On the completion of qualitative possibility measures

A relational description of a possibility introduced by D. Dubois and H. Prade in their 1988 book, called a qualitative possibility measure, is discussed. Among the requirements of these kinds of relationships is that they be complete. The focus is on the issue of completing these relationships. A measure associated with weak orderings, called buoyancy, is introduced. The principle of maximal buoyancy is suggested as a means for completion. The connection between the principle of maximal buoyancy and the principle of minimal specificity is shown. A special family of buoyancy measures, called BADD buoyancies, is also introduced that have the properties of entropy measures when the aggregates are restricted to be a probability distribution