Complementarity of the graphical analysis for interactive aid and dominance-based rough set approach applied to the classification of non-urban municipalities

Graphical analysis for interactive aid (GAIA) and the dominance-based rough set approach (DRSA) are compared as methods of explaining the solution to a multi-criteria ranking problem obtained using the preference ranking organization method for the enrichment of evaluations (PROMETHEE). The classification of 52 municipalities in Northern Quebec in terms of the socioeconomic situation is based on three attributes: home conditions, employment and demographic potential. The classification provided to the decision maker is aggregated information. To facilitate decision-making, the problem is first considered as a sorting task, in which municipalities are distributed into three categories: best (B), worst (W) or intermediate (I), based on the PROMETHEE ranking. In order to improve the position of a municipality thus categorized, the decision maker needs information that will answer the questions: What criteria are relevant to the municipality? What criteria are in conflict? What are the critical values of the criteria? We show that GAIA and DRSA provide convergent and complementary information that allow enrichment of the answers to these questions.