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Some General Inequalities for Choquet Integral
College of Science, China University of Mining and Technology, Xuzhou, China
College of Science, China University of Mining and Technology, Xuzhou, China
College of Science, China University of Mining and Technology, Xuzhou, China
- 1 College of Science, China University of Mining and Technology, Xuzhou, China
- 2 College of Science, China University of Mining and Technology, Xuzhou, China
- 3 College of Science, China University of Mining and Technology, Xuzhou, China
Applied Mathematics·Volume 06 (2015)·Pages 2292–2299·Published 21 December 2015·DOI10.4236/am.2015.614201
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Abstract
With the development of fuzzy measure theory, the integral inequalities based on Sugeno integral are extensively investigated. We concern on the inequalities of Choquuet integral. The main purpose of this paper is to prove the H?lder inequality for any arbitrary fuzzy measure-based Choquet integral whenever any two of these integrated functions f, g and h are comonotone, and there are three weights. Then we prove Minkowski inequality and Lyapunov inequality for Choquet integral. Moreover, when any two of these integrated functions f 1 , f 2 , … , f n are comonotone, we also obtain the H ö lder inequality, Minkowski inequality and Lyapunov inequality hold for Choquet integral.
KeywordsChoquet IntegralFuzzy MeasureComonotoneH&oumllder InequalityMinkowski InequalityLyapunov Inequality
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