Séminaire jeudi 26 Février 2009, 10h00-12h00 en salle D401
The necessary and the possible in decision analysis and operations research
Salvatore Greco, Faculté d'Economie, Université de Catane, Italie
We are presenting a general paradigm of decision support oriented to robust decision making. The robust decisions are considered in terms of possible and necessary consequences of foreseen scenarios. A consequence is necessary if it is true in all foreseen scenarios, while it is possible if it is true in at least one foreseen scenario. The paradigm of necessary and possible can be applied to many decision problems considered within operational research. In this paper, we present the general philosophy of this paradigm, and we focus our attention on multiple criteria decision support, where the concept of robustness concerns learning of preferences. This concept has been recently applied within an ordinal regression approach to multiple criteria decision support. The methods implementing this approach are called UTAGMS and GRIP.
UTAGMS and GRIP methods were proposed for building a set of additive utility functions compatible with preference information concerning a subset of alternatives, called reference alternatives, evaluated by multiple criteria. GRIP builds a set of additive value functions compatible with preference information composed of a partial preorder and required intensities of preference on reference alternatives. It constructs not only the preference relation in the considered set of alternatives, but it also gives information about intensities of preference for pairs of alternatives from this set for a given decision maker (DM). Distinguishing necessary and possible consequences of preference information on the all set of alternatives, GRIP answers questions of robustness analysis. The proposed methodology can be seen as an extension of UTA method based on ordinal regression. GRIP can also be compared to AHP method, which requires pairwise comparison of all alternatives and criteria, and yields a priority ranking of alternatives. As for the preference information being used, GRIP can be compared, moreover, to MACBETH method which also takes into account a preference order of alternatives and intensity of preference for pairs of alternatives. The preference information used in GRIP does not need, however, to be complete: the DM is asked to provide comparisons of only those pairs of reference alternatives on particular criteria for which his/her judgment is sufficiently certain. This is an important advantage comparing to methods which, instead, require comparison of all possible pairs of evaluations on all the considered criteria. Moreover, GRIP works with a set of general additive value functions compatible with the preference information, while other methods use a single and less general value function, such as the weighted-sum.
UTAGMS method has been extended to support group decisions. The method is called UTAGMS GROUP. From pairwise comparisons of some alternatives made by each particular DM, a set of compatible additive value functions is built by the UTAGMS method. Using the intersection of the set of value functions of all the DMs, one can define the necessary weak preference relation which holds for any two alternatives a, b from set A if and only if, for all compatible value functions, a is preferred to b, and the possible weak preference relation which holds for this pair if and only if, for at least one compatible value function, a is preferred to b. The preference information given by each DM can also include preference intensities between pairs of alternatives, with respect to both, single criteria and comprehensively.