Representation of preferences over a finite scale by a mean operator

Michel Grabisch (1)

1 CES - Centre d'économie de la Sorbonne

Suppose that a decision maker provides a weak order on a given set of alternatives, each alternative being described by a vector of scores, which are given on a finite ordinal scale $E$. The paper addresses the question of the representation of this weak order by some mean operator, and gives necessary and sufficient conditions for such a representation, with possible shrinking and/or refinement of the scale $E$.

Mots clés: preference representation; finite scale; mean<br />operator; aggregation of scores; refinement of scale

Domaines: Economies et finances; Mathématique discrète [cs.DM]; Recherche opérationnelle [math.OC]

Michel Grabisch. Representation of preferences over a finite scale by a mean operator. Mathematical Social Sciences, 2006, 52 (2), pp.131-151. ⟨10.1016/j.mathsocsci.2006.05.001⟩. ⟨halshs-00179069⟩