On possibilistic clustering with repulsion constraints for imprecise data

In possibilistic clustering 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 to all 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 to add a repulsion term among prototypes in the loss function forcing the prototypes to be far ‘enough’ from each other. Here, a possibilistic clustering algorithm with repulsion constraints for imprecise data, managed in terms of fuzzy sets, is introduced. Applications to synthetic and real fuzzy data are considered in order to analyze how the proposed clustering algorithm works in practice.