Processing additional information in a multiple criteria context with mixed evaluations: including the weak preference relation

In a multiple criteria decision context facing inevitable and various kinds of information imperfections (uncertainty, imprecision, ambiguity...), it is rather natural to seek additional information. In this paper, we propose a unified procedure for processing additional information in such a context. It is based on the Bayesian model and the adaptation of information revision rules from the uniattribute to the multiattribute context. It leads to prior and posterior global preference relations including the strict preference, the indifference, the incomparability and the weak preference relations. The impact of additional information can then be assessed through the comparison of prior and posterior results.