A note on convergence properties of interval-valued capacity functionals and Choquet integrals

Based on the classical theory of random sets, Feng and Nguyen (2007) studied the convergence of capacity functionals of random sets in terms of Choquet integrals. In this paper, we consider an interval-valued capacity functional which is motivated by the goal to generalize a capacity functional and the Choquet integral with respect to an interval-valued capacity. In particular, we discuss some convergence theorems for interval-valued capacity functionals and interval-valued probability measures in the Hausdorff metric and Choquet weak sense.