IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v178y2024ics0960077923012900.html
   My bibliography  Save this article

Linearity in Deng entropy

Author

Listed:
  • Zhao, Tong
  • Li, Zhen
  • Deng, Yong

Abstract

Linearity is considered as a fundamental property of significant importance in numerous domains. A linear mathematical expression is clear, concise, and convenient for solving problems, making it a valuable tool for approximating complex issues. In recent years, Deng entropy has been proposed as a generalization of Shannon entropy, applied to measure the uncertainty degree of the mass function in the power set. There are two main contributions in this paper. One is that the linearity can be observed in Deng entropy. We present a set of specific mass functions named power assigned mass function (PAMF), which could generate linear type Deng entropy (LTDE). The other is that we find the slope is nothing else but the information fractal dimension of mass function. Moreover, we discover that for any given slope within the range of 0 to ln3ln2, at least one mass function that yields Deng entropy corresponding to the given slope can be derived through the mass function generator (MFG), in a strict linear way. Some proofs, numerical examples, discussions and an error analysis are provided to validate the effectiveness of our findings.

Suggested Citation

  • Zhao, Tong & Li, Zhen & Deng, Yong, 2024. "Linearity in Deng entropy," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    • Handle: RePEc:eee:chsofr:v:178:y:2024:i:c:s0960077923012900
    DOI: 10.1016/j.chaos.2023.114388
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077923012900
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2023.114388?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. Cui, Huizi & Zhou, Lingge & Li, Yan & Kang, Bingyi, 2022. "Belief entropy-of-entropy and its application in the cardiac interbeat interval time series analysis," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    2. Kharazmi, Omid & Contreras-Reyes, Javier E., 2023. "Deng–Fisher information measure and its extensions: Application to Conway’s Game of Life," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    3. 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.
    4. 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.
    5. Yu, Zihan & Deng, Yong, 2022. "Derive power law distribution with maximum Deng entropy," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    6. Li, Siran & Xiao, Fuyuan, 2023. "Normal distribution based on maximum Deng entropy," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    7. Mohit Kumar & Neelesh S. Upadhye & A. K. B. Chand, 2022. "Linear Fractal Interpolation Function For Data Set With Random Noise," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(09), pages 1-17, December.
    8. Qianli Zhou & Yong Deng & Witold Pedrycz, 2022. "Information Dimension Of Galton Board," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(04), pages 1-11, June.
    9. Zhang, Qi & Li, Meizhu, 2022. "A betweenness structural entropy of complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    10. 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).
    11. Contreras-Reyes, Javier E., 2022. "Rényi entropy and divergence for VARFIMA processes based on characteristic and impulse response functions," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    12. Mohit Kumar & Neelesh S. Upadhye & A. K. B. Chand, 2021. "Distribution Of Linear Fractal Interpolation Function For Random Dataset With Stable Noise," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(04), pages 1-12, June.
    13. Zhou, Qianli & Deng, Yong, 2023. "Generating Sierpinski gasket from matrix calculus in Dempster–Shafer theory," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    14. Wang, Rui & Singh, Abhinandan Kumar & Kolan, Subash Reddy & Tsotsas, Evangelos, 2022. "Fractal analysis of aggregates: Correlation between the 2D and 3D box-counting fractal dimension and power law fractal dimension," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    15. Contreras-Reyes, Javier E., 2021. "Lerch distribution based on maximum nonsymmetric entropy principle: Application to Conway’s game of life cellular automaton," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    16. Zhao, Tong & Li, Zhen & Deng, Yong, 2023. "Information fractal dimension of Random Permutation Set," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    17. Chen, Yan-Cheng & Su, Chao-Ton, 2016. "Distance-based margin support vector machine for classification," Applied Mathematics and Computation, Elsevier, vol. 283(C), pages 141-152.
    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, 2023. "Information fractal dimension of Random Permutation Set," Chaos, Solitons & Fractals, Elsevier, vol. 174(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. Lei, Mingli, 2022. "Information dimension based on Deng entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).
    4. Kharazmi, Omid & Contreras-Reyes, Javier E., 2023. "Deng–Fisher information measure and its extensions: Application to Conway’s Game of Life," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    5. Yu, Zihan & Deng, Yong, 2022. "Derive power law distribution with maximum Deng entropy," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    6. 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).
    7. 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).
    8. Li, Siran & Xiao, Fuyuan, 2023. "Normal distribution based on maximum Deng entropy," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    9. 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).
    10. 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).
    11. Wu, Yali & Dong, Ang & Ren, Yuanguang & Jiang, Qiaoyong, 2023. "Identify influential nodes in complex networks: A k-orders entropy-based method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 632(P1).
    12. D'Acci, Luca S., 2023. "Is housing price distribution across cities, scale invariant? Fractal distribution of settlements' house prices as signature of self-organized complexity," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    13. Lamrhari, Soumaya & Ghazi, Hamid El & Oubrich, Mourad & Faker, Abdellatif El, 2022. "A social CRM analytic framework for improving customer retention, acquisition, and conversion," Technological Forecasting and Social Change, Elsevier, vol. 174(C).
    14. Rasheed, T. & Butt, S.I. & Pečarić, Đ. & Pečarić, J., 2022. "Generalized cyclic Jensen and information inequalities," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    15. Zhu, Ting & Wang, Wenbo & Yu, Min, 2022. "A novel blood glucose time series prediction framework based on a novel signal decomposition method," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    16. Refah Alotaibi & Faten S. Alamri & Ehab M. Almetwally & Min Wang & Hoda Rezk, 2022. "Classical and Bayesian Inference of a Progressive-Stress Model for the Nadarajah–Haghighi Distribution with Type II Progressive Censoring and Different Loss Functions," Mathematics, MDPI, vol. 10(9), pages 1-19, May.
    17. Xingyuan Chen & Yong Deng, 2022. "An Evidential Software Risk Evaluation Model," Mathematics, MDPI, vol. 10(13), pages 1-19, July.
    18. 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).
    19. Alkhaleel, Basem A., 2024. "Machine learning applications in the resilience of interdependent critical infrastructure systems—A systematic literature review," International Journal of Critical Infrastructure Protection, Elsevier, vol. 44(C).
    20. Yin, Haofei & Zhang, Aobo & Zeng, An, 2023. "Identifying hidden target nodes for spreading in complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 168(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:178:y:2024:i:c:s0960077923012900. 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.