A theoretical look at ordinal classification methods based on reference sets composed of characteristic actions

TL;DR

This paper provides a theoretical framework for ordinal classification methods based on reference sets of characteristic actions, unifying various existing methods under a common relational system.

Contribution

It introduces a general theoretical model for ordinal classification using preference relations, encompassing methods like ELECTRE TRI-nC and INTERCLASS-nC.

Findings

Framework unifies multiple ordinal classification methods

Methods satisfy fundamental properties under mild conditions

Electre TRI-nC and INTERCLASS-nC are special cases

Abstract

From a theoretical view, this paper addresses the general problem of designing ordinal classification methods based on comparing actions with subset of actions, which are representative of their classes (categories). The basic demand of the proposal consists in setting a relational system (D, S), where S is a reflexive relation compatible with the preferential order of the set of classes, and D is a transitive relation such that D is a subset of S. Different ordinal classification methods can be derived from diverse model of preferences fulfilling the basic conditions on S and D. Two complementary assignment procedures compose each method, which correspond through the transposition operation and should be used complementarily. The methods work under relatively slight conditions on the representative actions and satisfy several fundamental properties. ELECTRE TRI-nC, INTERCLASS-nC, and the hierarchical ELECTRE TRI-nC with interacting criteria, can be considered as particular cases of this general framework.