Annals of Management Science


One essential problem in Multicriteria Decision Aid is to assess the relative importance of different criteria. The use of weights gives the decision-maker the possibility to better modelize the real aspects of a decision problem and to express more freedom the preference structure he has in his mind. This task is not easy because a subjective component is always present and there exist great number of methods which try to approximate this problem. PROMETHEE Methods consider as outranking non-compensatory methods; give the possibility to calculate weight stability intervals. So it is very important to do sensibility analysis taking into account that changes in weights would be reflected in PROMETHEE decision axis and they could affect previous conclusions. The idea of weight stability intervals (WSI) was introduced by Mareschal (1988) in PROMETHEE Methods. It is well known that these methods work under a preorder preference structure, so we propose to calculate the WSI under a semiorder structure with the aim to study the stability and the robustness of the model from a more solid point of view. In this paper we propose to analyze in a first-order additive method, to say, with only one valued real function, specifically in PROMETHEE II, the sensibility of a Semiorder Preference Structure under changes in the weight vector. The task consists of defining New Weight Stability Intervals (NWSI) adapted to a Semiorder Preference Structure in PROMETHEE Methods.