Revisiting relational-based ordinal classification methods from a more flexible conception of characteristic profiles

One of the main ways to represent classes in multiple criteria ordinal classification is using characteristic profiles, conceived as typical actions of their respective class. In this paper, our primary focus is on deepening and making more flexible this concept. We propose a new relational-based ordinal classification method, in which profiles can be extended to be more general assignment examples, belonging to the “least preferred” and the “most preferred” preference part of each class, even belonging to the limiting boundaries between adjacent classes. Preferences are modeled by a general reflexive relation. The novel method provides a systematic framework for refining and improving both the reference set and the preference relation model. This proposal helps bridge the gap between different paradigms in relational multiple criteria ordinal classification. The method's remarkable adaptability in handling reference actions, combined with the general feature of the preference relation, distinguishes it from existing ordinal classification methods, which can be considered particular cases of this comprehensive approach. Not only it is a theoretical improvement, but it is also relevant from a practical standpoint because it allows for a greater number of assignment examples to provide a better characterization of classes and more appropriate assignments, as well as reduces the cognitive effort demanded from decision makers. The new approach offers a way to use the enhanced information provided by the increased number of profiles to help Decision-Makers to choose the final category. The proposal is illustrated with several simple examples.