Chain-based Sugeno-like operators: A new take on the Sugeno integral as a scientometric tool

The Sugeno integral is a highly versatile aggregation tool with extensive applications across various mathematical disciplines. Traditionally, its formula operates on a rearranged nonnegative vector with respect to a monotone measure, whose values are subsequently aggregated through maximum and minimum operations. A key element behind this process is the maximal chain of sets generated by permuting the input vector. In this work, we extend the Sugeno integral by introducing a chain-based approach and generalizing the aggregation operators. This leads to a novel formulation of the chain-based Sugeno-like operator, providing a robust framework for analyzing and extending scientometric indices. After exemplifying its special cases from the literature and establishing its fundamental properties, we demonstrate how numerous scientometric indices emerge as special cases of the CSu-operator, presenting their integral representations.