Kybernetika 52 no. 3, 329-347, 2016

On the Minkowski-Hölder type inequalities for generalized Sugeno integrals with an application

Michał Boczek and Marek KaluszkaDOI: 10.14736/kyb-2016-3-0329

Abstract:

In this paper, we use a new method to obtain the necessary and sufficient condition guaranteeing the validity of the Minkowski-Hölder type inequality for the generalized upper Sugeno integral in the case of functions belonging to a wider class than the comonotone functions. As a by-product, we show that the Minkowski type inequality for seminormed fuzzy integral presented by Daraby and Ghadimi \cite{daraby4} is not true. Next, we study the Minkowski-Hölder inequality for the lower Sugeno integral and the class of $\mu$-subadditive functions introduced in \cite{boczek1}. The results are applied to derive new metrics on the space of measurable functions in the setting of nonadditive measure theory. We also give a partial answer to the open problem $2.22$ posed in \cite{hutnik2}.

Keywords:

semicopula, monotone measure, seminormed fuzzy integral, Minkowski's inequality, Hölder's inequality, convergence in mean

Classification:

26E50, 28E10

paper.pdf

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