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) [5] 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.