A valued Ferrers relation for interval comparison

Meltem Öztürk (1) , Alexis Tsoukias (1)

1 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision

The paper deals with the valued comparison of intervals for decision making. Interval orders are classical preference structures where the comparison of intervals is done in an ordinal way. In this paper we focus on valued comparison where more information, especially the distance between end-points of intervals, is used in order to have more sophisticated preference structures. The generalization of an interval order as a valued structure requires the choice of de Morgan triplets. We propose a valued outranking relation for interval comparison and show that it satisfies different definitions of valued interval orders using different de Morgan triplet. The decomposition of our outranking relation into preference and indifference provides a valued preference structure where the preference is T-transitive and monotone.

Mots clés: decision making; preference modeling; valued binary relation; interval comparison; interval orders; Ferrer relation

Domaines: Intelligence artificielle [cs.AI]; Recherche opérationnelle [math.OC]

Meltem Öztürk, Alexis Tsoukias. A valued Ferrers relation for interval comparison. Fuzzy Sets and Systems, 2015, 266, pp.47-66. ⟨10.1016/j.fss.2014.09.004⟩. ⟨hal-02787810⟩