Continuity and completeness of lattice-valued possibilistic measures

摘要

Properties such as continuity from above and from below and various kinds of completeness are analysed when investigating set functions, in particular probabilistic and possibilistic measures and the relations of these properties to properties such as (σ)-additivity of probability measures or (complete) maxitivity of possibilistic measures are proved. In this work, the notions of continuity from above and from below are introduced for non-numerical possibilistic measures, taking their values in a complete lattice and at least for some relations valid for real-valued possibilistic measures of their analogies for lattice-valued possibilistic measures are stated and proved.