Geometrical representations for MCDA

In this paper geometrical representations for multicriteria decision problems are proposed. This new approach provides assistance to understand the conflictual aspects of the criteria and to tackle the problem of the weights associated to them. A generalized criterion, including a preference function, is first generated for each criterion. This allows to define unicriterion preference flows for which a geometrical representation can be obtained by using the Principal Components Analysis. The actions are represented by points and criteria by axes in the PCA plane. A decision axis taking into account the weights associated to the criteria can be defined. This technique provides the decision-maker with a considerable enrichment for the understanding of his problem: clusters of actions can be considered, the importance of the criteria can be evaluated, conflictual criteria are immediately detected, incomparability between actions is emphasized and explained, best compromise actions are easily selected, new decision-axes representing possible clusters of criteria can be considered, undesirable actions can be eliminated, … The technique consists in a powerful new qualitative decision tool. It is illustrated in the paper on some examples treated by the Promethee I and II methods. A didactic and user-friendly microcomputer code is available.