A max-based merging of incommensurable ranked belief bases based on finite scales

Recently, several approaches have been proposed to merge possibly contradictory belief bases. This paper focuses on max-based merging operators applied to incommensurable ranked belief bases. We first propose a characterization of a result of merging using Pareto-like ordering on a set of possible solutions. Then we propose two equivalent ways to recover the result of merging. The first one is based on the notion of compatible rankings defined on finite scales. The second one is only based on total pre-orders induced by ranked bases to merge.