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A New Belief Entropy in Dempster–Shafer Theory Based on Basic Probability Assignment and the Frame of Discernment

Jiapeng Li, Qian Pan
2020 Entropy  
The second component is the product of the cardinality of the frame of discernment (FOD) and Dubois entropy.  ...  DempsterShafer theory has been widely used in many applications, especially in the measurement of information uncertainty.  ...  Acknowledgments: The authors greatly appreciate the reviews' suggestions and the editor's encouragement. Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/e22060691 pmid:33286463 pmcid:PMC7517227 fatcat:2fllenxfr5h5zlikgeve6wlt7y

Transformation of basic probability assignments to probabilities based on a new entropy measure [article]

Xinyang Deng, Yong Deng
2015 arXiv   pre-print
In this paper, a novel approach of transforming basic probability assignments to probabilities is proposed based on Deng entropy which is a new measure for the uncertainty of BPA.  ...  In that theory, basic probability assignment (BPA) is the basic element for the expression and inference of uncertainty.  ...  In this paper, a novel probability transformation approach is proposed based on a new entropy measure of BPAs, Deng entropy [39] .  ... 
arXiv:1502.06956v1 fatcat:3zyr2atazvb6rb7ouetfmzfftq

Multiscale Probability Transformation of Basic Probability Assignment

Meizhu Li, Xi Lu, Qi Zhang, Yong Deng
2014 Mathematical Problems in Engineering  
In this paper, multiscale probability transformation of basic probability assignment based on the belief function and the plausibility function is proposed, which is a generalization of the pignistic probability  ...  Decision making is still an open issue in the application of Dempster-Shafer evidence theory. A lot of works have been presented for it.  ...  Acknowledgments The authors thank the anonymous reviewers for their valuable comments and suggestions that improved this paper.  ... 
doi:10.1155/2014/319264 fatcat:ehthuld7ujflni2ecluofomosi

Uncertainty Measure of Basic Probability Assignment Based on Renyi Entropy and Its Application in Decision-Making

Zichong Chen, Xianwen Luo
2021 IEEE Access  
Therefore, based on Renyi entropy, this paper proposes a novel method to measure the uncertainty of basic probability assignment in Dempster-Shafer evidence theory.  ...  However, how to measure the uncertainty of basic probability assignment in Dempster-Shafer evidence theory is still a problem worthy of attention.  ...  ACKNOWLEDGMENTS The authors declare that there is no conflict of interests regarding the publication of this paper.  ... 
doi:10.1109/access.2021.3113340 fatcat:6oosollnqzajnepefbbs2jbsm4

Meausre divergence degree of basic probability assignment based on Deng relative entropy

Liguo Fei, Yong Deng
2016 2016 Chinese Control and Decision Conference (CCDC)  
In this paper, a new relative entropy named as Deng relative entropy is proposed in order to measure the divergence between different basic probability assignments (BPAs).  ...  Dempster Shafer evidence theory (D-S theory) is more and more extensively applied to information fusion for the advantage dealing with uncertain information.  ...  This theory extends the elementary event space in probability theory to its power set named as frame of discernment and constructs the basic probability assignment(BPA) on it.  ... 
doi:10.1109/ccdc.2016.7531658 fatcat:4j7o43nwhngrpjzmo7x3my2lya

Deng Entropy: A Generalized Shannon Entropy To Measure Uncertainty

Yong Deng
2015 Zenodo  
However, it cannot handle the more uncertain situation when the uncertainty is represented by basic probability assignment (BPA), instead of probability distribution, under the framework of Dempster Shafer  ...  To address this issue, a new entropy, named as Deng entropy, is proposed.  ...  In Dempster-Shafer evidence theory, the epistemic uncertainty simultaneously contains nonspecificity and discord [23] which are coexisting in a basic probability assignment function (BPA).  ... 
doi:10.5281/zenodo.32211 fatcat:77ja4neipjbspns2i7gdhlc6su

A New Belief Entropy Based on Deng Entropy

Dan Wang, Jiale Gao, Daijun Wei
2019 Entropy  
For DempsterShafer evidence theory, how to measure the uncertainty of basic probability assignment (BPA) is still an open question.  ...  In the new proposed method, the scale of the frame of discernment (FOD) and the relative scale of a focal element with reference to FOD are considered.  ...  Dempster-Shafer evidence theory is regarded as an extension of the Bayesian theory. The basic probability assignment (BPA) is a fundamental concept in Dempster-Shafer evidence theory.  ... 
doi:10.3390/e21100987 fatcat:kgv2kdglenbk7pwrdzexoekpee

An Improved Belief Entropy and Its Application in Decision-Making

Deyun Zhou, Yongchuan Tang, Wen Jiang
2017 Complexity  
The improved belief entropy is a new method for uncertainty measure in Dempster-Shafer framework. Based on the new belief entropy, a decision-making approach is designed.  ...  However, the existing methods pay little attention to the scale of the frame of discernment (FOD), which means a loss of information.  ...  Acknowledgments The work is partially supported by National Natural Science  ... 
doi:10.1155/2017/4359195 fatcat:kwwybdkxhzgoxckurzqz67a2he

