scholarly journals An Extended Base Belief Function in Dempster–Shafer Evidence Theory and Its Application in Conflict Data Fusion

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2137
Author(s):  
Dingyi Gan ◽  
Bin Yang ◽  
Yongchuan Tang
Keyword(s):  
Data Fusion ◽  
Data Management ◽  
Information Fusion ◽  
Evidence Theory ◽  
Belief Function ◽  
Mass Function ◽  
Combination Rule ◽  
Basic Probability ◽  
Belief Entropy ◽  
Management Method

The Dempster–Shafer evidence theory has been widely applied in the field of information fusion. However, when the collected evidence data are highly conflicting, the Dempster combination rule (DCR) fails to produce intuitive results most of the time. In order to solve this problem, the base belief function is proposed to modify the basic probability assignment (BPA) in the exhaustive frame of discernment (FOD). However, in the non-exhaustive FOD, the mass function value of the empty set is nonzero, which makes the base belief function no longer applicable. In this paper, considering the influence of the size of the FOD and the mass function value of the empty set, a new belief function named the extended base belief function (EBBF) is proposed. This method can modify the BPA in the non-exhaustive FOD and obtain intuitive fusion results by taking into account the characteristics of the non-exhaustive FOD. In addition, the EBBF can degenerate into the base belief function in the exhaustive FOD. At the same time, by calculating the belief entropy of the modified BPA, we find that the value of belief entropy is higher than before. Belief entropy is used to measure the uncertainty of information, which can show the conflict more intuitively. The increase of the value of entropy belief is the consequence of conflict. This paper also designs an improved conflict data management method based on the EBBF to verify the rationality and effectiveness of the proposed method.

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

2020 ◽  
Vol 2020 ◽  
pp. 1-11 ◽  
Author(s):  
Yong Chen ◽  
Yongchuan Tang ◽  
Yan Lei
Keyword(s):  
Data Fusion ◽  
Evidence Theory ◽  
Mass Function ◽  
Sensor Data ◽  
Artificial Data ◽  
Probability Assignment ◽  
Basic Probability Assignment ◽  
Fusion Applications ◽  
Basic Probability ◽  
Belief Entropy

Uncertainty in data fusion applications has received great attention. Due to the effectiveness and flexibility in handling uncertainty, Dempster–Shafer evidence theory is widely used in numerous fields of data fusion. However, Dempster–Shafer evidence theory cannot be used directly for conflicting sensor data fusion since counterintuitive results may be attained. 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. First, the negation of BPA is applied to represent the information in a novel view. Then, by measuring the uncertainty of the evidence, the weighted belief entropy is adopted to indicate the relative importance of evidence. Finally, the ultimate weight of each body of evidence is applied to adjust the mass function before fusing by the Dempster combination rule. The validity of the proposed method is demonstrated in accordance with an experiment on artificial data and an application on fault diagnosis.

scholarly journals Improved Base Belief Function-Based Conflict Data Fusion Approach Considering Belief Entropy in the Evidence Theory

Entropy ◽  
2020 ◽  
Vol 22 (8) ◽  
pp. 801 ◽  
Author(s):  
Shuang Ni ◽  
Yan Lei ◽  
Yongchuan Tang
Keyword(s):  
Data Fusion ◽  
Evidence Theory ◽  
Belief Function ◽  
Combination Rule ◽  
Improved Method ◽  
Data Set ◽  
Numerical Examples ◽  
Initial Belief ◽  
Belief Entropy ◽  
Fusion Approach

Due to the nature of the Dempster combination rule, it may produce results contrary to intuition. Therefore, an improved method for conflict evidence fusion is proposed. In this paper, the belief entropy in D–S theory is used to measure the uncertainty in each evidence. First, the initial belief degree is constructed by using an improved base belief function. Then, the information volume of each evidence group is obtained through calculating the belief entropy which can modify the belief degree to get the final evidence that is more reasonable. Using the Dempster combination rule can get the final result after evidence modification, which is helpful to solve the conflict data fusion problems. The rationality and validity of the proposed method are verified by numerical examples and applications of the proposed method in a classification data set.

scholarly journals Incomplete Information Management Using an Improved Belief Entropy in Dempster-Shafer Evidence Theory

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 993 ◽  
Author(s):  
Bin Yang ◽  
Dingyi Gan ◽  
Yongchuan Tang ◽  
Yan Lei
Keyword(s):  
Data Fusion ◽  
Incomplete Information ◽  
Information Fusion ◽  
Evidence Theory ◽  
Sensor Data ◽  
Uncertain Information ◽  
Open World ◽  
Belief Entropy ◽  
Open World Assumption ◽  
Deng Entropy

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.

scholarly journals A Novel Belief Entropy for Measuring Uncertainty in Dempster-Shafer Evidence Theory Framework Based on Plausibility Transformation and Weighted Hartley Entropy

