A benchmark-type generalization of the Sugeno integral with applications in bibliometrics

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We propose a new generalization of the classical Sugeno integral motivated by the Hirsch, Woeginger, and other geometrically-inspired indices of scientific impact. The new integral adapts to the rank-size curve better as it allows for putting more emphasis on highly-valued items and/or the tail of the distribution (level measure). We study its fundamental properties and give the conditions guaranteeing the fulfillment of subadditivity as well as the Jensen, Liapunov, Hardy, Markov, and Paley-Zygmund type inequalities. We discuss its applications in scientometrics.