scholarly journals An Improved Belief Entropy to Measure Uncertainty of Basic Probability Assignments Based on Deng Entropy and Belief Interval

Entropy ◽  
2019 ◽  
Vol 21 (11) ◽  
pp. 1122 ◽  
Author(s):  
Yonggang Zhao ◽  
Duofa Ji ◽  
Xiaodong Yang ◽  
Liguo Fei ◽  
Changhai Zhai
Keyword(s):  
Belief Function ◽  
Total Uncertainty ◽  
Probability Assignment ◽  
Basic Probability Assignment ◽  
Dempster Shafer Theory ◽  
Basic Probability ◽  
Open Issue ◽  
Belief Entropy ◽  
Shafer Theory ◽  
Deng Entropy

It is still an open issue to measure uncertainty of the basic probability assignment function under Dempster-Shafer theory framework, which is the foundation and preliminary work for conflict degree measurement and combination of evidences. This paper proposes an improved belief entropy to measure uncertainty of the basic probability assignment based on Deng entropy and the belief interval, which takes the belief function and the plausibility function as the lower bound and the upper bound, respectively. Specifically, the center and the span of the belief interval are employed to define the total uncertainty degree. It can be proved that the improved belief entropy will be degenerated to Shannon entropy when the the basic probability assignment is Bayesian. The results of numerical examples and a case study show that its efficiency and flexibility are better compared with previous uncertainty measures.

scholarly journals Negation of Belief Function Based on the Total Uncertainty Measure

Entropy ◽  
2019 ◽  
Vol 21 (1) ◽  
pp. 73 ◽  
Author(s):  
Kangyang Xie ◽  
Fuyuan Xiao
Keyword(s):  
Probability Distribution ◽  
Belief Function ◽  
Uncertainty Measure ◽  
Classical Probability ◽  
Total Uncertainty ◽  
Probability Assignment ◽  
Basic Probability Assignment ◽  
Power Set ◽  
Basic Probability ◽  
Open Issue

The negation of probability provides a new way of looking at information representation. However, the negation of basic probability assignment (BPA) is still an open issue. To address this issue, a novel negation method of basic probability assignment based on total uncertainty measure is proposed in this paper. The uncertainty of non-singleton elements in the power set is taken into account. Compared with the negation method of a probability distribution, the proposed negation method of BPA differs becausethe BPA of a certain element is reassigned to the other elements in the power set where the weight of reassignment is proportional to the cardinality of intersection of the element and each remaining element in the power set. Notably, the proposed negation method of BPA reduces to the negation of probability distribution as BPA reduces to classical probability. Furthermore, it is proved mathematically that our proposed negation method of BPA is indeed based on the maximum uncertainty.

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

Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 691 ◽  
Author(s):  
Jiapeng Li ◽  
Qian Pan
Keyword(s):  
Shannon Entropy ◽  
Information Uncertainty ◽  
Numerical Examples ◽  
New Model ◽  
Dempster Shafer Theory ◽  
Basic Probability ◽  
Open Issue ◽  
Belief Entropy ◽  
Shafer Theory ◽  
The Impact

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.

scholarly journals A New Total Uncertainty Measure from A Perspective of Maximum Entropy Requirement

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 1061
Author(s):  
Yu Zhang ◽  
Fanghui Huang ◽  
Xinyang Deng ◽  
Wen Jiang
Keyword(s):  
Maximum Entropy ◽  
Information Fusion ◽  
Uncertainty Measure ◽  
Total Uncertainty ◽  
Numerical Examples ◽  
Dempster Shafer Theory ◽  
Basic Probability ◽  
Open Issue ◽  
Shafer Theory ◽  
Fusion Framework

