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首页> 外文期刊>International Journal of Uncertainty, Fuzziness, and Knowledge-based Systems >Statistical Fuzzy Convergence
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Statistical Fuzzy Convergence

机译：统计模糊收敛

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摘要

The goal of this work is the further development of neoclassical analysis, which extends the scope and results of the classical mathematical analysis by applying fuzzy logic to conventional mathematical objects, such as functions, sequences, and series. This allows us to reflect and model vagueness and uncertainty of our knowledge, which results from imprecision of measurement and inaccuracy of computation. Basing on the theory of fuzzy limits, we develop the structure of statistical fuzzy convergence and study its properties. Relations between statistical fuzzy convergence and fuzzy convergence are considered in the First Subsequence Theorem and the First Reduction Theorem. Algebraic structures of statistical fuzzy limits are described in the Linearity Theorem. Topological structures of statistical fuzzy limits are described in the Limit Set Theorem and Limit Fuzzy Set theorems. Relations between statistical convergence, statistical fuzzy convergence, ergodic systems, fuzzy convergence and convergence of statistical characteristics, such as the mean (average), and standard deviation, are studied in Secs. 2 and 4. Introduced constructions and obtained results open new directions for further research that are considered in the Conclusion.
机译：这项工作的目的是进一步发展新古典分析，通过将模糊逻辑应用于函数，序列和级数等常规数学对象，扩展了经典数学分析的范围和结果。这使我们能够反映和建模我们的知识的模糊性和不确定性，这是由于测量的不精确性和计算的不准确性造成的。基于模糊极限理论，我们发展了统计模糊收敛的结构并研究了它的性质。在第一子序列定理和第一归约定理中考虑了统计模糊收敛和模糊收敛之间的关系。线性定理描述了统计模糊极限的代数结构。极限集定理和极限模糊集定理描述了统计模糊极限的拓扑结构。在Secs中研究了统计收敛，统计模糊收敛，遍历系统，模糊收敛和统计特性（例如平均值（平均）和标准偏差）的收敛之间的关系。 2和4。介绍的结构和获得的结果为结论中考虑的进一步研究开辟了新的方向。

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