Dealing with interactivity between bi-polar multiple criteria preferences in outranking methods

In this paper we introduce the modelling of specific interactions between criteria expressing positive and negative preferences considered as reasons in favor and reasons against the comprehensive preferences. We can call this method the bi-polar approach to MCDA. In order to take into account, specific interactions between criteria in this context, especially the power of the opposing criteria, multiple criteria positive and negative preferences are aggregated using the bi-polar Choquet integral. The bi-polar approach is applied to the two most well-known classes of outranking methods: ELECTRE and PROMETHEE. The final result is a new way to deal with the outranking approach, which permits to take into account some very important preferential information which could not be modelled before by the existing MCDA methodologies. Our approach is related with most of the current advanced research subjects in MCDA and more specifically with the following domains: outranking approach, fuzzy integral approach, four-valued logic approach, non-additive and nontransitive models of conjoint measurement, non-compensatory preference structures, interpretation of the importance of criteria, methods for assessing the non-additive weights, and the aggregation functions.