A multiple criteria nominal classification method based on the concepts of similarity and dissimilarity

In this paper, we propose a new multiple criteria decision aiding method for nominal classification problems, where the categories are predefined and no order exists among them. A multiple criteria nominal classification problem consists of assigning actions, assessed according to multiple criteria, to nominal categories. The new method, designated Cat-SD (Categorization by Similarity-Dissimilarity), is based on the concepts of similarity and dissimilarity. We propose a way of modeling likeness between two actions, which includes the possibility of taking into account interaction effects between criteria. Each category is characterized by a set of reference actions. Then, each action to be assigned is compared to each set of reference actions in order to compute a related likeness degree. The comparison of the likeness degrees to the likeness thresholds (one per category) allows an action to be assigned to the most adequate categories, if any. The fundamental properties of the method and their proofs are provided. A numerical example is presented to illustrate the manner in which the proposed method can be applied.