Entropy ◽  
2019 ◽  
Vol 21 (2) ◽  
pp. 163 ◽  
Author(s):  
Qian Pan ◽  
Deyun Zhou ◽  
Yongchuan Tang ◽  
Xiaoyang Li ◽  
Jichuan Huang
Keyword(s):  
Evidence Theory ◽  
Mass Function ◽  
Probability Mass Function ◽  
Main Work ◽  
Basic Probability ◽  
Open Issue ◽  
Belief Entropy ◽  
Probability Mass ◽  
Hartley Entropy ◽  
Theory Framework

Dempster-Shafer evidence theory (DST) has shown its great advantages to tackle uncertainty in a wide variety of applications. However, how to quantify the information-based uncertainty of basic probability assignment (BPA) with belief entropy in DST framework is still an open issue. The main work of this study is to define a new belief entropy for measuring uncertainty of BPA. The proposed belief entropy has two components. The first component is based on the summation of the probability mass function (PMF) of single events contained in each BPA, which are obtained using plausibility transformation. The second component is the same as the weighted Hartley entropy. The two components could effectively measure the discord uncertainty and non-specificity uncertainty found in DST framework, respectively. The proposed belief entropy is proved to satisfy the majority of the desired properties for an uncertainty measure in DST framework. In addition, when BPA is probability distribution, the proposed method could degrade to Shannon entropy. The feasibility and superiority of the new belief entropy is verified according to the results of numerical experiments.

scholarly journals Combination of Evidential Sensor Reports with Distance Function and Belief Entropy in Fault Diagnosis

2019 ◽  
Vol 14 (3) ◽  
pp. 329-343 ◽  
Author(s):  
Yukun Dong ◽  
Jiantao Zhang ◽  
Zhen Li ◽  
Yong Hu ◽  
Yong Deng
Keyword(s):  
Fault Diagnosis ◽  
Data Fusion ◽  
Distance Function ◽  
Evidence Theory ◽  
Sensor Data ◽  
Combination Rule ◽  
Sensor Data Fusion ◽  
Real Application ◽  
Belief Entropy

Although evidence theory has been applied in sensor data fusion, it will have unreasonable results when handling highly conflicting sensor reports. To address the issue, an improved fusing method with evidence distance and belief entropy is proposed. Generally, the goal is to obtain the appropriate weights assigning to different reports. Specifically, the distribution difference between two sensor reports is measured by belief entropy. The diversity degree is presented by the combination of evidence distance and the distribution difference. Then, the weight of each sensor report is determined based on the proposed diversity degree. Finally, we can use Dempster combination rule to make the decision. A real application in fault diagnosis and an example show the efficiency of the proposed method. Compared with the existing methods, the method not only has a better performance of convergence, but also less uncertainty.

Uncertainty Measure Based on Evidence Theory

2013 ◽  
Vol 329 ◽  
pp. 344-348
Author(s):  
Shao Pu Zhang ◽  
Tao Feng
Keyword(s):  
Information System ◽  
Information Fusion ◽  
Rough Set Theory ◽  
Evidence Theory ◽  
Belief Function ◽  
Mass Function ◽  
Uncertainty Measure ◽  
Rough Approximation ◽  
Uncertainty Information ◽  
Uncertainty Method

Evidence theory is an effective method to deal with uncertainty information. And uncertainty measure is to reflect the uncertainty of an information system. Thus we want to merge evidence theory with uncertainty method in order to measure the roughness of a rough approximation space. This paper discusses the information fusion and uncertainty measure based on rough set theory. First, we propose a new method of information fusion based on the Bayse function, and define a pair of belief function and plausibility function using the fused mass function in an information system. Then we construct entropy for every decision class to measure the roughness of every decision class, and entropy for decision information system to measure the consistence of decision table.

scholarly journals A Novel Method for Conflict Data Fusion Using an Improved Belief Divergence Measure in Dempster–Shafer Evidence Theory

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Yifan Liu ◽  
Tiantian Bao ◽  
Huiyun Sang ◽  
Zhaokun Wei
Keyword(s):  
Data Fusion ◽  
Conflict Management ◽  
Evidence Theory ◽  
External Support ◽  
Divergence Measure ◽  
Fusion Method ◽  
Combination Rule ◽  
Special Cases ◽  
Novel Method ◽  
Belief Entropy

