模糊统计界限
Fuzzy Statistical Limits
摘要：
统计极限定义放松条件的常规收敛。序列l的统计收敛的主要思想是l中的大多数元素收敛，我们不关心其他元素发生了什么。同时，已知来自现实生活来源（例如测量和计算）的序列在一般情况下不允许测试它们在严格数学意义上是否收敛或统计收敛。为了克服这些局限性，模糊收敛在新古典分析的背景下被引入，本文引入并研究了模糊统计收敛。我们发现了序列的模糊统计收敛与序列的模糊统计收敛（定理2.1），以及序列的模糊统计收敛与序列的常规收敛（定理2.2）之间的关系。证明了序列上的运算会导致哪些具有模糊统计极限的运算（定理2.3），以及不同序列的模糊统计极限之间的相互影响（定理2.4）。第三节研究了模糊统计收敛与统计特征的模糊收敛之间的关系，如均值和标准差的模糊收敛（定理3.1和3.2）。
英文摘要：
Statistical limits are defined relaxing conditions on conventional convergence. The main idea of the statistical convergence of a sequence l is that the majority of elements from l converge and we do not care what is going on with other elements. At the same time, it is known that sequences that come from real life sources, such as measurement and computation, do not allow, in a general case, to test whether they converge or statistically converge in the strict mathematical sense. To overcome these limitations, fuzzy convergence was introduced earlier in the context of neoclassical analysis and fuzzy statistical convergence is introduced and studied in this paper. We find relations between fuzzy statistical convergence of a sequence and fuzzy statistical convergence of its subsequences (Theorem 2.1), as well as between fuzzy statistical convergence of a sequence and conventional convergence of its subsequences (Theorem 2.2). It is demonstrated what operations with fuzzy statistical limits are induced by operations on sequences (Theorem 2.3) and how fuzzy statistical limits of different sequences influence one another (Theorem 2.4). In Section 3, relations between fuzzy statistical convergence and fuzzy convergence of statistical characteristics, such as the mean (average) and standard deviation, are studied (Theorems 3.1 and 3.2).
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