In this work we propose a generalization of the Choquet integral starting from its definition in terms of the Mobius transform. We modify the product on the set of real numbers considered in the Lovasz extension form of the Choquet integral into a function $F$ , and we discuss the properties of this new functional. For a fixed $n$ , a complete description of all $F$ yielding an $n$ -ary aggregation function with a fixed diagonal section, independently of the considered fuzzy measure, is given, and several particular examples are presented. Finally, all functions $F$ yielding an aggregation function, independently of the number $n$ of inputs and of the considered fuzzy measure, are characterized, and related aggregation functions are shown to be just the Choquet integrals over the distorted inputs.

The usage of the standard h-index to compare scientists from different research fields is often misleading. To avoid this possible failure, based on Sugeno integrals, three new modified indices $H_{\alpha}$ , $H^{\beta}$ and $H_{\alpha}^{\beta}$ are proposed, thus allowing to compensate the lower number of citations or of papers characteristic for a considered field. Our approach has a transparent geometric interpretation and thus it offers good candidates to replace the standard h-index H in considered databases, such as WOS, SCOPUS or Google Scholar.