基于Choquet积分的Hlder不等式及其应用  

Hlder Inequality for Choquet Integral and Its Applications

作　　者：朱丽萍[1] 欧阳耀[1] 

机构地区：[1]湖州师范学院理学院,浙江湖州313000

出　　处：《模糊系统与数学》2011年第6期146-151,共6页Fuzzy Systems and Mathematics

基　　金：湖州师范学院数学与应用数学国家特色专业研究项目;浙江省自然科学基金资助项目(Y6110094)

摘　　要：基于Sugeno积分的不等式已被许多学者所研究。然而,基于Choquet积分不等式的研究却很少。最近,在集函数μ满足次模性质的假设之下王瑞省研究了基于Choquet积分的Hlder不等式以及其它几个不等式。本文的主要结果是用被积函数f,g的共同单调性来代替μ的次模性质,在此基础上证明了Hlder不等式。作为应用,我们还得到了Minkowski不等式和Lyapunov不等式。Inequalities based on Sugeno integral are extensively investigated. However, few efforts are given to inequalities based on Choquet integral. Recently, Wang Ruisheng proved some inequalities for Choquet integral when the fuzzy measure possesses submodular property. The main purpose of this paper is to prove the Holder inequality for any arbitrary fuzzy measure-based Choquet integral whenever the two integrated functions f,g are comonotone. As its applications, we also prove Minkowski inequality and Lyapunov inequality for Choquet integral.

关 键 词：CHOQUET积分 模糊测度 共同单调函数 Hlder不等式 MINKOWSKI不等式 Lyapunov不等式 

分 类 号：O159[理学—数学]