Ranking procedures for valued preference relations: A characterization of the ‘min’ procedure

The paper considers the situation where, in a multicriteria decision problem, the multidimensional information has been aggregated into a valued global preference relation on the possible alternatives. The problem is then to obtain a ranking of the alternatives on the basis of the valued preference relation. The paper gives an axiomatic characterization of the ‘min’ procedure which ranks the alternatives in decreasing order of their worst performance with respect to the other alternatives. This procedure can be advocated when the information contained in the valued preference relation must be considered as ordinal.