On the usefulness of taking the weights into account in the GAIA visualisations

In this paper we study the multicriteria decision aid (MCDA) methods PROMETHEE and GAIA. The PROMETHEE method provides the decision maker with a ranking. The GAIA method provides a two dimensional representation of the decision problem based on the flows computed by the PROMETHEE method. However, a limit of the GAIA method is the loss of information by its two-dimensional projection which may lead to inconsistencies with the PROMETHEE rankings. Recently, some extensions of the GAIA method have been proposed in Hayez et al. (2009) in order to decrease the number of inconsistencies. We propose in our paper to slightly adapt the proposed GAIA methods by taking the weights into account when representing the problem. The aim of this paper is thus to analyse the impact on the gain or loss of information of the GAIA. Different illustrative examples are given and numerical simulations have been made to justify this approach.