Remarks on monotone interval-valued set multifunctions

In this paper, motivated by the representation of uncertainty, we discuss the problem of interval-valued set multifunctions which are monotone with respect to Guo and Zhang order relation . We prove that a set multifunction image is a multisubmeasure in this order relation if and only if for every image being submeasures in the sense of Drewnowski . As application, related results concerning variation and continuity properties are established.