依测度收敛

关于Fuzzy测度空间中依测度收敛问题的研究

Research of Convergence in Measure on the Fuzzy Measure Space

文[2~4,6,7]研究了Fuzzy测度的重要性质，本文相应地给出并证明了Fuzzy测度关于依测度收敛的几个重要结果。

Papers [ 2 ~ 4 ,, 6,7 ] studied some important properties of the Fuzzy measure . In this paper , we give not only a few important results about convergence in measure of Fuzzy measure but also a demonstration of these results .

Orlicz空间中依测度收敛序列系数

Convergent sequence coefficient in measure of Orlicz space

最后，在文[7]的基础上给出了模糊集上的k-拟可加模糊积分序列的依测度收敛和一致收敛的定义及定理，并给出了理论证明。

Finally , we prove some convergence theorems of the k-quasi-additive fuzzy integral on fuzzy sets .

可测函数列在无限测度集上依测度收敛乘除成立的条件

The condition of multiplicating and dividing the convergence in measure of the measurable function sequence on infinite measurable set

本文给出拟收敛函数的定义，再与文[1]中的依测度收敛和几乎处处收敛函数作比较。

This paper defines the quasi & convergence function . Then it compares the convergence in measure in chapter [ 1 ] with the convergence function .

作为这一结果的推论，还得到了依测度收敛蕴涵广义模糊积分平均收敛的几个简洁、实用的充分性条件。

Furthermore , as its corollary , we still get several terse and pragmatic sufficiency conditions where the convergence in fuzzy measure implies the fuzzy mean convergence of ( G ) fuzzy integrals .

较系统地讨论和总结了可测函数列的一致收敛、近一致收敛、依测度收敛、处处收敛、几乎处处收敛之间的关系。

This article systematically discusses and summarizes the relationship between the uniform convergence , near uniform convergence , convergence in measure , everywhere convergence , and almost everywhere convergence of fathomable functional sequence .

另一方面，文中还给出了广义模糊积分平均收敛蕴涵依测度收敛的几个简洁的充分性条件，以及使两者等价的条件。

On the other hand , we also give several terse sufficiency conditions where the fuzzy mean convergence of ( G ) fuzzy integrals implies the convergence in fuzzy measure and making them equivalent .

给出了依测度收敛蕴涵广义模糊积分平均收敛的一个充分必要条件，这一结果是文[8]定理3的改进。

We give a sufficient and necessary condition where the convergence in fuzzy measure implies the fuzzy mean convergence of ( G ) fuzzy integrals . The result is an improvement of Theorem 3 in [ 8 ] .

讨论并建立了概率意义下取全局最小值的一个充分必要条件，证明了算法LDM是依概率测度收敛的。

Discuss and establish a sufficient and necessary condition for the global optimum in probability measure , and prove that the LDM algorithm is convergence in probability .

首先，提出了几类模糊随机变量序列的收敛性概念，包括：必然收敛、几乎必然收敛、一致收敛、几乎必然一致收敛、近一致收敛、依机会测度收敛以及与以上概念相对应的弱收敛；

First , we present various new convergence concepts for sequence of fuzzy random variables , including convergence sure , convergence almost sure , uniform convergence , uniform convergence almost sure , almost uniform convergence , convergence in chance measure , and their corresponding weak convergence .