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一致收敛函数序列

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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. Second, the relations among some types of convergence are studied. Finally, we design some algorithms about fuzzy random simulations to compute the mean chance of fuzzy random event, find the optimistic value of a return function, and evaluate the expected value of a fuzzy random variable.

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;其次,讨论了收敛性之间的关系;最后我们设计了模糊随机模拟算法,用于计算模糊随机事件的平均机会,寻找收益函数的乐观值,以及估计模糊随机变量的期望值。

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.

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;其次,讨论了收敛性之间的关系;最后我们设计了模糊随机模拟算法,用于计算模糊随机事件的平均机会,寻找收益函数的乐观值,以及估计模糊随机变量的期望值。

In this paper,first,a formula of the esˉtimation of functional iteration is discussed and a resultwhich is better than old one is obtained.Then a question of iterationlimit of functional serieses and uniform convergence is discussed.

首先讨论了函数迭代估计的一个关系式,得到了函数迭代估计的一个更好的结果;然后研究了函数序列在一致收敛下的一个迭代极限问题。

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