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An Extended Base Belief Function in Dempster–Shafer Evidence Theory and Its Application in Conflict Data Fusion

Author

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  • Dingyi Gan

    (School of Big Data and Software Engineering, Chongqing University, Chongqing 401331, China)

  • Bin Yang

    (School of Big Data and Software Engineering, Chongqing University, Chongqing 401331, China)

  • Yongchuan Tang

    (School of Big Data and Software Engineering, Chongqing University, Chongqing 401331, China)

Abstract

The Dempster–Shafer evidence theory has been widely applied in the field of information fusion. However, when the collected evidence data are highly conflicting, the Dempster combination rule (DCR) fails to produce intuitive results most of the time. In order to solve this problem, the base belief function is proposed to modify the basic probability assignment (BPA) in the exhaustive frame of discernment (FOD). However, in the non-exhaustive FOD, the mass function value of the empty set is nonzero, which makes the base belief function no longer applicable. In this paper, considering the influence of the size of the FOD and the mass function value of the empty set, a new belief function named the extended base belief function (EBBF) is proposed. This method can modify the BPA in the non-exhaustive FOD and obtain intuitive fusion results by taking into account the characteristics of the non-exhaustive FOD. In addition, the EBBF can degenerate into the base belief function in the exhaustive FOD. At the same time, by calculating the belief entropy of the modified BPA, we find that the value of belief entropy is higher than before. Belief entropy is used to measure the uncertainty of information, which can show the conflict more intuitively. The increase of the value of entropy belief is the consequence of conflict. This paper also designs an improved conflict data management method based on the EBBF to verify the rationality and effectiveness of the proposed method.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:12:p:2137-:d:454383
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    References listed on IDEAS

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    3. Yongchuan Tang & Deyun Zhou & Wen Jiang, 2016. "A New Fuzzy-Evidential Controller for Stabilization of the Planar Inverted Pendulum System," PLOS ONE, Public Library of Science, vol. 11(8), pages 1-16, August.
    4. Yong Chen & Yongchuan Tang & Yan Lei & Jen-Chih Yao, 2020. "An Improved Data Fusion Method Based on Weighted Belief Entropy considering the Negation of Basic Probability Assignment," Journal of Mathematics, Hindawi, vol. 2020, pages 1-11, November.
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