  Valuation based systems verifying an idempotent property are studied. A
partial order is defined between the valuations giving them a lattice
structure. Then, two different strategies are introduced to represent
valuations: as infimum of the most informative valuations or as supremum of the
least informative ones. It is studied how to carry out computations with both
representations in an efficient way. The particular cases of finite sets and
convex polytopes are considered.
