Multiattribute preference models with reference points

Abstract

In the context of multiple attribute decision making, preference models making use of reference points in an ordinal way have recently been introduced in the literature. This text proposes an axiomatic analysis of such models, with a particular emphasis on the case in which there is only one reference point. Our analysis uses a general conjoint measurement model resting on the study of traces induced on attributes by the preference relation and using conditions guaranteeing that these traces are complete. Models using reference points are shown to be a particular case of this general model. The number of reference points is linked to the number of equivalence classes distinguished by the traces. When there is only one reference point, the induced traces are quite rough, distinguishing at most two distinct equivalence classes. We study the relation between the model using a single reference point and other preference models proposed in the literature.

Reference-based ranking procedure for environmental decision making: Insights from an ex-post analysis

“…Finally, if we use the inferred S-RMP model presented in Table 9 to rank the 39 alternatives, we obtain the ranking presented in Table 12. It can be observed that this ranking does not fully match with the one proposed by the experts (only 33 out of the 38 provided pairwise comparisons 4 are restored, i.e. RA=86.4%).…”

“…In this paper we are interested in showing the benefits of using a recent multiple criteria ranking method, named Simple Ranking with Multiple Points (S-RMP, see [4,32,33,40]), to support Email addresses: v.ferretti@lse.ac.uk (V. Ferretti), jinyan.liu@centralesupelec.fr (J. Liu), vincent.mousseau@centralesupelec.fr (V. Mousseau), wassila.ouerdane@centralesupelec.fr (W. Ouerdane) complex decision-making processes. This ranking method is based on pairwise comparisons, but instead of directly comparing pairs of alternatives, it rather compares the alternatives to a set of predefined reference points.…”

Multicriteria Decision Making

“…Note that, contrary to the standard concordance relations introduced before (see Equations 10 to 12), the concordance relations with reference point are naturally transitive, which facilitates their use for choice and ranking problems. One can find in [Perny and Rolland, 2006;Rolland, 2013;Bouyssou and Marchant, 2013] other examples of concordance rules with reference points, as well as some axiomatic analysis concerning these rules.…”

A multi-criteria approach to sort and rank policies based on Delphi qualitative assessments and ELECTRE TRI: The case of smart grids in Brazil

“…Moreover, adding or deleting a policy might change the relative position of the remaining policies. The solution would need to be a reference-based ranking approach, based on sorting profiles, a type of approach that has been proposed and studied only in recent years [16,42].…”