A generalized approach to ordinal classification based on the comparison of actions with either limiting or characteristic profiles

This paper presents a general theoretical framework related with the assignment rules of ordinal classification (sorting) methods, which make use of pairwise comparisons of actions against limiting profiles (or boundaries) or subsets of representative elements of classes (characteristic profiles). The new assignment rules use both a reflexive binary relation, S, and its asymmetric part, P. The classification methods designed with the new rules fulfill a set of fundamental properties, as the ones stated for ELECTRE TRI. The conditions required to the limiting and the representative profiles are weakened by eliminating the dominance-based separability requirements of other popular pairwise classification methods. Since reflexivity is the single condition on S, many ordinal classification methods can be obtained from our proposal. Each method consists of two correlative assignment rules that have relevant symmetry and must be applied together. The “pessimistic” and “optimistic” ELECTRE TRI-nB procedures, the descending and ascending ELECTRE TRI-nC procedures, their hierarchical extensions with interacting criteria, and some recent interval extensions of these methods are basically particular cases of the generalized framework.