IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v184y2024ics0960077924005289.html
   My bibliography  Save this article

Generalized information entropy and generalized information dimension

Author

Listed:
  • Zhan, Tianxiang
  • Zhou, Jiefeng
  • Li, Zhen
  • Deng, Yong

Abstract

The concept of entropy has played a significant role in thermodynamics and information theory, and is also a current research hotspot. Information entropy, as a measure of information, has many different forms, such as Shannon entropy and Deng entropy, but there is no unified interpretation of information from a measurement perspective. To address this issue, this article proposes Generalized Information Entropy (GIE) that unifies entropies based on mass function. Meanwhile, GIE establishes the relationship between entropy, fractal dimension, and number of events. Therefore, Generalized Information Dimension (GID) has been proposed, which extends the definition of information dimension from probability to mass fusion. GIE plays a role in approximation calculation and coding systems. In the application of coding, information from the perspective of GIE exhibits a certain degree of particle nature that the same event can have different representational states, similar to the number of microscopic states in Boltzmann entropy.

Suggested Citation

  • Zhan, Tianxiang & Zhou, Jiefeng & Li, Zhen & Deng, Yong, 2024. "Generalized information entropy and generalized information dimension," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    • Handle: RePEc:eee:chsofr:v:184:y:2024:i:c:s0960077924005289
    DOI: 10.1016/j.chaos.2024.114976
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077924005289
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2024.114976?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.

    References listed on IDEAS

    as
    1. 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.
    2. Contreras-Reyes, Javier E. & Kharazmi, Omid, 2023. "Belief Fisher–Shannon information plane: Properties, extensions, and applications to time series analysis," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    3. Beavis,Brian & Dobbs,Ian, 1990. "Optimisation and Stability Theory for Economic Analysis," Cambridge Books, Cambridge University Press, number 9780521336055, November.
    4. Zhao, Tong & Li, Zhen & Deng, Yong, 2024. "Linearity in Deng entropy," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    5. Zhao, Tong & Li, Zhen & Deng, Yong, 2023. "Information fractal dimension of Random Permutation Set," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zhao, Tong & Li, Zhen & Deng, Yong, 2024. "Linearity in Deng entropy," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    2. Zhou, Qianli & Deng, Yong, 2023. "Generating Sierpinski gasket from matrix calculus in Dempster–Shafer theory," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    3. Li, Siran & Xiao, Fuyuan, 2023. "Normal distribution based on maximum Deng entropy," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    4. Ryo Itoh, 2010. "Economic Development And Non‐Monotonic Spatial Transitions," The Japanese Economic Review, Japanese Economic Association, vol. 61(2), pages 234-251, June.
    5. Picard, Pierre, 2000. "On the Design of Optimal Insurance Policies under Manipulation of Audit Cost," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(4), pages 1049-1071, November.
    6. Pierre Martinon & Pierre Picard & Anasuya Raj, 2017. "On the Design of Optimal Health Insurance Contracts under Ex Post Moral Hazard," Working Papers hal-01348551, HAL.
    7. Ben White, 2000. "A Review of the Economics of Biological Natural Resources," Journal of Agricultural Economics, Wiley Blackwell, vol. 51(3), pages 419-462, September.
    8. Gilberto Tadeu Lima, 2004. "Endogenous Technological Innovation, Capital Accumulation And Distributional Dynamics," Metroeconomica, Wiley Blackwell, vol. 55(4), pages 386-408, November.
    9. Lei, Mingli, 2022. "Information dimension based on Deng entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).
    10. Reisch, Lucia A. & Sunstein, Cass R. & Kaiser, Micha, 2021. "What do people want to know? Information avoidance and food policy implications," Food Policy, Elsevier, vol. 102(C).
    11. Rostaghi, Mostafa & Rostaghi, Reza & Humeau-Heurtier, Anne & Azami, Hamed, 2024. "Refined composite multivariate multiscale fuzzy dispersion entropy: Theoretical analysis and applications," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    12. Rodríguez-Pastor, D.A. & Carvajal, E. & Becerra, J.A. & Soltero, V.M. & Chacartegui, R., 2024. "Methanol-based thermochemical energy storage (TCES) for district heating networks," Energy, Elsevier, vol. 298(C).
    13. Aleš Černý, 2003. "Generalised Sharpe Ratios and Asset Pricing in Incomplete Markets," Review of Finance, European Finance Association, vol. 7(2), pages 191-233.
    14. Yu, Zihan & Deng, Yong, 2022. "Derive power law distribution with maximum Deng entropy," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    15. C.J. O’Donnell, 2017. "Estimating Total Factor Productivity Change When No Price or Value-Share Data are Available," CEPA Working Papers Series WP012017, School of Economics, University of Queensland, Australia.
    16. van Wegberg, M.J., 1995. "Can R&D alliances facilitate the formation of a cartel? The example of the European IT industry," Research Memorandum 004, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    17. Zhao, Tong & Li, Zhen & Deng, Yong, 2023. "Information fractal dimension of Random Permutation Set," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    18. 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).
    19. Giorgio Giorgi & Cesare Zuccotti, 2015. "An Overview on D-stable Matrices," DEM Working Papers Series 097, University of Pavia, Department of Economics and Management.
    20. 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).

    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:eee:chsofr:v:184:y:2024:i:c:s0960077924005289. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-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.