Superdecomposition integrals

This study introduces and discusses a new class of integrals based on superdecompositions of integrated functions, including an analysis of their relationship with decomposition integrals, which were introduced recently by Even and Lehrer. The proposed superdecomposition integrals have several properties that are similar or dual with respect to decomposition integrals, but they also have some significant differences. The convex integral is obtained by considering all possible superdecompositions with no constraints on the applied sets, which can be treated as the greatest convex homogeneous functional that is bounded from above by the measure we consider. The relationship with the universal integral of Klement et al. is also discussed. Finally, some possible generalizations are outlined.