Continuity and completeness of lattice-valued possibilistic measures

Abstract

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.

Keywords:

• Partially ordered set
• Complete lattice
• Lattice-valued possibilistic measure
• Continuity from above and from below
• Completeness
• Possibilistic distribution

Acknowledgements

This work was partially supported by grant No. IAA100300503 of GA AS CR and by the Institutional Research Plan AV0Z10300504 ‘Computer Science for the Information Society: Models, Algorithms, Applications’.