Partial Convergence and Continuity of Lattice-Valued Possibilistic Measures

keywords: Partially ordered set, (complete) lattice, set function, lattice-valued possibilistic (possibility) measure, (complete) maxitivity, convergence and continuity from above (upper convergence and continuity), convergence and continuity from below (lower convergence and continuity)
The notion of continuity from above (upper continuity) for lattice-valued possibilistic measures as investigated in cite7 has been proved to be a rather strong condition when imposed as demand on such a measure. Hence, our aim will be to introduce some versions of this upper continuity weakened in the sense that the conditions imposed in cite7 to the whole definition domain of the possibilistic measure in question will be restricted just to certain subdomains. The resulting notion of partial upper convergence and continuity of lattice-valued possibilistic measures will be analyzed in more detail and some results will be introduced and proved.
reference: Vol. 27, 2008, No. 3, pp. 297–313