Hierarchy and interaction of criteria in robust ordinal regression

Abstract

All decision making problems we deal with along our lives, have a multiple criteria structure, that is several alternatives are evaluated with respect to some points of view, technically called evaluation criteria, and then compared in order to make the ``best'' decision. Multiple Criteria Decision Aiding, proposes methodologies useful to take decisions explicitly considering the preferences of the Decision Maker. In many real world problems, the criteria are not independent but interacting, being possible to observe a certain degree of synergy or redundancy between the evaluation criteria and often the criteria may be not all at the same level, but structured in a hierarchical way. In this thesis we dealt with both above problematics. Regarding the hierarchy of criteria, we have aggregated the evaluations of the alternatives using utility functions, outranking methods and Choquet integral; regarding the interaction of criteria, we have extended the multiple criteria PROMETHEE methods to the bipolar PROMETHEE methods; we have integrated the SMAA methodology with the Choquet integral and finally we have extended the customer satisfaction method MUSA to the case in which synergy or redundancy between criteria is also considered.