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Entropy 2019, 21(2), 163; https://doi.org/10.3390/e21020163

A Novel Belief Entropy for Measuring Uncertainty in Dempster-Shafer Evidence Theory Framework Based on Plausibility Transformation and Weighted Hartley Entropy

1
School of Electronics and Information, Northwestern Polytechnical University, Xi’an 710072, China
2
First Military Representative Office of Air Force Equipment Department, People’s Liberation Army Air Force, Chengdu 610013, China
*
Author to whom correspondence should be addressed.
Received: 22 January 2019 / Revised: 5 February 2019 / Accepted: 7 February 2019 / Published: 10 February 2019
PDF [866 KB, uploaded 10 February 2019]

Abstract

Dempster-Shafer evidence theory (DST) has shown its great advantages to tackle uncertainty in a wide variety of applications. However, how to quantify the information-based uncertainty of basic probability assignment (BPA) with belief entropy in DST framework is still an open issue. The main work of this study is to define a new belief entropy for measuring uncertainty of BPA. The proposed belief entropy has two components. The first component is based on the summation of the probability mass function (PMF) of single events contained in each BPA, which are obtained using plausibility transformation. The second component is the same as the weighted Hartley entropy. The two components could effectively measure the discord uncertainty and non-specificity uncertainty found in DST framework, respectively. The proposed belief entropy is proved to satisfy the majority of the desired properties for an uncertainty measure in DST framework. In addition, when BPA is probability distribution, the proposed method could degrade to Shannon entropy. The feasibility and superiority of the new belief entropy is verified according to the results of numerical experiments.
Keywords: Dempster-Shafer evidence theory; uncertainty of basic probability assignment; belief entropy; plausibility transformation; weighted Hartley entropy; Shannon entropy Dempster-Shafer evidence theory; uncertainty of basic probability assignment; belief entropy; plausibility transformation; weighted Hartley entropy; Shannon entropy
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Pan, Q.; Zhou, D.; Tang, Y.; Li, X.; Huang, J. A Novel Belief Entropy for Measuring Uncertainty in Dempster-Shafer Evidence Theory Framework Based on Plausibility Transformation and Weighted Hartley Entropy. Entropy 2019, 21, 163.

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