A Novel Belief Entropy for Measuring Uncertainty in Dempster-Shafer Evidence Theory Framework Based on Plausibility Transformation and Weighted Hartley Entropy
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...
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MDPI AG
2019-02-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/21/2/163 |
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| author | Qian Pan Deyun Zhou Yongchuan Tang Xiaoyang Li Jichuan Huang |
| author_facet | Qian Pan Deyun Zhou Yongchuan Tang Xiaoyang Li Jichuan Huang |
| author_sort | Qian Pan |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-14T05:14:50Z |
| format | Article |
| id | doaj.art-cff554d447e2435f8750b9e6b696b8fe |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-14T05:14:50Z |
| publishDate | 2019-02-01 |
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| series | Entropy |
| spelling | doaj.art-cff554d447e2435f8750b9e6b696b8fe2022-12-22T02:10:24ZengMDPI AGEntropy1099-43002019-02-0121216310.3390/e21020163e21020163A Novel Belief Entropy for Measuring Uncertainty in Dempster-Shafer Evidence Theory Framework Based on Plausibility Transformation and Weighted Hartley EntropyQian Pan0Deyun Zhou1Yongchuan Tang2Xiaoyang Li3Jichuan Huang4School of Electronics and Information, Northwestern Polytechnical University, Xi’an 710072, ChinaSchool of Electronics and Information, Northwestern Polytechnical University, Xi’an 710072, ChinaSchool of Electronics and Information, Northwestern Polytechnical University, Xi’an 710072, ChinaSchool of Electronics and Information, Northwestern Polytechnical University, Xi’an 710072, ChinaFirst Military Representative Office of Air Force Equipment Department, People’s Liberation Army Air Force, Chengdu 610013, ChinaDempster-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.https://www.mdpi.com/1099-4300/21/2/163Dempster-Shafer evidence theoryuncertainty of basic probability assignmentbelief entropyplausibility transformationweighted Hartley entropyShannon entropy |
| spellingShingle | Qian Pan Deyun Zhou Yongchuan Tang Xiaoyang Li Jichuan Huang A Novel Belief Entropy for Measuring Uncertainty in Dempster-Shafer Evidence Theory Framework Based on Plausibility Transformation and Weighted Hartley Entropy Entropy Dempster-Shafer evidence theory uncertainty of basic probability assignment belief entropy plausibility transformation weighted Hartley entropy Shannon entropy |
| title | A Novel Belief Entropy for Measuring Uncertainty in Dempster-Shafer Evidence Theory Framework Based on Plausibility Transformation and Weighted Hartley Entropy |
| title_full | A Novel Belief Entropy for Measuring Uncertainty in Dempster-Shafer Evidence Theory Framework Based on Plausibility Transformation and Weighted Hartley Entropy |
| title_fullStr | A Novel Belief Entropy for Measuring Uncertainty in Dempster-Shafer Evidence Theory Framework Based on Plausibility Transformation and Weighted Hartley Entropy |
| title_full_unstemmed | A Novel Belief Entropy for Measuring Uncertainty in Dempster-Shafer Evidence Theory Framework Based on Plausibility Transformation and Weighted Hartley Entropy |
| title_short | A Novel Belief Entropy for Measuring Uncertainty in Dempster-Shafer Evidence Theory Framework Based on Plausibility Transformation and Weighted Hartley Entropy |
| title_sort | novel belief entropy for measuring uncertainty in dempster shafer evidence theory framework based on plausibility transformation and weighted hartley entropy |
| topic | Dempster-Shafer evidence theory uncertainty of basic probability assignment belief entropy plausibility transformation weighted Hartley entropy Shannon entropy |
| url | https://www.mdpi.com/1099-4300/21/2/163 |
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