There has been immense interest in uncertainty measurement because most real-world problems are accompanied by uncertain events. Therefore, Deng entropy has been proposed to measure the uncertainty in the probability theory and evidence theory. In this paper, we show that the uncertainty of the basic probability assignment (BPA) separated through the maximum Deng entropy separation rule (MDESR) is larger than the maximum Deng entropy of the original BPA. In addition, when the cardinality of the frame of discernment increases, the maximum information volume becomes larger and converges slower. The information volume fractal dimension is then proposed to describe the fractal property of uncertainty about the separated BPA distribution, which indicates the inherent physical meanings of Deng entropy from the perspective of statistics. This work can inspire further research on the fractal property of Deng entropy. Some experiments are applied to show the applicability of our proposed information volume fractal dimension.

中文翻译：

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信息量分形维数

不确定性测量引起了极大的兴趣，因为大多数现实世界的问题都伴随着不确定事件。因此，邓熵被提出来衡量概率论和证据论中的不确定性。在本文中，我们表明通过最大邓熵分离规则（MDESR）分离的基本概率分配（BPA）的不确定性大于原始BPA的最大邓熵。此外，当识别框架的基数增加时，最大信息量变大，收敛速度变慢。然后提出信息量分形维数来描述分离的BPA分布的不确定性的分形性质，从统计学的角度说明了邓熵的内在物理意义。这项工作可以激发对邓熵分形性质的进一步研究。一些实验被用来证明我们提出的信息量分形维数的适用性。