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

Michał Boczek; Marek Kaluszka

Kybernetika (2016)

  • Volume: 52, Issue: 3, page 329-347
  • ISSN: 0023-5954

Abstract

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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 [11] is not true. Next, we study the Minkowski-Hölder inequality for the lower Sugeno integral and the class of μ -subadditive functions introduced in [20]. 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 [5].

How to cite

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Boczek, Michał, and Kaluszka, Marek. "On the Minkowski-Hölder type inequalities for generalized Sugeno integrals with an application." Kybernetika 52.3 (2016): 329-347. <http://eudml.org/doc/281548>.

@article{Boczek2016,
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 [11] is not true. Next, we study the Minkowski-Hölder inequality for the lower Sugeno integral and the class of $\mu $-subadditive functions introduced in [20]. 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 [5].},
author = {Boczek, Michał, Kaluszka, Marek},
journal = {Kybernetika},
keywords = {seminormed fuzzy integral; semicopula; monotone measure; Minkowski's inequality; Hölder's inequality; convergence in mean},
language = {eng},
number = {3},
pages = {329-347},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On the Minkowski-Hölder type inequalities for generalized Sugeno integrals with an application},
url = {http://eudml.org/doc/281548},
volume = {52},
year = {2016},
}

TY - JOUR
AU - Boczek, Michał
AU - Kaluszka, Marek
TI - On the Minkowski-Hölder type inequalities for generalized Sugeno integrals with an application
JO - Kybernetika
PY - 2016
PB - Institute of Information Theory and Automation AS CR
VL - 52
IS - 3
SP - 329
EP - 347
AB - 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 [11] is not true. Next, we study the Minkowski-Hölder inequality for the lower Sugeno integral and the class of $\mu $-subadditive functions introduced in [20]. 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 [5].
LA - eng
KW - seminormed fuzzy integral; semicopula; monotone measure; Minkowski's inequality; Hölder's inequality; convergence in mean
UR - http://eudml.org/doc/281548
ER -

References

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