Interval-based extensions of two outranking methods for multi-criteria ordinal classification

We present two new interval-based extensions of ELECTRE TRI-nB and ELECTRE TRI-nC, in which the preference relations are built by using the interval outranking approach. The boundaries between adjacent classes (or categories) are described by a set of limiting profiles, whose criteria could take on values which are interval numbers. Compared to INTERCLASS (a recently proposed interval-based ordinal classification method), the assignments suggested by our first extension come from enhanced preference relations between the actions and limiting boundaries and are likely to be more appropriate. In addition, it can suggest assignments from a pseudo-conjunctive logic. In our second extension, each class is characterized by a set of representative actions, again allowing interval numbers as criterion scores. The outranking relations between actions and classes are enhanced by having several representative actions in each category. Both new extensions can handle imperfect knowledge of the model parameters (weights, veto thresholds, credibility threshold), even missing criterion scores. Some fundamental properties and results are proved to guarantee the consistency of the methods, which are also illustrated with some numerical examples.