Extreme ranking analysis in robust ordinal regression

We extend the principle of robust ordinal regression with an analysis of extreme ranking results. In our proposal, we consider the whole set of instances of a preference model that is compatible with preference information provided by the DM. We refer to both, the well-known UTAGMS method, which builds the set of general additive value functions compatible with DM's preferences, and newly introduced in this paper PROMETHEEGKS, which constructs the set of compatible outranking models via robust ordinal regression. Then, we consider all complete rankings that follow the use of the compatible preference models, and we determine the best and the worst attained ranks for each alternative. In this way, we are able to assess its position in an overall ranking, and not only in terms of pairwise comparisons, as it is the case in original robust ordinal regression methods. Additionally, we analyze the ranges of possible comprehensive scores (values or net outranking flows). We also discuss extensions of the presented approach on other multiple criteria problems than ranking. Finally, we show how the presented methodology can be applied in practical decision support, reporting results of three illustrative studies.