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 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 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 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 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 A Method for Recognizing Fatigue Driving Based on Dempster-Shafer Theory and Fuzzy Neural Network

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
WenBo Zhu ◽  
Huicheng Yang ◽  
Yi Jin ◽  
Bingyou Liu
Keyword(s):  
Neural Network ◽  
Fuzzy Neural Network ◽  
Multiple Features ◽  
Dempster Shafer Theory ◽  
Recognition Result ◽  
Fuzzy Neural ◽  
Basic Probability ◽  
Definition Of ◽  
Shafer Theory ◽  
Fatigue Driving

This study proposes a method based on Dempster-Shafer theory (DST) and fuzzy neural network (FNN) to improve the reliability of recognizing fatigue driving. This method measures driving states using multifeature fusion. First, FNN is introduced to obtain the basic probability assignment (BPA) of each piece of evidence given the lack of a general solution to the definition of BPA function. Second, a modified algorithm that revises conflict evidence is proposed to reduce unreasonable fusion results when unreliable information exists. Finally, the recognition result is given according to the combination of revised evidence based on Dempster’s rule. Experiment results demonstrate that the recognition method proposed in this paper can obtain reasonable results with the combination of information given by multiple features. The proposed method can also effectively and accurately describe driving states.

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.

scholarly journals Integration of Artificial Intelligence into Dempster Shafer Theory: A Review on Decision Making in Condition Monitoring

2015 ◽  
Vol 773-774 ◽  
pp. 154-157 ◽  
Author(s):  
Muhammad Firdaus Rosli ◽  
Lim Meng Hee ◽  
M. Salman Leong
Keyword(s):  
Artificial Intelligence ◽  
Decision Making ◽  
Condition Monitoring ◽  
Support Vector ◽  
Dempster Shafer Theory ◽  
Basic Probability ◽  
Human Interpretation ◽  
The Individual ◽  
Shafer Theory ◽  
Automated Decision Making

Machines are the heart of most industries. By ensuring the health of machines, one could easily increase the company revenue and eliminates any safety threat related to machinery catastrophic failures. In condition monitoring (CM), questions often arise during decision making time whether the machine is still safe to run or not? Traditional CM approach depends heavily on human interpretation of results whereby decision is made solely based on the individual experience and knowledge about the machines. The advent of artificial intelligence (AI) and automated ways for decision making in CM provides a more objective and unbiased approach for CM industry and has become a topic of interest in the recent years. This paper reviews the techniques used for automated decision making in CM with emphasis given on Dempster-Shafer (D-S) evident theory and other basic probability assignment (BPA) techniques such as support vector machine (SVM) and etc.

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

2020 ◽  
Author(s):  
Hanwen Li ◽  
Rui Cai
Keyword(s):  
Fault Diagnosis ◽  
Information Quality ◽  
Numerical Examples ◽  
Probability Assignment ◽  
Basic Probability Assignment ◽  
Basic Probability ◽  
Open Issue

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

scholarly journals The Impact of Understaffing on Delaying Early-Stage SARS-CoV-2 Outbreak Detection

2020 ◽  
Author(s):  
BOUKARI WADJIDOU ◽  
Ivana Todorovic ◽  
Long Fenjie
Keyword(s):  
Early Stage ◽  
Public Health Care ◽  
Outbreak Detection ◽  
Employment Policy ◽  
Wuhan City ◽  
Dempster Shafer Theory ◽  
Shenzhen City ◽  
Minimum Number ◽  
Shafer Theory ◽  
The Impact

Abstract Background Having a minimum number of workers in medical services is widely regarded as a key component of disease prevention. However, with the delay in confirming cases of SARS-CoV-2, the understaffed medical providers informed late and the virus has rapidly spread nationally. Methods This study, based on the Dempster-Shafer theory method and Evidential Reasoning, assesses the risks posed by understaffing for the SARS-CoV-2 outbreak. Results The findings examine six (6) factor risks and show that the understaffing risk in 2019 was 0.14% in magnitude in Wuhan, compared to 0.27% in Shenzhen. When ranking understaffing risks from low to high, the findings show that they increased from 3.979 to 3.983% and from 3.998 to 4.002% in Wuhan and Shenzhen, respectively. Conclusions We first conclude that from the SARS-CoV-1 to the SARS-CoV-2 outbreak, understaffing risk equally increased at 0.004% in both cities. However, Shenzhen city is at a higher risk than Wuhan city. Second, Shenzhen understaffing delayed SARS-CoV-2 outbreak prevention 0.13% more than Wuhan city. We generally conclude that Shenzhen city could be doubly worse off than Wuhan city if it was the epicenter of the SARS-CoV-2 outbreak. Therefore, public health care training and employment policy must be optimized to complete the lack not only in both cities but also in other cities to prevent future outbreaks.

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