The fractal dimension of fractional Brownian motion can effectively describe random sets, reflecting the regularity implicit in complex random sets. Data mining algorithms based on fractal theory usually follow the calculation of the fractal dimension of fractional Brownian motion. However, the existing fractal dimension calculation methods of fractal Brownian motion have high time complexity and space complexity, which greatly reduces the efficiency of the algorithm and makes it difficult for the algorithm to adapt to high-speed and massive data flow environments. Therefore, several existing fractal dimension calculation methods of fractional Brownian motion are summarized and analyzed, and a random method is proposed, which uses a fixed memory space to quickly estimate the associated dimension of the data stream. Finally, a comparison experiment with existing algorithms proves the effectiveness of this random algorithm. Second, in the sense of two different measures, based on the principle of stochastic comparison, the stability of the stochastic fuzzy differential equations is derived using the stability of the comparison equations, and the practical stability criterion of two measures according to probability is obtained. Then, the stochastic fuzzy differential equations are discussed. The definition of stochastic exponential stability is given and the stochastic exponential stability criterion is proved.

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基于随机集的分数布朗运动的分形维数

分数布朗运动的分形维数可以有效地描述随机集，反映了复杂随机集隐含的规律性。基于分形理论的数据挖掘算法通常遵循分数布朗运动的分形维数计算。然而，现有分形布朗运动的分形维数计算方法时间复杂度和空间复杂度较高，大大降低了算法的效率，使得算法难以适应高速、海量数据流环境。因此，对现有分数布朗运动的几种分形维数计算方法进行了总结和分析，提出了一种随机方法，利用固定的存储空间快速估计数据流的关联维数。最后，与现有算法的对比实验证明了这种随机算法的有效性。其次，在两种不同测度意义上，基于随机比较原理，利用比较方程的稳定性推导随机模糊微分方程的稳定性，得到两种测度根据概率的实际稳定性判据。然后，讨论了随机模糊微分方程。给出了随机指数稳定性的定义，证明了随机指数稳定性判据。利用比较方程的稳定性推导了随机模糊微分方程的稳定性，得到了两种按概率测度的实际稳定性判据。然后，讨论了随机模糊微分方程。给出了随机指数稳定性的定义，证明了随机指数稳定性判据。利用比较方程的稳定性推导了随机模糊微分方程的稳定性，得到了两种按概率测度的实际稳定性判据。然后，讨论了随机模糊微分方程。给出了随机指数稳定性的定义，证明了随机指数稳定性判据。