Fuzzy Prototypes Based on Typicality Degrees

This paper considers the task of constructing fuzzy prototypes for numerical data in order to characterize the data subgroups obtained after a clustering step. The proposed solution is motivated by the will of describing prototypes with a richer representation than point-based methods, and also to provide a characterization of the groups that catches not only the common features of the data pertaining to a group, but also their specificity. It transposes a method that has been designed for fuzzy data to numerical data, based on a prior computation of typicality degrees that are defined according to concepts used in cognitive science and psychology. The paper discusses the construction of prototypes and how their desirable semantics and properties can guide the selection of the various operators involved in the construction process.