New general extensions of Chebyshev type inequalities for Sugeno integrals

Agahi, Hamzeh; Mesiar, Radko; Ouyang, Yao

doi:10.1016/j.ijar.2009.09.006

Cited by 44 publications

(17 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…holds for comonotone functions f, g and ϕ is a continuous and strictly increasing function and for any measurable set A [1,21]. Also, it also deserves investigation when the equality…”

Section: Resultsmentioning

confidence: 99%

“…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%

See 2 more Smart Citations

On Non-additive Probabilistic Inequalities of Hölder-type

et al. 2011

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…holds for comonotone functions f, g and ϕ is a continuous and strictly increasing function and for any measurable set A [1,21]. Also, it also deserves investigation when the equality…”

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On Non-additive Probabilistic Inequalities of Hölder-type

et al. 2011

Self Cite

View full text Add to dashboard Cite

show abstract

“…The study of inequalities for Sugeno integral was initiated by Román-Flores et al [32], and then followed by the authors [1,2,18,26,27,29]. In [10], a Chebyshev type inequality for a special case for Sugeno integral was obtained which has been generalized by Ouyang et al [27].…”

Section: Introductionmentioning

confidence: 99%