A New Criterion for Obtaining a Fuzzy Partition from a Hybrid Fuzzy/Hierarchical Clustering Method

Classical fuzzy clustering methods are not able to compute a partition into a set of points, when classes have non-convex shape. Furthermore, we know that in this case, the usual criteria of class validity, such as fuzzy hyper volume or compactness - separability, do not allow one to find the optimal partition.The purpose of our paper is to provide a criterion allowing one to find the optimal fuzzy partition in a set of points including classes of any shape. To that effect we shall use the Fuzzy C Means algorithm to divide the set of points into an overspecified number of subclasses. A fuzzy relation is established between them in order to extract the structure of the set of points. The subclasses are merged according to this relation and the criterion that we propose allows one to find the optimal regrouping.