The Dempster-Shafer theory (DST) is an information fusion framework and widely used in many fields. However, the uncertainty measure of a basic probability assignment (BPA) is still an open issue in DST. There are many methods to quantify the uncertainty of BPAs. However, the existing methods have some limitations. In this paper, a new total uncertainty measure from a perspective of maximum entropy requirement is proposed. The proposed method can measure both dissonance and non-specificity in BPA, which includes two components. The first component is consistent with Yager’s dissonance measure. The second component is the non-specificity measurement with different functions. We also prove the desirable properties of the proposed method. Besides, numerical examples and applications are provided to illustrate the effectiveness of the proposed total uncertainty measure.

scholarly journals Multiscale Probability Transformation of Basic Probability Assignment

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Meizhu Li ◽  
Xi Lu ◽  
Qi Zhang ◽  
Yong Deng
Keyword(s):  
Decision Making ◽  
Probability Function ◽  
Evidence Theory ◽  
Belief Function ◽  
Probability Assignment ◽  
Basic Probability Assignment ◽  
Probability Transformation ◽  
Basic Probability ◽  
Open Issue ◽  
Belief Model

Decision making is still an open issue in the application of Dempster-Shafer evidence theory. A lot of works have been presented for it. In the transferable belief model (TBM), pignistic probabilities based on the basic probability assignments are used for decision making. 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 transformation. In the multiscale probability function, a factorqbased on the Tsallis entropy is used to make the multiscale probabilities diversified. An example showing that the multiscale probability transformation is more reasonable in the decision making is given.

scholarly journals A New Belief Entropy to Measure Uncertainty of Basic Probability Assignments Based on Belief Function and Plausibility Function

Entropy ◽  
2018 ◽  
Vol 20 (11) ◽  
pp. 842 ◽  
Author(s):  
Lipeng Pan ◽  
Yong Deng
Keyword(s):  
Measurement Uncertainty ◽  
Belief Function ◽  
Probability Interval ◽  
Numerical Examples ◽  
Main Work ◽  
Lower And Upper Probabilities ◽  
Basic Probability ◽  
Open Issue ◽  
Belief Entropy ◽  
Deng Entropy

How to measure the uncertainty of the basic probability assignment (BPA) function is an open issue in Dempster–Shafer (D–S) theory. The main work of this paper is to propose a new belief entropy, which is mainly used to measure the uncertainty of BPA. The proposed belief entropy is based on Deng entropy and probability interval consisting of lower and upper probabilities. In addition, under certain conditions, it can be transformed into Shannon entropy. Numerical examples are used to illustrate the efficiency of the new belief entropy in measurement uncertainty.

scholarly journals A novel method to determine basic probability assignment in Dempster–Shafer theory and its application in multi-sensor information fusion

2019 ◽  
Vol 15 (7) ◽  
pp. 155014771986587 ◽  
Author(s):  
Liguo Fei ◽  
Jun Xia ◽  
Yuqiang Feng ◽  
Luning Liu
Keyword(s):  
Information Fusion ◽  
Generation Model ◽  
Processing Unit ◽  
K Nearest Neighbor ◽  
Probability Assignment ◽  
Basic Probability Assignment ◽  
Dempster Shafer Theory ◽  
Basic Probability ◽  
Sensor Information ◽  
Shafer Theory

Multi-sensor information fusion occurs in a vast variety of applications, including medical diagnosis, automatic drive, speech recognition, and so on. Often these problems can be modeled by Dempster–Shafer theory. In Dempster–Shafer theory, the most primary processing unit is the basic probability assignment, which is a description of objective information in the real world. How to make this description more effective is a vital but open issue. A novel basic probability assignment generation model is proposed in this article whose objective is to provide perspective with respect to how basic probability assignment can be determined based on learning algorithms. First, the basic probability assignment generation model is constructed based on clustering idea using K-means method, which is employed to determine basic probability assignment with the proposed basic probability assignment generation method. Moreover, the proposed basic probability assignment generation method is extended by K–nearest neighbor (K-NN) algorithm. The detailed implementation of the proposed method is demonstrated by several numerical examples. As an extension, a classifier called KKC is constructed according to the developed approach, and its classification effect is compared with several famous classification algorithms. Experiments manifest desirable results with regard to classification accuracy, which illustrates the applicability of the proposed method to determine basic probability assignment.

