The fuzzy c partition of a set of qualitative data is the problem of selecting the optimal c centroids that are the most representative of the whole population. Moreover, a set of weights wij must be determined, describing the fuzzy membership function of pattern i to the cluster represented by centroid j. Both problems are formulated by a single mathematical programming problem, that is an extension of the classic p-median models often used for clustering. The new objective function is neither concave nor convex and the application requires the clustering of many thousands of data, therefore heuristic methods are to be developed to find the best fuzzy partition.
