The standard techniques of lower and upper approximations, used in
order to define the inner and outer measures given a σ-additive measure, perhaps a probabilistic one, are applied to possibilistic measures. The conditions under which this approach can be reasonable and useful are investigated and the most elernentary properties of the resulting inner and outer possibilistic measures are briefly sketched.
Non-riumerical fuzzy and possibilistic measures taking their values in
partially ordered sets, semilattices or lattices are introduced. Using the operations of supremurn and infimum in these structures, the inner and outer (lower and upper) extensions of the original measures are investigated and defined. The conditions under which the resulting functions -extend conservatively the original ones and possess the properties of fuzzy or possibilistic measures, are explicitly stated and relevant assertions are proved.