Fractal plays an important role in nonlinear science. The most important parameter to model fractal is fractal dimension. Existing information dimension can calculate the dimension of probability distribution. However, given a mass function which is the generalization of probability distribution, how to determine its fractal dimension is still an open problem of immense interest. The main contribution of this work is to propose an information fractal dimension of mass function. Numerical examples are illustrated to show the effectiveness of our proposed dimension. We discover an important property in that the dimension of mass function with the maximum Deng entropy is $\frac{ln3}{ln2}\approx 1.585$, which is the well-known fractal dimension of Sierpi\'nski triangle.
翻译：分形在非线性科学中起着重要作用。 模型分形维度最重要的参数是分形维度。 现有信息维度可以计算概率分布的维度。 但是, 如果质量函数是概率分布的通用, 如何确定其分形维度仍然是一个非常令人感兴趣的开放问题。 这项工作的主要贡献是提出质量函数的信息分形维度。 数字示例显示了我们拟议维度的有效性。 我们发现了一个重要属性, 即最大登 entropy 的质函数的维度是 $\ frac{ ln3 ⁇ 2 ⁇ agrox 1. 585$, 这是Sierpi\' nski 三角形的著名分形维度 。
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