Information fractal dimension of mass function
Information Theory
2022-10-26 v1 math.IT
Abstract
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 , which is the well-known fractal dimension of Sierpi\'nski triangle.
Cite
@article{arxiv.2112.04246,
title = {Information fractal dimension of mass function},
author = {Chenhui Qiang and Yong Deng and Kang Hao Cheong},
journal= {arXiv preprint arXiv:2112.04246},
year = {2022}
}