An approach to pseudo-integration of set-valued functions

The set-valued function in general is an important mathematical notion that plays a crucial role in several practical areas. This paper does not focus only on the pseudo-integration of set-valued functions in general, but also on a special case, namely on the pseudo-integration of interval-valued functions. Therefore, an approach to the integration of set (interval)valued functions based on both classical Aumann's approach and pseudo-analysis' tools is given. Also, some important properties of this type of integral are investigated. (C) 2011 Elsevier Inc. All rights reserved.