Multifractal analysis of mass function

In order to explore the fractal characteristic in Dempster-Shafer evidence theory, a fractal dimension of mass function is proposed recently, to reveal the invariance of scale of belief entropy. When mass function degenerates to probability, the fractal dimension is equivalent to classical Renyi information dimension only with a = 1, which can measure the change rate of Shannon entropy with the size of framework. For Renyi dimension, different parameters a represent the relationship between different entropies and framework size. However, this compatibility is not shown in existing fractal dimension. Thus, in this paper, we introduce parameter a to generalize the existing dimension. Due to the diversity of the value of a, we name the new dimension: multifractal dimension of mass function. In addition, inspired by multifractal spectrum of Cantor set, we explore the relation between the belief degree of focal element and the number of focal element with same belief degree for some special assignments. Relevant results are also presented by spectrum. We provide a static discounting coefficient generating method to modify mass function to improve the accuracy of classify result. The experiment is conducted in three datasets, and the result shows the effectiveness of our method.

Automated summary

In this paper, a new multifractal dimension of mass function is proposed by introducing parameter a to generalize the existing dimension. Furthermore, the relationship between the belief degree of focal element and the number of focal element with same belief degree is explored based on the inspiration from the multifractal spectrum of Cantor set, and the relevant results are presented by spectrum. Additionally, a static discounting coefficient generating method is provided to improve the accuracy of classify result of mass function, and the experiment conducted in three datasets shows the effectiveness of our method.