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Information Fractal Dimension Of Mass Function

Author

Listed:
  • 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)

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.

Suggested Citation

  • Chenhui Qiang & Yong Deng & Kang Hao Cheong, 2022. "Information Fractal Dimension Of Mass Function," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(06), pages 1-12, September.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:06:n:s0218348x22501109
    DOI: 10.1142/S0218348X22501109
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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. Zhao, Tong & Li, Zhen & Deng, Yong, 2023. "Information fractal dimension of Random Permutation Set," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    4. Yu, Zihan & Deng, Yong, 2022. "Derive power law distribution with maximum Deng entropy," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    5. 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).
    6. Zhan, Tianxiang & Zhou, Jiefeng & Li, Zhen & Deng, Yong, 2024. "Generalized information entropy and generalized information dimension," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    7. Zhao, Tong & Li, Zhen & Deng, Yong, 2024. "Linearity in Deng entropy," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    8. Zeng, Ziyue & Xiao, Fuyuan, 2023. "A new complex belief entropy of χ2 divergence with its application in cardiac interbeat interval time series analysis," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    9. Li, Siran & Xiao, Fuyuan, 2023. "Normal distribution based on maximum Deng entropy," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).

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