Robust Ordinal Regression

Within disaggregation–aggregation approach,

ordinal regression

aims at inducing parameters of a preference model, for example, parameters of a value function, which represent some holistic preference comparisons of alternatives given by the Decision Maker (DM). Usually, from among many sets of parameters of a preference model representing the preference information given by the DM, only one specific set is selected and used to work out a recommendation. For example, while there exist many value functions representing the holistic preference information given by the DM, only one value function is typically used to recommend the best choice, sorting, or ranking of alternatives. Since the selection of one from among many sets of parameters compatible with the preference information given by the DM is rather arbitrary,

robust ordinal regression

proposes taking into account all the sets of parameters compatible with the preference information, in order to give a recommendation in terms of necessary and possible consequences of applying all the compatible preference models on the considered set of alternatives. In this chapter, we present the basic principle of robust ordinal regression, and the main multiple criteria decision methods to which it has been applied. In particular,

UTA

GMS

and

GRIP

methods are described, dealing with choice and ranking problems, then

UTADIS

GMS

, dealing with sorting (ordinal classification) problems. Next, we present robust ordinal regression applied to Choquet integral for choice, sorting, and ranking problems, with the aim of representing interactions between criteria. This is followed by a characterization of robust ordinal regression applied to outranking methods and to multiple criteria group decisions. Finally, we describe an interactive multiobjective optimization methodology based on robust ordinal regression, and an evolutionary multiobjective optimization method, called

NEMO

, which is also using the principle of robust ordinal regression.