Generalized level measure based on a family of conditional aggregation operators

TL;DR

This paper introduces a generalized level measure using conditional aggregation operators, exploring its properties, connections with existing measures, and applications in scientometrics and information science.

Contribution

It presents a novel generalized level measure based on a family of conditional aggregation operators, extending traditional level measures.

Findings

Established properties and connections of the generalized level measure

Linked the measure with the generalized survival function and hyperset transformations

Demonstrated applications in scientometrics and information science

Abstract

Extending the concept of level measure $\mu(\{f\ge a\})$ we introduce a generalized level measure based on a~family of conditional aggregations operators. We investigate in detail several basic properties, including connections with the family of level measures, the generalized survival function and the transformation of monotone measures to hyperset. Applications in scientometrics and information science are described.