INFORMATION FRACTAL DIMENSION OF MASS FUNCTION

Chenhui Qiang, Yong Deng and Kang Hao Cheong
Additional contact information
Chenhui Qiang: Institute of Fundamental and Frontier Science, University of Electronic Science and Technology of China, 610054 Chengdu, P. R. China2Yingcai Honors College, University of Electronic Science and Technology of China, Chengdu 610054, P. R. China
Yong Deng: Institute of Fundamental and Frontier Science, University of Electronic Science and Technology of China, 610054 Chengdu, P. R. China3School of Education, Shaanxi Normal University, Xi’an 710062, P. R. China4School of Knowledge Science, Japan Advanced Institute of Science and Technology, Nomi, Ishikawa 923-1211, Japan5Department of Management, Technology and Economics, ETH Zrich, Zurich, Switzerland
Kang Hao Cheong: Science, Mathematics and Technology Cluster, Singapore University of Technology and Design (SUTD), S487372, Singapore

FRACTALS (fractals), 2022, vol. 30, issue 06, 1-12

Abstract: Fractals play an important role in nonlinear science. The most important parameter when modeling a fractal is the fractal dimension. Existing information dimension can calculate the dimension of probability distribution. However, calculating the fractal dimension given a mass function, which is the generalization of probability, 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 given 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 ln 3 ln 2 ≈ 1.585, which is the well-known fractal dimension of Sierpiski triangle. The application in complexity analysis of time series illustrates the effectiveness of our method.

Keywords: Fractal; Information Dimension; Probability Distribution; Mass Function; Shannon Entropy; Deng Entropy; Sierpiski Triangle; Time Series (search for similar items in EconPapers)
Date: 2022
References: Add references at CitEc
Citations: View citations in EconPapers (9)

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0218348X22501109
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:fracta:v:30:y:2022:i:06:n:s0218348x22501109

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0218348X22501109

Access Statistics for this article

FRACTALS (fractals) is currently edited by Tara Taylor

More articles in FRACTALS (fractals) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().