IDEAS home Printed from https://ideas.repec.org/a/wsi/fracta/v30y2022i06ns0218348x22501109.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0218348X22501109
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0218348X22501109?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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).
    6. Li, Siran & Xiao, Fuyuan, 2023. "Normal distribution based on maximum Deng entropy," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wsi:fracta:v:30:y:2022:i:06:n:s0218348x22501109. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Tai Tone Lim (email available below). General contact details of provider: https://www.worldscientific.com/worldscinet/fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.