In this paper we introduce a median operator between two sets of interpretations (worlds) in a finite propositional language. Our definition is based on morphological operations and Hausdorff distance. It provides a result which lies “halfway” between both sets and accounts for the “extension” or “shape” of the sets. We prove several interesting properties of this operator and compare it with fusion operators. This new operator allows performing mediation between two sets of beliefs, preferences, demands, in an original way, showing an interesting behavior that was not possible to achieve using existing operators.