Research Article
Open Access
Cross and Relative Entropies of Mass Functions Inspired by the Plausibility Entropy
1
School of Electronics and Information, Northwestern Polytechnical University, Xi'an 710072, China
* Corresponding Author:
Xinyang Deng,
[email protected]
Volume 2, Issue 3
2025
Received: 19 March 2025
Accepted: 23 July 2025
Published: 18 September 2025
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CC BY 4.0 License
Article Information
Published in
Chinese Journal of Information Fusion
Volume/Issue
Volume 2, Issue 3, 2025
Pages
212-222
Cited by
1 (Crossref)
1 (Scopus)
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
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.
References
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Cited By (1)
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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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TY - JOUR AU - Deng, Xinyang AU - Jiang, Wen PY - 2025 DA - 2025/09/18 TI - Cross and Relative Entropies of Mass Functions Inspired by the Plausibility Entropy JO - Chinese Journal of Information Fusion T2 - Chinese Journal of Information Fusion JF - Chinese Journal of Information Fusion VL - 2 IS - 3 SP - 212 EP - 222 DO - 10.62762/CJIF.2025.592789 UR - https://www.icck.org/article/abs/CJIF.2025.592789 KW - cross entropy KW - relative entropy KW - plausibility entropy KW - mass functions KW - dempster-shafer theory KW - uncertainty AB - 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. SN - 2998-3371 PB - Institute of Central Computation and Knowledge LA - English ER -
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@article{Deng2025Cross,
author = {Xinyang Deng and Wen Jiang},
title = {Cross and Relative Entropies of Mass Functions Inspired by the Plausibility Entropy},
journal = {Chinese Journal of Information Fusion},
year = {2025},
volume = {2},
number = {3},
pages = {212-222},
doi = {10.62762/CJIF.2025.592789},
url = {https://www.icck.org/article/abs/CJIF.2025.592789},
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.},
keywords = {cross entropy, relative entropy, plausibility entropy, mass functions, dempster-shafer theory, uncertainty},
issn = {2998-3371},
publisher = {Institute of Central Computation and Knowledge}
}
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