In standard propositional belief merging, one implicit assumption is that all sources have exactly the same importance. But there are many situations where the sources have different importance/reliability/expertise that have to be taken into account in the merging process. In this work we study the problem of weighted merging operators, which aimed to take these weights into account in a sensible way. We give a syntactical characterization of these operators, and then we state a representation theorem in terms of plausibility preorders on interpretations. We also propose a general method to build weighted distance-based merging operators, and provide some concrete examples, using two different weight functions.

In this work, we explore the links between the Borda voting rule and belief merging operators. More precisely, we define two families of merging operators inspired by the definition of the Borda voting rule. We also introduce a notion of cancellation in belief merging, inspired by the axiomatization of the Borda voting rule proposed by Young. This allows us to provide a characterization of the drastic merging operator.