Dempster–Shafer (D-S) evidence theory plays an important role in multisource data fusion. Due to the nature of the Dempster combination rule, there can be counterintuitive results when fusing highly conflicting evidence data. To date, conflict management in D-S evidence theory is still an open issue. Inspired by evidence modification considering internal indeterminacy and external support, a novel method for conflict data fusion is proposed based on an improved belief divergence, evidence distance, and belief entropy. First, an improved belief divergence measure is defined to characterize the discrepancy and conflict between bodies of evidence (BOEs). Second, evidence credibility is generated to describe the external support based on the complementary advantages of the improved belief divergence and evidence distance. Third, belief entropy is utilized to quantify the internal indeterminacy and further determine evidence weight. Lastly, the classical Dempster combination rule is applied to fuse the BOEs modified by their credibility degrees and weights. As the results of numerical examples and an application show, the proposed divergence measure can overcome the invalidity of the existing measures in some special cases. Additionally, the proposed fusion method recognizes the correct target with the highest belief value of 98.96%, which outperforms other related methods in conflict management. The proposed fusion method also displays better convergence, validity, and robustness.

scholarly journals An Improved Multi-Source Data Fusion Method Based on the Belief Entropy and Divergence Measure

Entropy ◽  
2019 ◽  
Vol 21 (6) ◽  
pp. 611 ◽  
Author(s):  
Zhe Wang ◽  
Fuyuan Xiao
Keyword(s):  
Data Fusion ◽  
Evidence Theory ◽  
Weighted Average ◽  
Weights Of Evidence ◽  
Experimental Result ◽  
Fusion Method ◽  
Combination Rule ◽  
Combination Rules ◽  
Source Data ◽  
Belief Entropy

Dempster–Shafer (DS) evidence theory is widely applied in multi-source data fusion technology. However, classical DS combination rule fails to deal with the situation when evidence is highly in conflict. To address this problem, a novel multi-source data fusion method is proposed in this paper. The main steps of the proposed method are presented as follows. Firstly, the credibility weight of each piece of evidence is obtained after transforming the belief Jenson–Shannon divergence into belief similarities. Next, the belief entropy of each piece of evidence is calculated and the information volume weights of evidence are generated. Then, both credibility weights and information volume weights of evidence are unified to generate the final weight of each piece of evidence before the weighted average evidence is calculated. Then, the classical DS combination rule is used multiple times on the modified evidence to generate the fusing results. A numerical example compares the fusing result of the proposed method with that of other existing combination rules. Further, a practical application of fault diagnosis is presented to illustrate the plausibility and efficiency of the proposed method. The experimental result shows that the targeted type of fault is recognized most accurately by the proposed method in comparing with other combination rules.

Information Fusion Based on Improved D-S Evidence Theory

2013 ◽  
Vol 411-414 ◽  
pp. 49-52 ◽  
Author(s):  
Guang Pan ◽  
Lin Li Wu
Keyword(s):  
Data Fusion ◽  
Information Fusion ◽  
Efficient Method ◽  
Evidence Theory ◽  
Combination Rule ◽  
Information Quantity

Dempster-Shafer evidence theory is an efficient method to process uncertain, incomplete and vague information in data fusion. Aiming at the failure of conditional D-S evidence theory in dealing with conflicting evidences, an improved D-S combination rule is recommended. The proposed method utilizes the information quantity of evidence and assigns the conflict factor to every focus element based on average support degree. The simulations show that the proposed D-S combination rule can effectively solve thorny problems for conflicting evidences.

scholarly journals Multisensor Fusion Method Based on the Belief Entropy and DS Evidence Theory

2020 ◽  
Vol 2020 ◽  
pp. 1-16 ◽  
Author(s):  
Xiaojing Fan ◽  
Yinjing Guo ◽  
Yuanyuan Ju ◽  
Jiankang Bao ◽  
Wenhong Lyu
Keyword(s):  
Information Fusion ◽  
Evidence Theory ◽  
Case Analysis ◽  
Entire Body ◽  
Combination Rule ◽  
Target Concentration ◽  
Conflicting Evidence ◽  
Multisensor Information Fusion ◽  
Belief Entropy ◽  
Weighted Factor

The Dempster–Shafer evidence theory has been widely applied in multisensor information fusion. Nevertheless, illogical results may occur when fusing highly conflicting evidence. To solve this problem, a new method of the grouping of evidence is proposed in this paper. This method uses a combination of the belief entropy and the degree of conflict of the evidence as the judgment rule and divides the entire body of evidence into two separate groups. For the grouped evidence, both the credibility weighted factor based on the belief entropy function and the support weighted factor based on the Jousselme distance function are taken into consideration. The two determined weighted factors are integrated to adjust the evidence before applying the DS combination rule. Numerical examples are provided to demonstrate the theoretical feasibility and rationality of the proposed method. The fusion results indicate that the proposed method is more accurate than the compared algorithms in handling the paradoxes. A decision-making case analysis of the biological system is performed to validate the practical applicability of the proposed method. The results confirm that the proposed method has the highest belief degree of the target concentration (50.98%) and has superior accuracy compared to other related methods.

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