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A modified belief entropy in Dempster-Shafer framework

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  • Deyun Zhou
  • Yongchuan Tang
  • Wen Jiang

Abstract

How to quantify the uncertain information in the framework of Dempster-Shafer evidence theory is still an open issue. Quite a few uncertainty measures have been proposed in Dempster-Shafer framework, however, the existing studies mainly focus on the mass function itself, the available information represented by the scale of the frame of discernment (FOD) in the body of evidence is ignored. Without taking full advantage of the information in the body of evidence, the existing methods are somehow not that efficient. In this paper, a modified belief entropy is proposed by considering the scale of FOD and the relative scale of a focal element with respect to FOD. Inspired by Deng entropy, the new belief entropy is consistent with Shannon entropy in the sense of probability consistency. What’s more, with less information loss, the new measure can overcome the shortage of some other uncertainty measures. A few numerical examples and a case study are presented to show the efficiency and superiority of the proposed method.

Suggested Citation

  • Deyun Zhou & Yongchuan Tang & Wen Jiang, 2017. "A modified belief entropy in Dempster-Shafer framework," PLOS ONE, Public Library of Science, vol. 12(5), pages 1-17, May.
    • Handle: RePEc:plo:pone00:0176832
    DOI: 10.1371/journal.pone.0176832
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    Cited by:

    1. Lei Chen & Ling Diao & Jun Sang, 2019. "A novel weighted evidence combination rule based on improved entropy function with a diagnosis application," International Journal of Distributed Sensor Networks, , vol. 15(1), pages 15501477188, January.
    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. Dingyi Gan & Bin Yang & Yongchuan Tang, 2020. "An Extended Base Belief Function in Dempster–Shafer Evidence Theory and Its Application in Conflict Data Fusion," Mathematics, MDPI, vol. 8(12), pages 1-19, December.
    4. Moral-García, Serafín & Abellán, Joaquín, 2020. "Critique of modified Deng entropies under the evidence theory," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    5. Shijun Xu & Yi Hou & Xinpu Deng & Kewei Ouyang & Ye Zhang & Shilin Zhou, 2021. "Conflict Management for Target Recognition Based on PPT Entropy and Entropy Distance," Energies, MDPI, vol. 14(4), pages 1-25, February.

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