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An Improved Belief Entropy to Measure Uncertainty of Basic Probability Assignments Based on Deng Entropy and Belief Interval

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Key lab of Structures Dynamic Behaviour and Control of the Ministry of Education, Harbin Institute of Technology, Harbin 150090, China
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Key lab of Smart Prevention and Mitigation of Civil Engineering Disasters of the Ministry of Industry and Information Technology, Harbin Institute of Technology, Harbin 150090, China
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School of Management, Harbin Institute of Technology, Harbin 150001, China
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Author to whom correspondence should be addressed.
Entropy 2019, 21(11), 1122; https://doi.org/10.3390/e21111122
Received: 23 October 2019 / Revised: 11 November 2019 / Accepted: 12 November 2019 / Published: 15 November 2019
(This article belongs to the Section Entropy and Biology)
It is still an open issue to measure uncertainty of the basic probability assignment function under Dempster-Shafer theory framework, which is the foundation and preliminary work for conflict degree measurement and combination of evidences. This paper proposes an improved belief entropy to measure uncertainty of the basic probability assignment based on Deng entropy and the belief interval, which takes the belief function and the plausibility function as the lower bound and the upper bound, respectively. Specifically, the center and the span of the belief interval are employed to define the total uncertainty degree. It can be proved that the improved belief entropy will be degenerated to Shannon entropy when the the basic probability assignment is Bayesian. The results of numerical examples and a case study show that its efficiency and flexibility are better compared with previous uncertainty measures. View Full-Text
Keywords: Dempster-Shafer theory; uncertainty measure; Deng entropy; belief interval Dempster-Shafer theory; uncertainty measure; Deng entropy; belief interval
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Zhao, Y.; Ji, D.; Yang, X.; Fei, L.; Zhai, C. An Improved Belief Entropy to Measure Uncertainty of Basic Probability Assignments Based on Deng Entropy and Belief Interval. Entropy 2019, 21, 1122.

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