H-Index and Other Sugeno Integrals: Some Defects and Their Compensation

The famous Hirsch index has been introduced just ca. ten years ago. Despite that, it is already widely used in many decision-making tasks, like in evaluation of individual scientists, research grant allocation, or even production planning. It is known that the h-index is related to the discrete Sugeno integral and the Ky Fan metric introduced in the 1940s. The aim of this paper is to propose a few modifications of this index as well as other fuzzy integrals-also on bounded chains-that lead to better discrimination of some types of data that are to be aggregated. All of the suggested compensation methods try to retain the simplicity of the original measure.