On possibilistic clustering with repulsion constraints for imprecise data

In possibilistic clustering the objects are assigned to clusters according to the so-called membership degrees taking values in the unit interval. Differently from fuzzy clustering, it is not required that the sum of the membership degrees of an object in all the clusters is equal to one. This is very helpful in the presence of outliers, which are usually assigned to the clusters with membership degrees close to zero. Unfortunately, a drawback of the possibilistic approach is the tendency to produce coincident clusters. A remedy is represented by the use of a repulsion term among prototypes in the loss function forcing the prototypes to be ‘enough’ far from each other. Here, a possibilistic clustering model with repulsion constraints for imprecise data, managed in term of fuzzy sets, is introduced. Two applications to synthetic and real fuzzy data are considered in order to analyze how the proposed clustering model works in practice.