Minimax decomposition integrals

In this contribution we introduce two new classes of integrals, referred to as the minimax and the maximin decomposition integrals, based on decomposition systems. We examine some of their basic properties that include super- and sub-additivity, non-decreasingness, positive homogeneity, and piecewise linearity. Some examples illustrating our proposal are given. Concluding remarks include directions of our future research and possible applications of these new integrals. & COPY; 2023 Elsevier B.V. All rights reserved.