Extending Deng Entropy to the Open World in the Evidence Theory

Quantifying uncertainty is a hot topic for uncertain information processing in the framework of evidence theory, but there is limited research on belief entropy in the open world assumption. In this paper, an uncertainty measurement method that is based on Deng entropy, named Open Deng entropy (ODE), is proposed. In the open world assumption, the frame of discernment (FOD) may be incomplete, and ODE can reasonably and effectively quantify uncertain incomplete information. On the basis of Deng entropy, the ODE adopts the mass value of the empty set, the cardinality of FOD, and the natural constant e to construct a new uncertainty factor for modeling the uncertainty in the FOD. Numerical example shows that, in the closed world assumption, ODE can be degenerated to Deng entropy. An ODE-based information fusion method for sensor data fusion is proposed in uncertain environments. By applying it to the sensor data fusion experiment, the rationality and effectiveness of ODE and its application in uncertain information fusion are verified.

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An Improved Approach of Incomplete Information Fusion and Its Application in Sensor Data-Based Fault Diagnosis

Mathematics ◽

10.3390/math9111292 ◽

2021 ◽

Vol 9 (11) ◽

pp. 1292

Author(s):

Yutong Chen ◽

Yongchuan Tang

Keyword(s):

Fault Diagnosis ◽

Incomplete Information ◽

Partial Information ◽

Evidence Theory ◽

Sensor Data ◽

Uncertain Information ◽

Combination Rules ◽

Open World ◽

Open World Assumption ◽

Deng Entropy

The Dempster–Shafer evidence theory has been widely used in the field of data fusion. However, with further research, incomplete information under the open world assumption has been discovered as a new type of uncertain information. The classical Dempster’s combination rules are difficult to solve the related problems of incomplete information under the open world assumption. At the same time, partial information entropy, such as the Deng entropy is also not applicable to deal with problems under the open world assumption. Therefore, this paper proposes a new method framework to process uncertain information and fuse incomplete data. This method is based on an extension to the Deng entropy in the open world assumption, negation of basic probability assignment (BPA), and the generalized combination rule. The proposed method can solve the problem of incomplete information under the open world assumption, and obtain more uncertain information through the negative processing of BPA, which improves the accuracy of the results. The results of applying this method to fault diagnosis of electronic rotor examples show that, compared with the other uncertain information processing and fusion methods, the proposed method has wider adaptability and higher accuracy, and is more conducive to practical engineering applications.

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Measuring the Uncertainty in the Original and Negation of Evidence Using Belief Entropy for Conflict Data Fusion

Entropy ◽

10.3390/e23040402 ◽

2021 ◽

Vol 23 (4) ◽

pp. 402

Author(s):

Yutong Chen ◽

Yongchuan Tang

Keyword(s):

Information Processing ◽

Data Fusion ◽

Evidence Theory ◽

Uncertain Information ◽

Dempster Shafer Theory ◽

Open World ◽

Uncertainty Measurement ◽

Basic Probability ◽

Shafer Theory ◽

Deng Entropy

Dempster-Shafer (DS) evidence theory is widely used in various fields of uncertain information processing, but it may produce counterintuitive results when dealing with conflicting data. Therefore, this paper proposes a new data fusion method which combines the Deng entropy and the negation of basic probability assignment (BPA). In this method, the uncertain degree in the original BPA and the negation of BPA are considered simultaneously. The degree of uncertainty of BPA and negation of BPA is measured by the Deng entropy, and the two uncertain measurement results are integrated as the final uncertainty degree of the evidence. This new method can not only deal with the data fusion of conflicting evidence, but it can also obtain more uncertain information through the negation of BPA, which is of great help to improve the accuracy of information processing and to reduce the loss of information. We apply it to numerical examples and fault diagnosis experiments to verify the effectiveness and superiority of the method. In addition, some open issues existing in current work, such as the limitations of the Dempster–Shafer theory (DST) under the open world assumption and the necessary properties of uncertainty measurement methods, are also discussed in this paper.

