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A New Belief Entropy in Dempster–Shafer Theory Based on Basic Probability Assignment and the Frame of Discernment
2020
Entropy
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The second component is the product of the cardinality of the frame of discernment (FOD) and Dubois entropy. ...
Dempster–Shafer 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]
2015
arXiv
pre-print
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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
2014
Mathematical Problems in Engineering
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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
2021
IEEE Access
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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
2016
2016 Chinese Control and Decision Conference (CCDC)
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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
2015
Zenodo
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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
2019
Entropy
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For Dempster–Shafer 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
2017
Complexity
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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
2017
PLoS ONE
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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
2020
IEEE Access
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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
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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]
2019
arXiv
pre-print
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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
2020
Journal of Mathematics
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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, Dempster–Shafer 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
2021
Journal of Sensors
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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
2020
IEEE Access
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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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