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In this paper, we define new functionals generalizing scientometric indicesproposed by Mesiar and G\k{a}golewski in 2016 to overcome some limitations ofh-index. These functionals are integrals with respect to a monotone measure aswell as aggregation functions under some mild conditions. We derive numerousproperties of the new integrals and analyze subadditivity property in detail.We also give a partial solution to the problem posed by Mesiar andStup\v{n}anov\'a to find an algorithm for computing the pseudo-decompositionintegral of n-th order based on operations $\oplus=+$ and $\odot=\wedge,$ whichwill be useful in multi-criteria decision problems.

New monotone measure-based integrals inspired by scientific impact problem