×

Chebyshev type inequality for Choquet integral and comonotonicity. (English) Zbl 1229.28028

Summary: We supply a Chebyshev type inequality for Choquet integral and link this inequality with comonotonicity.

MSC:

28E10 Fuzzy measure theory
Full Text: DOI

References:

[1] Agahi, H.; Mesiar, R.; Ouyang, Y., New general extension of Chebyshev type inequalities for Sugeno integrals, International Journal of Approximate Reasoning, 51, 135-140 (2009) · Zbl 1196.28026
[2] Agahi, H.; Mesiar, R.; Ouyang, Y., Further development of Chebyshev type inequalities for Sugeno integrals and T-(S-)evaluators, Kybernetika, 46, 83-95 (2010) · Zbl 1188.28014
[3] Armstrong, T. E., Chebyshev inequalities and comonotonicity, Real Analysis Exchange, 19, 1, 266-268 (1993/94) · Zbl 0801.60009
[4] Bhaskara Rao, K. P.S.; Bhaskara Rao, M., Theory of Charges (1983), Academic Press: Academic Press London · Zbl 0516.28001
[5] Denneberg, D., Non-Additive Measure and Integral (1994), Kluwer Academic Publisher: Kluwer Academic Publisher Dordrecht · Zbl 0826.28002
[6] Girotto, B.; Holzer, S., A Chebyshev type inequality for Sugeno integral and comonotonicity, International Journal of Approximate Reasoning, 52, 444-448 (2011) · Zbl 1221.28023
[7] Mesiar, R.; Li, J.; Pap, E., The Choquet integral as Lebesgue integral and related inequalities, Kybernetika, 46, 1098-1107 (2010) · Zbl 1210.28025
[8] Mesiar, R.; Ouyang, Y., General Chebyshev type inequalities for Sugeno integrals, Fuzzy Sets and Systems, 160, 58-64 (2009) · Zbl 1183.28035
[9] Wang, R.-S., Some inequalities and convergence theorems for Choquet integrals, Journal of Applied Mathematics and Computing, 35, 305-321 (2011) · Zbl 1210.28028
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.