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Deng Entropy Weighted Risk Priority Number Model for Failure Mode and Effects Analysis

Entropy ◽

10.3390/e22030280 ◽

2020 ◽

Vol 22 (3) ◽

pp. 280 ◽

Cited By ~ 7

Author(s):

Haixia Zheng ◽

Yongchuan Tang

Keyword(s):

Risk Factors ◽

Risk Factor ◽

Failure Mode ◽

Evidence Theory ◽

Relative Weight ◽

Relative Importance ◽

Risk Priority Number ◽

Domain Experts ◽

Entropy Weighted ◽

Deng Entropy

Failure mode and effects analysis (FMEA), as a commonly used risk management method, has been extensively applied to the engineering domain. A vital parameter in FMEA is the risk priority number (RPN), which is the product of occurrence (O), severity (S), and detection (D) of a failure mode. To deal with the uncertainty in the assessments given by domain experts, a novel Deng entropy weighted risk priority number (DEWRPN) for FMEA is proposed in the framework of Dempster–Shafer evidence theory (DST). DEWRPN takes into consideration the relative importance in both risk factors and FMEA experts. The uncertain degree of objective assessments coming from experts are measured by the Deng entropy. An expert’s weight is comprised of the three risk factors’ weights obtained independently from expert’s assessments. In DEWRPN, the strategy of assigning weight for each expert is flexible and compatible to the real decision-making situation. The entropy-based relative weight symbolizes the relative importance. In detail, the higher the uncertain degree of a risk factor from an expert is, the lower the weight of the corresponding risk factor will be and vice versa. We utilize Deng entropy to construct the exponential weight of each risk factor as well as an expert’s relative importance on an FMEA item in a state-of-the-art way. A case study is adopted to verify the practicability and effectiveness of the proposed model.

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Determination of Generalized Basic Probability Assignment Based on Interval Numbers

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.644-650.934 ◽

2014 ◽

Vol 644-650 ◽

pp. 934-938

Author(s):

Rui Hong Wang ◽

Pei Da Xu ◽

Xin Chen ◽

Yong Deng

Keyword(s):

Fuzzy Theory ◽

Evidence Theory ◽

Interval Number ◽

Interval Numbers ◽

Probability Assignment ◽

Basic Probability Assignment ◽

Open World ◽

Basic Probability

On the basis of the determination of basic probability assignment based on interval numbers, and combine the generalized evidence theory in the open world, the paper proposed an approach to determine generalized basic probability assignment based on the interval number, which offered a new idea of the determination of generalized basic probability besides the determination based on fuzzy theory. The rationality and effectiveness are verified by the experiments.

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Fractional Deng Entropy and Extropy and Some Applications

Entropy ◽

10.3390/e23050623 ◽

2021 ◽

Vol 23 (5) ◽

pp. 623

Author(s):

Mohammad Reza Kazemi ◽

Saeid Tahmasebi ◽

Francesco Buono ◽

Maria Longobardi

Keyword(s):

Pattern Recognition ◽

Evidence Theory ◽

Two Measures ◽

Deng Entropy

Deng entropy and extropy are two measures useful in the Dempster–Shafer evidence theory (DST) to study uncertainty, following the idea that extropy is the dual concept of entropy. In this paper, we present their fractional versions named fractional Deng entropy and extropy and compare them to other measures in the framework of DST. Here, we study the maximum for both of them and give several examples. Finally, we analyze a problem of classification in pattern recognition in order to highlight the importance of these new measures.

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The Pseudo-Pascal Triangle of Maximum Deng Entropy

International Journal of Computers Communications & Control ◽

10.15837/ijccc.2020.1.3735 ◽

2020 ◽

Vol 15 (1) ◽

Cited By ~ 21

Author(s):

Xiaozhuan Gao ◽

Yong Deng

Keyword(s):

Information Science ◽

Evidence Theory ◽

Uncertain Information ◽

Uncertainty Measure ◽

Pascal Triangle ◽

Basic Probability ◽

Open Issue ◽

Relationship Of ◽

Entropy Functions ◽

Deng Entropy

PPascal triangle (known as Yang Hui Triangle in Chinese) is an important model in mathematics while the entropy has been heavily studied in physics or as uncertainty measure in information science. How to construct the the connection between Pascal triangle and uncertainty measure is an interesting topic. One of the most used entropy, Tasllis entropy, has been modelled with Pascal triangle. But the relationship of the other entropy functions with Pascal triangle is still an open issue. Dempster-Shafer evidence theory takes the advantage to deal with uncertainty than probability theory since the probability distribution is generalized as basic probability assignment, which is more efficient to model and handle uncertain information. Given a basic probability assignment, its corresponding uncertainty measure can be determined by Deng entropy, which is the generalization of Shannon entropy. In this paper, a Pseudo-Pascal triangle based the maximum Deng entropy is constructed. Similar to the Pascal triangle modelling of Tasllis entropy, this work provides the a possible way of Deng entropy in physics and information theory.

