Confidence relations and qualitative possibility

In this paper, we deal with the order-theoretic characterization of possibility measures. We define the notion of a qualitative possibility ordering, which is a generalization of Dubois’ qualitative possibility relations [10, 11] in the following sense: they are defined on arbitrary, not necessarily finite universes, and they allow for incomparability. At the same time, we show that any qualitative possibility ordering is not necessarily determined by its distribution relation, and that in general, special extra conditions must be imposed in order to make sure that it would be.