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

Pan, Qian; Zhou, Deyun; Tang, Yongchuan; Li, Xiaoyang; Huang, Jichuan

doi:10.3390/e21020163

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

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School of Electronics and Information, Northwestern Polytechnical University, Xi’an 710072, China

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.

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

Received: 22 January 2019 / Revised: 5 February 2019 / Accepted: 7 February 2019 / Published: 10 February 2019

(This article belongs to the Special Issue Entropy Measures for Data Analysis: Theory, Algorithms and Applications)

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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. View Full-Text

Keywords: Dempster-Shafer evidence theory; uncertainty of basic probability assignment; belief entropy; plausibility transformation; weighted Hartley entropy; Shannon entropy

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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. https://doi.org/10.3390/e21020163

AMA Style

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(2):163. https://doi.org/10.3390/e21020163

Chicago/Turabian Style

Pan, Qian, Deyun Zhou, Yongchuan Tang, Xiaoyang Li, and Jichuan Huang. 2019. "A Novel Belief Entropy for Measuring Uncertainty in Dempster-Shafer Evidence Theory Framework Based on Plausibility Transformation and Weighted Hartley Entropy" Entropy 21, no. 2: 163. https://doi.org/10.3390/e21020163

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

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