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 [7]. We prove that a set multifunction μ:C→Pkc(R+) is a multisubmeasure in this order relation if and only if for every A∈C,μ(A)=[m1(A),m2(A)],m1,m2:C→R+ being submeasures in the sense of Drewnowski [5]. As application, related results concerning variation and continuity properties are established.