Jensen type inequalities for pseudo-integrals of set-valued functions

The set-valued function in general is an important mathematical notion that plays a crucial role in several practical areas. Also, the Jensen integral inequality is a significant mathematical tool that has applications in many areas, such as statistics, statistical physics, information theory, etc. Since the pseudo-analysis is, as well, a theory of the vast area of possible applications, this paper is focused on the generalization of Jensen integral inequality for the set-valued functions done in the pseudo-analysis' background. For this purpose two cases of the semirings and the corresponding pseudo-integrals of set-valued functions have been considered.