共查询到15条相似文献,搜索用时 687 毫秒
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单调集函数的连续性与可测函数序列的收敛 总被引:3,自引:0,他引:3
引了单调集函数的几种连续性并且讨论了它们与可测函数依测度收敛之间的关系,给出可加测度论中的Lesbegue定理在单调测度空间上的4种推广形式。讨论单调集函数的连续性和模糊积分与Choquet积分的单调收敛定理之间的等价性。证明Choquet积分的控制收敛定理。 相似文献
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研究一种取值于模糊数集的 Choquet积分 ,该积分的被积函数是单值函数 ,所用的测度是模糊值模糊测度。给出其定义、性质和收敛定理 相似文献
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模糊值Choquet积分(Ⅱ)--函数关于模糊值模糊测度的Choquet积分 总被引:2,自引:0,他引:2
研究一种取值于模糊数集的Choquet积分,该积分的被积函数是单值函数,所用的测度是模糊值模糊测度。给出其定义、性质和收敛定理。 相似文献
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研究了Lebesgue-Stieltjes形式的Choquet积分的收敛性定理,如单调收敛定理、法都引理、控制收敛定理等. 相似文献
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F值Choquet积分(I):F值函数关于F测度的Choquet积分 总被引:2,自引:2,他引:0
本文为取值于F数的Choquet积分系列之一,探讨了F值函数关于F测度的Choquet积分。我们以区间分析为工具,在定义区间值函数Choquet积分的基础上,给出了F值函数Choquet积分的定义,得到了各种性质和收敛定理。 相似文献
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模糊数值函数Henstock积分的收敛定理 总被引:1,自引:0,他引:1
给出模糊数值函数Henstock积分的收敛定理,特别给出了Kaleva积分的收敛定理,该结果推广了Kaleva积分以前若干个收敛定理。 相似文献
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模糊积分变换与模糊Choquet积分的一致连续性 总被引:2,自引:0,他引:2
在一般非负单调函数空间 m[0 ,a]上引入模糊积分变换与距离的概念 ,证明了这种模糊积分变换与模糊 Choquet积分在 m[0 ,a]上关于这种距离是一致连续的 ,从而说明当 m[0 ,a]上两个函数变化不大时 ,不会使相应的模糊积分变换与模糊 Choquet积分产生较大的变化 . 相似文献
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为了解决一些收敛定理,我们给出基于半环([0,1],, )的伪可加分解测度的积分这种模糊积分被深入研究.在给出这种积分的性质的基础上,我们得到一些收敛定理,它们是经典收敛定理的扩张,同时我们得到关于这种模糊测度的Egorof定理. 相似文献
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为了解决一些收敛定理 ,我们给出基于半环 ( [0 ,1 ], , )的伪可加分解测度的积分这种模糊积分被深入研究 .在给出这种积分的性质的基础上 ,我们得到一些收敛定理 ,它们是经典收敛定理的扩张 ,同时我们得到关于这种模糊测度的 Egorof定理 相似文献
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The introduction of linguistic quantifiers has provided an important tool to model a large number of issues in intelligent systems. Ying [M.S. Ying, Linguistic quantifiers modeled by Sugeno integrals, Artificial Intelligence 170 (2006) 581–606] recently introduced a new framework for modeling quantifiers in natural languages in which each linguistic quantifier is represented by a family of fuzzy measures, and the truth value of a quantified proposition is evaluated by using Sugeno’s integral. Representing linguistic quantifiers by fuzzy measures, this paper evaluates linguistic quantified propositions by the Choquet integral. Some elegant logical properties of linguistic quantifiers are derived within this approach, including a prenex normal form theorem stronger than that in Ying’s model. In addition, our Choquet integral approach to the evaluation of quantified statements is compared with others, in particular with Ying’s Sugeno integral approach. 相似文献
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Rui-Sheng Wang 《Journal of Applied Mathematics and Computing》2011,35(1-2):305-321
Fuzzy measure (or non-additive measure), which has been comprehensively investigated, is a generalization of additive probability measure. Several important kinds of non-additive integrals have been built on it. Integral inequalities play important roles in classical probability and measure theory. In this paper, we discuss some of these inequalities for one kind of non-additive integrals—Choquet integral, including Markov type inequality, Jensen type inequality, Hölder type inequality and Minkowski type inequality. As applications of these inequalities, we also present several convergence concepts and convergence theorems as complements to Choquet integral theory. 相似文献
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Michel Grabisch Christophe Labreuche 《4OR: A Quarterly Journal of Operations Research》2008,6(1):1-44
The main advances regarding the use of the Choquet and Sugeno integrals in multi-criteria decision aid over the last decade
are reviewed. They concern mainly a bipolar extension of both the Choquet integral and the Sugeno integral, interesting particular
submodels, new learning techniques, a better interpretation of the models and a better use of the Choquet integral in multi-criteria
decision aid. Parallel to these theoretical works, the Choquet integral has been applied to many new fields, and several softwares
and libraries dedicated to this model have been developed.
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