A New Belief Entropy Based on Deng Entropy

Wang, Dan; Gao, Jiale; Wei, Daijun

doi:10.3390/e21100987

Cited by 34 publications

(30 citation statements)

References 39 publications

(55 reference statements)

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“…W [ 34 ] is another modified model based on Deng entropy:

where

is a constant and

is the function about the cardinality of X .

is a change number; it can take different values to represent different entropies.…”

Section: The Development Of Entropy Based On D-s Theorymentioning

confidence: 99%

“…

is a change number; it can take different values to represent different entropies. However, as the parameter

changes, it has little effect on the value of W entropy [ 34 ].…”

Section: The Development Of Entropy Based On D-s Theorymentioning

confidence: 99%

“…Thus, Höhle [ 25 ] was the earliest to combine D-S theory and Shannon entropy, namely Höhle entropy. Subsequently, Nguyen [ 26 ], Dubois and Prade [ 27 ], Klir [ 28 ], Jiroušek and Shenoy [ 29 ], Nikhil R. Pal [ 30 , 31 ], Deng [ 32 ], Pan and Deng [ 33 ], and Wang [ 34 ] defined their uncertainty models. Some of them have been successfully applied in real situations [ 35 , 36 ].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Pan

2020

Entropy

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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.

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“…W [ 34 ] is another modified model based on Deng entropy:

where

is a constant and

is the function about the cardinality of X .

is a change number; it can take different values to represent different entropies.…”

Section: The Development Of Entropy Based On D-s Theorymentioning

confidence: 99%

“…

is a change number; it can take different values to represent different entropies. However, as the parameter

changes, it has little effect on the value of W entropy [ 34 ].…”

Section: The Development Of Entropy Based On D-s Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Pan

2020

Entropy

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show abstract

“…The larger the value of entropy, the bigger the uncertainty of information. [70], generalized belief entropy [71] and so on [72]- [74]. Based on Gini entropy [25], information quality is proposed by Yager and Petry as another way to measure the degree of uncertainty of information [24].…”

Section: B Information Qualitymentioning

confidence: 99%

An Improved Expression for Information Quality of Basic Probability Assignment and Its Application in Fault Diagnosis

Li¹

2020

Preprint

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<div>Information quality is widely used in many applications. However, how to measure infor </div><div>mation quality in basic probability assignment accurately is still an open issue. Generalized expression for </div><div>information quality is an effective method to measure information quality in basic probability assignment. </div><div>Nevertheless, the counter-intuitive results may be obtained when statements are of intersection. To address </div><div>this issue, a new expression for information quality of basic probability assignment is proposed in this paper </div><div>considering the frame of discernment and the inflfluence of intersection among statements which can cause </div><div>changes of uncertainty. Numerical examples are illustrated to demonstrate the effectiveness of the proposed </div><div>method. In addition, an application in fault diagnosis is used to show the effectiveness of the proposed </div><div>method. </div>

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“…Besides, D‐S evidence theory can handle imprecise and unknown information by assigning probabilities to the power set of events, which has attracted many people to study . For this reason, D‐S evidence theory has been used in many fields thanks to the flexibility and effectiveness in modelling uncertainties, such as pattern recognition, decision‐making, conflicting management, evidential reasoning and uncertainty modelling …”

Section: Introductionmentioning

confidence: 99%

Quantum model of mass function

Gao

Deng

2019

Int J Intell Syst

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Dempster-Shafer (D-S) evidence theory has been used in many fields due to the flexibility and effectiveness in modelling uncertainties, which is the extension of classical probability. Uncertainty principle is one of the most important principles in quantum theory, which has been used in many fields. How to set the connection between quantum theory and D-S evidence theory is also an open issue. Hence, the paper proposed the quantum model of mass function to consider the quantum theory and D-S evidence theory. In the proposed quantum method, quantum mass function uses euler formula to represent. The paper also discusses some operations based on the quantum model of the mass function. Moreover, the paper also discusses the relationship between quantum mass function and classical mass function by using some numerical examples. Classical mass function is a special case when there is no interference in quantum mass function. Similar to the other quantum models, this study provides a more wide application in quantum information. K E Y W O R D S basic probability assignment, belief function, Dempster-Shafer evidence theory, mass function, quantum theory

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A New Belief Entropy Based on Deng Entropy

Cited by 34 publications

References 39 publications

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

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

An Improved Expression for Information Quality of Basic Probability Assignment and Its Application in Fault Diagnosis

Quantum model of mass function

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