Uncertainty measure in evidence theory
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. REVIEW .
November 2020, Vol. 63 210201:1–210201:19 https://doi.org/10.1007/s11432-020-3006-9
Special Focus on Multi-source Information Fusion
Uncertainty measure in evidence theory Yong DENG1,2 1
The Institute of Fundamental and Frontier Science, University of Electronic Science and Technology of China, Chengdu 610054, China; 2 School of Education, Shannxi Normal University, Xi’an 710062, China Received 27 May 2020/Accepted 1 July 2020/Published online 20 October 2020
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. Keywords
evidence theory, uncertainty measure, Deng entropy, Shannon entropy
Citation Deng Y. Uncertainty measure in evidence theory. Sci China Inf Sci, 2020, 63(11): 210201, https://doi. org/10.1007/s11432-020-3006-9
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Introduction
Uncertainty plays a fundamental role in real life, such as decision-making [1, 2], information fusion [3–5], reliability analysis [6, 7], and other applications [8, 9]. How to better handle uncertainty has attracted the attention of many researchers over the past few years [10]. Currently, many methodologies exist for describing uncertain information, such as fuzzy sets [11], rough sets [12], Dempster-Shafer evidence theory (D-S evidence theory) [13, 14], and so on [15–17]. Many of these tools can be transformed into a framework on evidence theory. D-S evidence theory has attracted much attention because it can better represent uncertain information by using basic probability assignment (BPA) and implementing uncertainty reasoning [18]. D-S evidence theory not only provides an elegant mathematical framework for modeling uncertainty, but al
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