A New Belief Entropy in Dempster–Shafer Theory Based on Basic Probability Assignment and the Frame of Discernment
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 con...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-06-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/22/6/691 |
| _version_ | 1827714539005673472 |
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| author | Jiapeng Li Qian Pan |
| author_facet | Jiapeng Li Qian Pan |
| author_sort | Jiapeng Li |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T19:00:01Z |
| format | Article |
| id | doaj.art-3ce8bb2aab0b4fb09cd099b1723e64ae |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T19:00:01Z |
| publishDate | 2020-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-3ce8bb2aab0b4fb09cd099b1723e64ae2023-11-20T04:28:27ZengMDPI AGEntropy1099-43002020-06-0122669110.3390/e22060691A New Belief Entropy in Dempster–Shafer Theory Based on Basic Probability Assignment and the Frame of DiscernmentJiapeng Li0Qian Pan1School of Automation, Northwestern Polytechnical University, Xi’an 710072, ChinaSchool of Electronics and Information, Northwestern Polytechnical University, Xi’an 710072, ChinaDempster–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.https://www.mdpi.com/1099-4300/22/6/691Dempster–Shafer theorybasic probability assignmentframe of discernmentuncertainty measurebelief entropyShannon entropy |
| spellingShingle | Jiapeng Li Qian Pan A New Belief Entropy in Dempster–Shafer Theory Based on Basic Probability Assignment and the Frame of Discernment Entropy Dempster–Shafer theory basic probability assignment frame of discernment uncertainty measure belief entropy Shannon entropy |
| title | A New Belief Entropy in Dempster–Shafer Theory Based on Basic Probability Assignment and the Frame of Discernment |
| title_full | A New Belief Entropy in Dempster–Shafer Theory Based on Basic Probability Assignment and the Frame of Discernment |
| title_fullStr | A New Belief Entropy in Dempster–Shafer Theory Based on Basic Probability Assignment and the Frame of Discernment |
| title_full_unstemmed | A New Belief Entropy in Dempster–Shafer Theory Based on Basic Probability Assignment and the Frame of Discernment |
| title_short | A New Belief Entropy in Dempster–Shafer Theory Based on Basic Probability Assignment and the Frame of Discernment |
| title_sort | new belief entropy in dempster shafer theory based on basic probability assignment and the frame of discernment |
| topic | Dempster–Shafer theory basic probability assignment frame of discernment uncertainty measure belief entropy Shannon entropy |
| url | https://www.mdpi.com/1099-4300/22/6/691 |
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