Jensen type inequality for the pseudo-integral based on the smallest universal integral

Abstract

Choquet and Sugeno integrals have wide applications in several practical areas, especially as aggregation functions in decision theory. Universal integral is a generalization of Choquet and Sugeno integrals. The Jensen type inequality related to the smallest universal integral which special cases are Sugeno, Shilkret, seminormed fuzzy integrals and pseudo-integral has been recently proposed. Based on this result, we have obtained the Jensen's inequality for the pseudo-integral and sufficient conditions under which that inequality holds.