Choquet integration and the AHP: Inconsistency and non-additivity

Abstract

We propose to extend the aggregation scheme of the AHP, from the standard weighted averaging to the more general Choquet integration. In our model, a measure of dominance inconsistency between criteria is derived from the main pairwise comparison matrix of the AHP and it is used to construct a non-additive capacity, whose associated Choquet integral reduces to the standard weighted mean of the AHP in the consistency case. In the general inconsistency case, however, the new AHP aggregation scheme based on Choquet integration tends to attenuate (resp. emphasize) the priority weights of the criteria with higher (resp. lower) average dominance inconsistency with the other criteria. © 2012 Springer-Verlag.