A monotone convergence related to pseudo-integral

Abstract

The pseudo-integral is based on a class of set functions which are a generalization of the classical measure. In this paper we have observed how to transform a pseudo-integral into another pseudo-integral that enables us to give the relationship between the pseudo-integral and other integrals based on monotone set functions such as the universal, Sugeno and Shilkret integrals. Also, using the transformed pseudo-integral we have obtained a monotone convergence theorem for the pseudo-integral. As a consequence of the monotone convergence theorem we get the Fatou's lemma for the pseudo-integral.