A New Uncertainty Measure in Belief Entropy Framework

Mambe, Moise Digrais; ́e, Tchimou N’Takp; Georges, Nogbou; Oumtanaga, Souleymane

doi:10.14569/ijacsa.2018.091184

Cited by 9 publications

(4 citation statements)

References 39 publications

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“…In addition, based on the Example 11, we also get the uncertainty measure of Deng entropy, Zhou et.al's belief entropy and some entropies published lately [73], [74], and compare the uncertainty of them. The result is shown in Figure 2.…”

Section: B Examplementioning

confidence: 99%

An Improved Belief Entropy in Evidence Theory

Yan

Deng

2020

IEEE Access

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Uncertainty measurement of the basic probability assignment function has always been a hot issue in Dempster-Shafer evidence. Many existing studies mainly consider the influence of the mass function itself and the size of the frame of discernment, so that the correlation between the subsets is ignored in the power set of the frame of discernment. Without making full use of the information contained in the evidence, the existing methods are less effective in some cases given in the paper. In this paper, inspired by Shannon entropy and Deng entropy, we propose an improved entropy that not only inherits the many advantages of Shannon entropy and Deng entropy, but also fully considers the relationship between subsets, which makes the improved entropy overcome the shortcomings of existing methods and have greater advantages in uncertainty measurement. Many numerical examples are used to demonstrate the validity and superiority of our proposed entropy in this paper.

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Section: B Examplementioning

confidence: 99%

An Improved Belief Entropy in Evidence Theory

Yan

Deng

2020

IEEE Access

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“…Deng entropy has attracted more and more attention [57][58][59][60][61] and has been improved from multiple perspectives [62][63][64][65][66] and applied in different fields [67][68][69][70][71]. For more details on Deng entropy, please refer to [25].…”

Section: The Definition Of Deng Entropymentioning

confidence: 99%

Uncertainty measure in evidence theory

Deng

2020

Sci. China Inf. Sci.

289

108

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As an extension of probability theory, evidence theory is able to better handle unknown and imprecise information. Owing to its advantages, evidence theory has more flexibility and effectiveness for modeling and processing uncertain information. Uncertainty measure plays an essential role both in evidence theory and probability theory. In probability theory, Shannon entropy provides a novel perspective for measuring uncertainty. Various entropies exist for measuring the uncertainty of basic probability assignment (BPA) in evidence theory. However, from the standpoint of the requirements of uncertainty measurement and physics, these entropies are controversial. Therefore, the process for measuring BPA uncertainty currently remains an open issue in the literature. Firstly, this paper reviews the measures of uncertainty in evidence theory followed by an analysis of some related controversies. Secondly, we discuss the development of Deng entropy as an effective way to measure uncertainty, including introducing its definition, analyzing its properties, and comparing it to other measures. We also examine the concept of maximum Deng entropy, the pseudo-Pascal triangle of maximum Deng entropy, generalized belief entropy, and measures of divergence. In addition, we conduct an analysis of the application of Deng entropy and further examine the challenges for future studies on uncertainty measurement in evidence theory. Finally, a conclusion is provided to summarize this study.

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“…In addition, entropy plays an essential role in the measurement of uncertainty and has attracted much attention . Next, there are some entropies introduced.…”

Section: Preliminariesmentioning

confidence: 99%

Uncertainty measure based on Tsallis entropy in evidence theory

et al. 2019

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Dempster-Shafer evidence theory has been widely used in many applications due to its advantages with weaker conditions than Bayes probability. How to measure the uncertainty of basic probability assignment (BPA) in Dempster-Shafer evidence theory is an open and essential issue. Tsallis entropy as nonextensive entropy proposed according to multifractals has been used in many fields. In this paper, a new uncertainty measure of BPA is presented based on Tsallis entropy. The key issue is to determine the value of q in Tsallis entropy. In addition, this paper also analyzes the properties of proposed uncertainty measure. Some numerical examples are used to illustrate the efficiency of the proposed method. Finally, the paper also discusses the application of the proposed method in decision-making. K E Y W O R D S basic probability assignment, belief function, Dempster-Shafer evidence theory, Tsallis entropy, uncertainty | INTRODUCTIONUncertainty plays an important role in real-world and is inevitable in decision-making. 1-5 To handle uncertainty, a lot of theories have been developed, for example, probability theory, 6,7 Dempster-Shafer (D-S) evidence theory, 8,9 fuzzy sets, 10-13 gray model, 14 and Z number. [15][16][17][18] Among these methods, D-S evidence theory has attracted many research' attention due to its extension of Bayesian theory, [19][20][21][22] with the efficiency to deal with imprecise information. 8,23 Measuring the uncertainty of basic probability assignment function (BPA) in D-S theory is essential [24][25][26][27] and can be applied in many applications. [28][29][30]

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A New Uncertainty Measure in Belief Entropy Framework

Cited by 9 publications

References 39 publications

An Improved Belief Entropy in Evidence Theory

An Improved Belief Entropy in Evidence Theory

Uncertainty measure in evidence theory

Uncertainty measure based on Tsallis entropy in evidence theory

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