General Minkowski type inequalities for Sugeno integrals

Agahi, Hamzeh; Mesiar, Radko; Ouyang, Yao

doi:10.1016/j.fss.2009.10.007

Cited by 77 publications

(27 citation statements)

References 21 publications

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“…The generalizations of different classical integral inequalities in the frame of the pseudo-analysis, such as Minkowski, Hölder, Berwald, Jensen and Cauchy-Schwarz inequalities were studied in [2][3][4]8,13]. All of these indicate the importance and usefulness of researching this type of inequalities, especially due to the frequent applications in the decision theory, premium principle, probability theory etc.…”

Section: Introductionmentioning

confidence: 99%

Inequalities of the Chebyshev type based on pseudo-integrals

Grbic

Medic

Perović

et al. 2016

Fuzzy Sets and Systems

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Section: Introductionmentioning

confidence: 99%

Inequalities of the Chebyshev type based on pseudo-integrals

Grbic

Medic

Perović

et al. 2016

Fuzzy Sets and Systems

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“…The study of inequalities for Sugeno integral was initiated by Román-Flores et al [10,25], and then followed by some authors [1,[3][4][5]16,[19][20][21]. Recently, the authors generalized several classical inequalities, including Minkowski's and Chebyshev's inequalities, to the frame of Sugeno integral [1,4,20].…”

Section: Introductionmentioning

confidence: 99%

“…Recently, the authors generalized several classical inequalities, including Minkowski's and Chebyshev's inequalities, to the frame of Sugeno integral [1,4,20]. Therefore, it would be an interesting topic to generalize an inequality from the frame of Sugeno integral to some integrals which contains Sugeno integral as special cases, such as it was done in [6,18].…”

Section: Introductionmentioning

confidence: 99%

On Non-additive Probabilistic Inequalities of Hölder-type

et al. 2011

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Non-additive measure is a generalization of additive probability measure. Integral inequalities play important roles in classical probability and measure theory. Some well-known inequalities such as the Minkowski inequality and the Hölder inequality play important roles not only in the theoretical area but also in application. Non-additive integrals are useful tools in several theoretical and applied statistics which have been built on non-additive measure. For instance, in decision theory and applied statistics, the use of the non-additive integrals can be envisaged from two points of view: decision under uncertainty and multi-criteria decision-making. In fact, the non-additive integrals provide useful tools in many problems in engineering and social choice where the aggregation of data is required. In this paper, Hölder and Minkowski type inequalities for semi(co)normed non-additive integrals are discussed. The main results of this paper generalize some previous results obtained by the authors. Mathematics Subject Classification (2000). Primary 99Z99; Secondary 00A00.

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“…Recently, there were obtained generalizations of the classical integral inequalities for integrals with respect to non-additive measures [1,2,8,12,13,28].…”

Section: Introductionmentioning

confidence: 99%