Groupe d’études et de recherche en analyse des décisions

Preferences on Intervals

Alexis Tsoukiàs LAMSADE, Université Paris Dauphine, France

The idea to use intervals (or values and thresholds) as numerical representations of objects to be compared in order to take in account possible sources of hesitation dates back to the seminal work of Luce on the semi-orders.

In this paper we introduce a general theoretical framework for the construction of any preference model resulting from the comparison of intervals and we study the underlying common structure of such models. Further on we show a number of results (mainly representation theorems and alternative logical formulations) for a number of specific preference structures such as PQI interval orders, double threshold orders etc...