information processing, it is reasonable to first classify the situations into a few meaningful classes (clusters), find the best decision for each class, and then, for each new situation, to apply the decision which is the best for the corresponding class. One of the most efficient clustering methodologies is fuzzy clustering, which is based on the use of fuzzy logic. Usually, heuristic clustering are used, i.e., methods which are selected based on their empirical efficiency rather than on their proven optimality. Because of the importance of the corresponding decision-making situations, it is therefore desirable to theoretically analyze these empirical choices. In this paper, we formulate the problem of choosing the optimal fuzzy clustering as a precise mathematical problem, and we show that in the simplest cases, the empirically best fuzzy clustering methods are indeed optimal