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Open AccessArticle

A New Belief Entropy in Dempster–Shafer Theory Based on Basic Probability Assignment and the Frame of Discernment

by Jiapeng Li 1,* and Qian Pan 2,*
1
School of Automation, Northwestern Polytechnical University, Xi’an 710072, China
2
School of Electronics and Information, Northwestern Polytechnical University, Xi’an 710072, China
*
Authors to whom correspondence should be addressed.
Entropy 2020, 22(6), 691; https://doi.org/10.3390/e22060691
Received: 30 April 2020 / Revised: 8 June 2020 / Accepted: 10 June 2020 / Published: 20 June 2020
(This article belongs to the Section Information Theory, Probability and Statistics)
Dempster–Shafer theory has been widely used in many applications, especially in the measurement of information uncertainty. However, under the D-S theory, how to use the belief entropy to measure the uncertainty is still an open issue. In this paper, we list some significant properties. The main contribution of this paper is to propose a new entropy, for which some properties are discussed. Our new model has two components. The first is Nguyen entropy. The second component is the product of the cardinality of the frame of discernment (FOD) and Dubois entropy. In addition, under certain conditions, the new belief entropy can be transformed into Shannon entropy. Compared with the others, the new entropy considers the impact of FOD. Through some numerical examples and simulation, the proposed belief entropy is proven to be able to measure uncertainty accurately. View Full-Text
Keywords: Dempster–Shafer theory; basic probability assignment; frame of discernment; uncertainty measure; belief entropy; Shannon entropy Dempster–Shafer theory; basic probability assignment; frame of discernment; uncertainty measure; belief entropy; Shannon entropy
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Li, J.; Pan, Q. A New Belief Entropy in Dempster–Shafer Theory Based on Basic Probability Assignment and the Frame of Discernment. Entropy 2020, 22, 691.

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