A modified belief entropy in Dempster-Shafer framework

Deyun Zhou, Yongchuan Tang, Wen Jiang, Yongtang Shi
2017 PLoS ONE  
But Shannon entropy can't be used directly in the framework of Dempster-Shafer evidence theory, because a mass function in evidence theory is a generalized probability assigned on the power set of FOD.  ...  Dempster-Shafer evidence theory Let O = {θ 1 , θ 2 , . . ., θ i , . . ., θ N } be be a finite nonempty set of mutually exclusive and exhaustive events, O is called the frame of discernment (FOD).  ...  Acknowledgments The authors are very grateful to the anonymous referees for the valuable and constructive comments which have led to improve the manuscript significantly.  ... 
doi:10.1371/journal.pone.0176832 pmid:28481914 pmcid:PMC5421761 fatcat:ejnjcevgs5dtrohzfakz3s5rmq

Weighted Conflict Evidence Combination Method Based on Hellinger Distance and the Belief Entropy

Junwei Li, Baolin Xie, Yong Jin, Zhentao Hu, Lin Zhou
2020 IEEE Access  
Qin et al. defined a new uncertainty measure based on the number of elements in the frame of discernment and the conflict of basic belief assignments (BBAs) [51] , and so on.  ...  Zhou et al. proposed an improved belief entropy based on the scale of frame of discernment [48] . Tang et al. improved on Deng entropy and defined weighted belief entropy [49] .  ...  APPENDIX Proof of the Hellinger distance property: Let m 1 and m 2 be the two BBAs on the same frame of discernment Θ, the two BBAs m 1 and m 2 are shown as m 1 ({θ 1 }), m 1 ({θ 2 }), · · · , m 1 ({θ  ... 
doi:10.1109/access.2020.3044605 fatcat:geivtbywrnd5bakxrot3wtlf44

A Weighted Belief Entropy-Based Uncertainty Measure for Multi-Sensor Data Fusion

2017 Sensors  
In this paper, in the frame of Dempster-Shafer evidence theory, a weighted belief entropy based on Deng entropy is proposed to quantify the uncertainty of uncertain information.  ...  The weight of the proposed belief entropy is based on the relative scale of a proposition with regard to the frame of discernment (FOD).  ...  The founding sponsors had no role in the design of the study; in the collection, analyses or interpretation of data; in the writing of the manuscript; nor in the decision to publish the results.  ... 
doi:10.3390/s17040928 pmid:28441736 pmcid:PMC5426924 fatcat:ca4ycgqm6naydkt3w65mupq3t4

On the negation of a Dempster-Shafer belief structure based on maximum uncertainty allocation [article]

Xinyang Deng, Wen Jiang
2019 arXiv   pre-print
Recent study suggested a transformation to obtain the negation of a probability distribution based on the maximum entropy.  ...  Correspondingly, determining the negation of a belief structure, however, is still an open issue in Dempster-Shafer theory, which is very important in theoretical research and practical applications.  ...  In Dempster-Shafer theory, set Ω is called a frame of discernment (FOD), and a belief structure is a mapping m from the power set of Θ, denoted as 2 Θ , to Bel(A) = B⊆A m(B), (2) P l(A) = 1 − Bel(Ā)  ... 
arXiv:1901.10072v1 fatcat:lui6o2smbne4bfk3fdtfxroxze

An Improved Data Fusion Method Based on Weighted Belief Entropy considering the Negation of Basic Probability Assignment

Yong Chen, Yongchuan Tang, Yan Lei, Jen-Chih Yao
2020 Journal of Mathematics  
In order to handle this issue, a new method for data fusion based on weighted belief entropy and the negation of basic probability assignment (BPA) is proposed.  ...  Due to the effectiveness and flexibility in handling uncertainty, DempsterShafer evidence theory is widely used in numerous fields of data fusion.  ...  Secondly, the new method based on the negation of BPA and the weighted belief entropy is capable to address more uncertain information in the Dempster-Shafer evidence theory framework, which contributes  ... 
doi:10.1155/2020/1594967 fatcat:2uvuiftrzbdlfdl7p364g6xsum

An Improved Method for Multisensor High Conflict Data Fusion

Like Wang, Yu Bao, Eduard Llobet
2021 Journal of Sensors  
At the same time, inspired by Deng entropy, the modified belief entropy is proposed by considering the scale of the frame of discernment (FOD) and the relative scale of the intersection between evidences  ...  Dempster-Shafer evidence theory can effectively process imperfect information and is widely used in a data fusion system.  ...  Although D-S evidence theory is a useful mathematical theory for information fusion in real applications, the classical Dempster's rule of combination and the basic probability assignment (BPA) cannot  ... 
doi:10.1155/2021/9335300 fatcat:iwg5nhcjnvec5kbx4dqfdioxmi

Power law and dimension of the maximum value for belief distribution with the maximum Deng entropy

Ruonan Zhu, Jiaqi Chen, Bingyi Kang
2020 IEEE Access  
In this paper, power law and dimension of the maximum value for belief distribution with the max Deng entropy are presented, which partially uncover the inherent physical meanings of Deng entropy from  ...  Deng entropy is a novel and efficient uncertainty measure to deal with imprecise phenomenon, which is an extension of Shannon entropy.  ...  How to measure the uncertainty of the basic probability assignment (BPA) accurately and efficiently is significant and also an open issue in Dempster-Shafer theory (DST).  ... 
doi:10.1109/access.2020.2979060 fatcat:qvs3xabwabgtzldnnwjn44ds7a
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