Preference representation with 3-points intervals

  • Authors:

  • Meltem Öztürk;Alexis Tsoukiàs

  • Affiliations:

  • LAMSADE-CNRS, Université Paris Dauphine, email: {ozturk,tsoukias}@lamsade.dauphine.fr;LAMSADE-CNRS, Université Paris Dauphine, email: {ozturk,tsoukias}@lamsade.dauphine.fr

  • Venue:
  • Proceedings of the 2006 conference on ECAI 2006: 17th European Conference on Artificial Intelligence August 29 -- September 1, 2006, Riva del Garda, Italy
  • Year:
  • 2006

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Abstract

In this article we are interested in the representation of qualitative preferences with the help of 3-points intervals (a vector of three increasingly ordered points). Preferences are crucial when an agent has to autonomously make a choice over several possible actions. We provide first of all an axiomatization in order to characterize our representation and then we construct a general framework for the comparison of 3-points intervals. Our study shows that from the fifteen possible different ways to compare 3-points intervals, seven different preference structures can be defined, allowing the representation of sophisticated preferences. We show the usefulness of our results in two classical problematics: the comparison of alternatives and the numerical representation of preference structures. Concerning the former one, we propose procedures to construct non classical preference relations (intransitive preferences for example) over objects being described by three ordered points. Concerning the latter one, assuming that preferences on the pairwise comparisons of objects are known, we show how to associate a 3-points interval to every object, and how to define some comparison rules on these intervals in order to have a compact representation of preferences described with these pairwise comparisons.