The Convex Fuzzy c-Medoids Problem
Clustering, Fuzzy Partitions, Multiple Medoids, Convexity.
This work proposes the Convex Fuzzy c-Medoids Problem, which is a medoid-based clustering problem, which considers fuzzy partitions and defines multiple representatives for each cluster. A medoid is a representative object of a cluster whose sum of dissimilarities for all cluster objects is minimal. Fuzzy partitions allow an object to be assigned to more than one cluster, which makes it possible to identify the simultaneous relation of this object to the objects of the clusters to which it is not assigned. The Convex Fuzzy c-Medoids Problem generalizes the Fuzzy c-Medoids Problem, by defining multiple representatives (medoids) per cluster, which allows to obtain more detailed information about the internal structure of each cluster.