The Aumann-Pettis-Sugeno integral for vector multifunctions relative to a vector fuzzy multimeasure

Abstract

In this paper, we define and study the general Aumann-Pettis-Sugeno integral for a vector multifunction relative to a vector fuzzy multimeasure, both taking values in a locally convex space X, ordered by a closed convex pointed cone X+, with nonempty interior. For the selections of the multifunctions we use the general Pettis-Sugeno integral. Several classic properties of this integral and some comparative results are established.