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Information Volume Fractal Dimension

Author

Listed:
  • QIUYA GAO

    (Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610054, P. R. China)

  • TAO WEN

    (Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610054, P. R. China)

  • YONG DENG

    (Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610054, P. R. China2School of Education, Shaanxi Normal University, Xi’an 710062, P. R. China3School of Knowledge Science, Japan Advanced Institute of Science and Technology, Nomi, Ishikawa 923-1211, Japan4Department of Management, Technology, and Economics, ETH Zurich, Zurich, Switzerland)

Abstract

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.

Suggested Citation

  • Qiuya Gao & Tao Wen & Yong Deng, 2021. "Information Volume Fractal Dimension," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(08), pages 1-9, December.
    • Handle: RePEc:wsi:fracta:v:29:y:2021:i:08:n:s0218348x21502637
    DOI: 10.1142/S0218348X21502637
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    Citations

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    Cited by:

    1. Zhou, Qianli & Deng, Yong, 2023. "Generating Sierpinski gasket from matrix calculus in Dempster–Shafer theory," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    2. Lei, Mingli, 2022. "Information dimension based on Deng entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).
    3. Ortiz-Vilchis, Pilar & Lei, Mingli & Ramirez-Arellano, Aldo, 2024. "Reformulation of Deng information dimension of complex networks based on a sigmoid asymptote," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    4. Balakrishnan, Narayanaswamy & Buono, Francesco & Longobardi, Maria, 2022. "A unified formulation of entropy and its application," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 596(C).
    5. Zhao, Tong & Li, Zhen & Deng, Yong, 2024. "Linearity in Deng entropy," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    6. Hu, Yuntong & Xiao, Fuyuan, 2022. "An efficient forecasting method for time series based on visibility graph and multi-subgraph similarity," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).

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