Controlled clustering, uni-norm operators and OWA operators

Clustering processes now have widespread applications. Their purpose is to separate data into groups of similar characteristics. Usually these processes are data driven, and, thus, we don´t have effective mechanism to control them. The standard procedure is to set the number of clusters (in supervised clustering we can also set centers of clusters). But as soon as we fix the number of clusters we don´t have further control on the number of points in each cluster. So, the problem now is how to manage the distribution of points. The distribution of points in clusters reflects the level of concentration: if almost all points are in one cluster then the level of concentration is very high; if points are equally distributed across clusters then the level of concentration is low. Therefore, the first problem is to find the way to measure the level of concentration. After this we proceed to describe the clustering process that permits us to control concentration. We then apply uni-norm operators and OWA operators to managing of the clustering process