Multiple criteria hierarchy process in robust ordinal regression

A great majority of methods designed for Multiple Criteria Decision Aiding (MCDA) assume that all evaluation criteria are considered at the same level, however, it is often the case that a practical application is imposing a hierarchical structure of criteria. The hierarchy helps decomposing complex decision making problems into smaller and manageable subtasks, and thus, it is very attractive for users. To handle the hierarchy of criteria in MCDA, we propose a methodology called Multiple Criteria Hierarchy Process (MCHP) which permits consideration of preference relations with respect to a subset of criteria at any level of the hierarchy. MCHP can be applied to any MCDA method. In this paper, we apply MCHP to Robust Ordinal Regression (ROR) being a family of MCDA methods that takes into account all sets of parameters of an assumed preference model, which are compatible with preference information elicited by a Decision Maker (DM). As a result of ROR, one gets necessary and possible preference relations in the set of alternatives, which hold for all compatible sets of parameters or for at least one compatible set of parameters, respectively. Applying MCHP to ROR one gets to know not only necessary and possible preference relations with respect to the whole set of criteria, but also necessary and possible preference relations related to subsets of criteria at different levels of the hierarchy. We also show how MCHP can be extended to handle group decision and interactions among criteria.