Unsupervised fuzzy classification method based on a fuzzy proximity graph and on a graduated hierarchy

The purpose of the paper is to provide a classification method able to divide a set of points into classes of complex shape without knowing a priori their number. We show that it's possible to reconcile a fuzzy clustering method with a hierarchical ascending method while maintaining a fuzzy partition. To that effect we use the fuzzy c means algorithm to divide the set of points into subclasses. We show that there is a fuzzy order relation which can be represented by a fuzzy proximity graph or a graduated hierarchy. Finally we set up a possible criterion sufficient to find the level of the cut to be made, in order to recover the real classes. Then we describe the fusion of the subclasses.