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A Weighted Evidence Combination Method Based on the Pignistic Probability Distance and Deng Entropy

Journal of Aerospace Technology and Management ◽

10.5028/jatm.v12.1173 ◽

2020 ◽

Author(s):

Lifan Sun ◽

Yuting Chang ◽

Jiexin Pu ◽

Haofang Yu ◽

Zhe Yang

Keyword(s):

Information Fusion ◽

Evidence Theory ◽

Combination Method ◽

Uncertain Information ◽

Combination Rule ◽

Simulation Experiments ◽

Sensor Information ◽

Bodies Of Evidence ◽

Probability Distance ◽

Deng Entropy

The Dempster-Shafer (D-S) theory is widely applied in various fields involved with multi-sensor information fusion for radar target tracking, which offers a useful tool for decision-making. However, the application of D-S evidence theory has some limitations when evidences are conflicting. This paper proposed a new method combining the Pignistic probability distance and the Deng entropy to address the problem. First, the Pignistic probability distance is applied to measure the conflict degree of evidences. Then, the uncertain information is measured by introducing the Deng entropy. Finally, the evidence correction factor is calculated for modifying the bodies of evidence, and the Dempster’s combination rule is adopted for evidence fusion. Simulation experiments illustrate the effectiveness of the proposed method dealing with conflicting evidences.

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An Uncertainty Measure for Interval-valued Evidences

International Journal of Computers Communications & Control ◽

10.15837/ijccc.2017.5.2950 ◽

2017 ◽

Vol 12 (5) ◽

pp. 631 ◽

Cited By ~ 43

Author(s):

Wen Jiang ◽

Shiyu Wang

Keyword(s):

Evidence Theory ◽

Uncertain Information ◽

Uncertainty Measure ◽

Interval Numbers ◽

Numerical Examples ◽

Belief Structure ◽

Belief Structures ◽

Open Issue ◽

Deng Entropy ◽

Interval Valued

Interval-valued belief structure (IBS), as an extension of single-valued belief structures in Dempster-Shafer evidence theory, is gradually applied in many fields. An IBS assigns belief degrees to interval numbers rather than precise numbers, thereby it can handle more complex uncertain information. However, how to measure the uncertainty of an IBS is still an open issue. In this paper, a new method based on Deng entropy denoted as UIV is proposed to measure the uncertainty of the IBS. Moreover, it is proved that UIV meets some desirable axiomatic requirements. Numerical examples are shown in the paper to demonstrate the efficiency of UIV by comparing the proposed UIV with existing approaches.

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A New Belief Entropy Based on Deng Entropy

Entropy ◽

10.3390/e21100987 ◽

2019 ◽

Vol 21 (10) ◽

pp. 987 ◽

Cited By ~ 7

Author(s):

Dan Wang ◽

Jiale Gao ◽

Daijun Wei

Keyword(s):

Evidence Theory ◽

Theory Method ◽

Entropy Theory ◽

Special Situation ◽

Numerical Examples ◽

Basic Probability ◽

Belief Entropy ◽

Focal Element ◽

Open Question ◽

Deng Entropy

For Dempster–Shafer evidence theory, how to measure the uncertainty of basic probability assignment (BPA) is still an open question. Deng entropy is one of the methods for measuring the uncertainty of Dempster–Shafer evidence. Recently, some limitations of Deng entropy theory are found. For overcoming these limitations, some modified theories are given based on Deng entropy. However, only one special situation is considered in each theory method. In this paper, a unified form of the belief entropy is proposed on the basis of Deng entropy. 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. Meanwhile, for an example, some properties of the belief entropy are obtained based on a special situation of a unified form. Some numerical examples are illustrated to show the efficiency and accuracy of the proposed belief entropy.

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