Building a set of additive value functions representing a reference preorder and intensities of preference: GRIP method

To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.ejor.2008.02.006 Byline: Jose Rui Figueira (a), Salvatore Greco (b), Roman SAowiAski (c)(d) Keywords: Multiple criteria decision analysis; Preference model; Value function; Ordinal regression; Intensity of preference Abstract: We present a method called Generalized Regression with Intensities of Preference (GRIP) for ranking a finite set of actions evaluated on 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 a subset of actions, called reference actions. It constructs not only the preference relation in the considered set of actions, but it also gives information about intensities of preference for pairs of actions from this set for a given decision maker (DM). Distinguishing necessary and possible consequences of preference information on the considered set of actions, GRIP answers questions of robustness analysis. The proposed methodology can be seen as an extension of the UTA method based on ordinal regression. GRIP can also be compared to the AHP method, which requires pairwise comparison of all actions and criteria, and yields a priority ranking of actions. As for the preference information being used, GRIP can be compared, moreover, to the MACBETH method which also takes into account a preference order of actions and intensity of preference for pairs of actions. 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 actions 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 actions 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. Author Affiliation: (a) CEG-IST, Center for Management Studies, Instituto Superior Tecnico, Technical University of Lisbon, Tagus Park, Av. Cavaco Silva, 2780-990 Porto Salvo, Portugal (b) Faculty of Economics, University of Catania, Corso Italia 55, 95 129 Catania, Italy (c) Institute of Computing Science, PoznaA University of Technology, Street Piotrowo 2, 60-965 PoznaA, Poland (d) Institute for Systems Research, Polish Academy of Sciences, 01-447 Warsaw, Poland Article History: Received 2 March 2007; Accepted 5 February 2008