scholarly journals A Novel Conflict Management Method Based on Uncertainty of Evidence and Reinforcement Learning for Multi-Sensor Information Fusion

Entropy ◽  
2021 ◽  
Vol 23 (9) ◽  
pp. 1222
Author(s):  
Fanghui Huang ◽  
Yu Zhang ◽  
Ziqing Wang ◽  
Xinyang Deng
Keyword(s):  
Reinforcement Learning ◽  
Information Fusion ◽  
Information Quality ◽  
Uncertain Information ◽  
Dempster Shafer Theory ◽  
Conflicting Evidence ◽  
Basic Probability ◽  
Sensor Information ◽  
Shafer Theory ◽  
Deng Entropy

Dempster–Shafer theory (DST), which is widely used in information fusion, can process uncertain information without prior information; however, when the evidence to combine is highly conflicting, it may lead to counter-intuitive results. Moreover, the existing methods are not strong enough to process real-time and online conflicting evidence. In order to solve the above problems, a novel information fusion method is proposed in this paper. The proposed method combines the uncertainty of evidence and reinforcement learning (RL). Specifically, we consider two uncertainty degrees: the uncertainty of the original basic probability assignment (BPA) and the uncertainty of its negation. Then, Deng entropy is used to measure the uncertainty of BPAs. Two uncertainty degrees are considered as the condition of measuring information quality. Then, the adaptive conflict processing is performed by RL and the combination two uncertainty degrees. The next step is to compute Dempster’s combination rule (DCR) to achieve multi-sensor information fusion. Finally, a decision scheme based on correlation coefficient is used to make the decision. The proposed method not only realizes adaptive conflict evidence management, but also improves the accuracy of multi-sensor information fusion and reduces information loss. Numerical examples verify the effectiveness of the proposed method.

scholarly journals The improvement of uncertainty measurements accuracy in sensor networks based on fuzzy dempster-shafer theory

2020 ◽  
Vol 6 (2) ◽  
pp. 149
Author(s):  
Ehsan Azimirad ◽  
Seyyed Reza Movahhed Ghodsinya
Keyword(s):  
Sensor Networks ◽  
Threat Assessment ◽  
Defense System ◽  
Computational Accuracy ◽  
Total Uncertainty ◽  
Air Defense ◽  
Fuzzy Membership Functions ◽  
Dempster Shafer Theory ◽  
Basic Probability ◽  
Shafer Theory

Threat Assessment is one of the most important components in combat management systems. However, uncertainty is one of the problems that occur in the input data of these systems that have been provided using several sensors in sensor networks. In literature, there are some theories that state and model uncertainty in the information. One of the new methods is the Fuzzy Dempster-Shafer Theory. In this paper, a model-based uncertainty is presented in the air defense system based on the Fuzzy Dempster-Shafer Theory to measure uncertainty and its accuracy. This model uses the two concepts naming of the Fuzzy Sets Theory, and the Dempster-Shafer Theory. The input parameters to sensors are fuzzy membership functions, and the basic probability assignment values are earned from the Dempster-Shafer Theory. Therefore, in this paper, the combination of two methods has been used to calculate uncertainty in the air defense system. By using these methods and the output of the Dempster-Shafer theory are calculated and presented the uncertainty diagrams. The advantage of the combination of two theories is the better modeling of uncertainties. This makes that the output of the air defense system is more reliable and accurate. In this method, the air defense system’s total uncertainty is measured using the best uncertainty measure based on the Fuzzy Dempster-Shafer Theory. The simulation results show that this new method has increased the accuracy to 97% that is more computational toward other theories. This matter significantly increases the computational accuracy of the air defense system in targets threat assessment.

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