Preference representation with 3-points intervals
Meltem Öztürk, A. Tsoukias · HAL (Le Centre pour la Communication Scientifique Directe) · 2006
In this article we are interested in the representation ofqualitative preferences with the help of 3-points intervals (a vector ofthree increasingly ordered points). Preferences are crucial when anagent has to autonomously make a choice over several possible ac-tions. We provide first of all an axiomatization in order to character-ize our representation and then we construct a general framework forthe comparison of 3-points intervals. Our study shows that from thefifteen possible different ways to compare 3-points intervals, sevendifferent preference structures can be defined, allowing the represen-tation of sophisticated preferences. We show the usefulness of ourresults in two classical problematics: the comparison of alternativesand the numerical representation of preference structures. Concern-ing the former one, we propose procedures to construct non classicalpreference relations (intransitive preferences for example) over ob-jects being described by three ordered points. Concerning the latterone, assuming that preferences on the pairwise comparisons of ob-jects are known, we show how to associate a 3-points interval to everyobject, and how to define some comparison rules on these intervalsin order to have a compact representation of preferences describedwith these pairwise comparisons.