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Uncertainty measure in evidence theory

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Abstract

As an extension of probability theory, evidence theory is able to better handle unknown and imprecise information. Owing to its advantages, evidence theory has more flexibility and effectiveness for modeling and processing uncertain information. Uncertainty measure plays an essential role both in evidence theory and probability theory. In probability theory, Shannon entropy provides a novel perspective for measuring uncertainty. Various entropies exist for measuring the uncertainty of basic probability assignment (BPA) in evidence theory. However, from the standpoint of the requirements of uncertainty measurement and physics, these entropies are controversial. Therefore, the process for measuring BPA uncertainty currently remains an open issue in the literature. Firstly, this paper reviews the measures of uncertainty in evidence theory followed by an analysis of some related controversies. Secondly, we discuss the development of Deng entropy as an effective way to measure uncertainty, including introducing its definition, analyzing its properties, and comparing it to other measures. We also examine the concept of maximum Deng entropy, the pseudo-Pascal triangle of maximum Deng entropy, generalized belief entropy, and measures of divergence. In addition, we conduct an analysis of the application of Deng entropy and further examine the challenges for future studies on uncertainty measurement in evidence theory. Finally, a conclusion is provided to summarize this study.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 61973332).

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  1. The Institute of Fundamental and Frontier Science, University of Electronic Science and Technology of China, Chengdu, 610054, China

    Yong Deng

  2. School of Education, Shannxi Normal University, Xi’an, 710062, China

    Yong Deng

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Deng, Y. Uncertainty measure in evidence theory. Sci. China Inf. Sci. 63, 210201 (2020). https://doi.org/10.1007/s11432-020-3006-9

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