Robustness Analysis for Interacting Criteria in Advanced Decision Support Systems

Decisions inspire our reflections everyday. They are intrinsically related to a plurality of points of view and are often characterized by uncertainty, imperfect knowledge or ill-determination. So, it frequently occurs that decisions are faced in conditions of arbitrariness, incompleteness and imprecision. Decision aiding is the activity that, through the use of some formalized models, helps to obtain recommendations to the questions posed by a Decision Maker (DM) in a decision process. A further source of complexity of real decision problems originates from the fact that they can be affected by many different issues at the same time which can not be neglected. To deal with this complexity, it seems natural to support the DM by providing integrated approaches which, trying to remaining intelligible, are able to manage the different features that decision problems can conjointly present. Since the uncertainty and the ambiguity which characterize decision problems can be treated by generalizing the deterministic cases, it appear natural to explore methods and procedures that analyze what happens when certain parameters of the models are not stable. According with this point of view, through this work we analyze some advantages to adopt in detail two families of methods which are frequently used to cope with a plurality of instances compatible with the preferences information provided by a DM. In particular, these methods provide results in terms of proportions or in terms of relations which are both inferred by considering a whole set of parameters that, in turn, represents all possible preferences which a DM can own. The methods which deal with uncertainty and imprecision can be usefully applied also when the preferences can not be restored by using simple mathematical models. In the last part of this thesis, we analyze the advantages to adopt a decision support model that merges the capacity to represent a wide range of preferences together with the utility to support the recommendations in terms of their robustness.