Monotone measures and universal integrals in a uniform framework for the scientific impact assessment problem

•Universal integrals are useful tools, e.g. in automated decision making.•A model for the construction of bibliometric impact indices is introduced.•Most important and notable scientific impact indices may be obtained.

The Choquet, Sugeno, and Shilkret integrals with respect to monotone measures, as well as their generalization – the universal integral, stand for a useful tool in decision support systems. In this paper we propose a general construction method for aggregation operators that may be used in assessing output of scientists. We show that the most often currently used indices of bibliometric impact, like Hirsch’s h, Woeginger’s w, Egghe’s g, Kosmulski’s MAXPROD, and similar constructions, may be obtained by means of our framework. Moreover, the model easily leads to some new, very interesting functions.