Robust Ordinal Regression

Any multiple Criteria Decision Aiding (MCDA) method needs some preference parameters. The Decision Maker (DM) could be asked to provide directly all these parameters; however, because it needs a great cognitive effort, the indirect preference information is more used in practice. Starting from the indirect preference information, usually there could be more than one set of preference parameters compatible with the information provided by the DM and the choice of only one of them could be considered arbitrary and meaningless. Robust Ordinal Regression (ROR) considers all the sets of compatible preference parameters using the possible and necessary preference relations. The necessary preference relation holds between two alternatives a and b if a is at least as good as b for all sets of compatible preference parameters, whereas the possible preference relations holds between a and b if a is at least as good as b for at least one set of compatible preference parameters. In this article, we introduce the basic concepts and the main developments of ROR