Convergences of sequences of set-valued and fuzzy-set-valued functions

Abstract

We define some metrics on the space of integrably bounded multivalued functions and the space of integrably bounded fuzzy random variables with values in a separable Banach space. We also define various convergence of sequences of set-valued and fuzzy-set-valued functions. We investigate relationships among those convergences. Finally, we obtain Lebesguedominated convergence theorem for a sequence of fuzzy random variables.