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Cross and Relative Entropies of Mass Functions Inspired by the Plausibility Entropy
Research Article | Published: 18 September 2025
Chinese Journal of Information Fusion Volume 2, Issue 3, 2025: 212-222
Volume 2, Issue 3, Chinese Journal of Information Fusion
Volume 2, Issue 3, 2025
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Jun Liu
Jun Liu
Hangzhou Dianzi University, China
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Chinese Journal of Information Fusion, Volume 2, Issue 3, 2025: 212-222

Open Access | Research Article | 18 September 2025
Cross and Relative Entropies of Mass Functions Inspired by the Plausibility Entropy
by
Xinyang Deng Xinyang Deng 1 *
Wen Jiang Wen Jiang 1
1 School of Electronics and Information, Northwestern Polytechnical University, Xi'an 710072, China
* Corresponding Author: Xinyang Deng, [email protected]
DOI: 10.62762/CJIF.2025.592789
Received: 19 March 2025, Accepted: 23 July 2025, Published: 18 September 2025  
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Abstract
Related concepts of entropy play a very important role in dealing with uncertainty in terms of Shannon's information theory. However, for uncertain information involving epistemic uncertainty, which is usually modelled by using Dempster-Shafer theory, the concepts of cross entropy and relative entropy are still not well defined currently. Facing this issue, by reviewing and importing existing related work, this study gives new definitions of cross entropy and relative entropy of mass functions, which are respectively named as cross plausibility entropy and relative plausibility entropy since they are both based on an uncertainty measure called plausibility entropy. The properties of cross and relative plausibility entropies are also given, which shows a strong connection with classical cross entropy and relative entropy in Shannon's information theory. An example of application regarding parameter estimation is provided to show the effectiveness and reasonability of the presented entropies, which has implemented the parameter estimation for a generalized Bernoulli distribution with plausibility distribution observations.
Graphical Abstract
Cross and Relative Entropies of Mass Functions Inspired by the Plausibility Entropy
Keywords
cross entropy
relative entropy
plausibility entropy
mass functions
dempster-shafer theory
uncertainty
Data Availability Statement
Data will be made available on request.
Funding
The work was partially supported by the National Natural Science Foundation of China under Grant 62173272.
Conflicts of Interest
The authors declare no conflicts of interest.
Ethical Approval and Consent to Participate
Not applicable.
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Cite This Article
APA Style
Deng, X., & Jiang, W. (2025). Cross and Relative Entropies of Mass Functions Inspired by the Plausibility Entropy. Chinese Journal of Information Fusion, 2(3), 212–222. https://doi.org/10.62762/CJIF.2025.592789
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