Set-valued Choquet integrals revisited

This paper performs a further investigation on the set-valued Choquet integral given by Jang and Kwon (Fuzzy Sets and Systems 112 (2000) 233), some incorrect properties are revised. It is pointed out that the definition for convergence of sequence of sets or setvalued functions is unreasonable. By using the usual Kuratowskiʹs convergence, some new convergence theorems for the set-valued Choquet integral are shown. Meanwhile some other properties are obtained.