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 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 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 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 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 Engine fault diagnosis based on sensor data fusion considering information quality and evidence theory

2018 ◽  
Vol 10 (11) ◽  
pp. 168781401880918 ◽  
Author(s):  
Hepeng Zhang ◽  
Yong Deng
Keyword(s):  
Fault Diagnosis ◽  
Probability Distribution ◽  
Information Quality ◽  
Evidence Theory ◽  
Sensor Data ◽  
Processing Variable ◽  
Probability Assignment ◽  
Basic Probability Assignment ◽  
The Status ◽  
Basic Probability

Fault diagnosis is a problem processing variable information obtained from different sources in nature. Evidence theory, efficient to deal with information viewed as evidence, is widely used in fault diagnosis. However, a shortcoming of the existing fault diagnosis methods only gets probability distribution rather than the basic probability assignment. A novel method of generating basic probability assignment that takes information quality into account is proposed. The probability distribution is determined by the preliminary matrix and sampling matrix that are constructed by sensor data. And the quality of probability distribution is taken as the discount factor and the rest of belief is assigned to the universal set. Hence, the basic probability assignment is obtained. Then, basic probability assignment can be combined with Dempster and Shafer evidence theory to determine the status of the engine. An application of engine fault is shown to illustrate the practicability of the proposed method. Then by comparing the result of the method which takes information quality into account (the proposed method) and does not do it, the former is better than the latter. Finally, the reliability analysis shows that the proposed method has strong reliability because performance accuracy is 100% when the error rate is less than 10%.

scholarly journals A Method to Determine Generalized Basic Probability Assignment in the Open World

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Wen Jiang ◽  
Jun Zhan ◽  
Deyun Zhou ◽  
Xin Li
Keyword(s):  
Information Fusion ◽  
Evidence Theory ◽  
Triangular Fuzzy Number ◽  
Probability Assignment ◽  
Basic Probability Assignment ◽  
Open World ◽  
Differentiation Degree ◽  
Basic Probability ◽  
Open Issue ◽  
The Given

Dempster-Shafer evidence theory (D-S theory) has been widely used in many information fusion systems since it was proposed by Dempster and extended by Shafer. However, how to determine the basic probability assignment (BPA), which is the main and first step in D-S theory, is still an open issue, especially when the given environment is in an open world, which means the frame of discernment is incomplete. In this paper, a method to determine generalized basic probability assignment in an open world is proposed. Frame of discernment in an open world is established first, and then the triangular fuzzy number models to identify target in the proposed frame of discernment are established. Pessimistic strategy based on the differentiation degree between model and sample is defined to yield the BPAs for known targets. If the sum of all the BPAs of known targets is over one, then they will be normalized and the BPA of unknown target is assigned to0; otherwise the BPA of unknown target is equal to1minus the sum of all the known targets BPAs. IRIS classification examples illustrated the effectiveness of the proposed method.

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

2020 ◽  
Author(s):  
Hanwen Li
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 infor </div><div>mation quality in basic probability assignment accurately is still an open issue. Generalized expression for </div><div>information quality is an effective method to measure information quality in basic probability assignment. </div><div>Nevertheless, the counter-intuitive results may be obtained when statements are of intersection. To address </div><div>this issue, a new expression for information quality of basic probability assignment is proposed in this paper </div><div>considering the frame of discernment and the inflfluence of intersection among statements which can cause </div><div>changes of uncertainty. Numerical examples are illustrated to demonstrate the effectiveness of the proposed </div><div>method. In addition, an application in fault diagnosis is used to show the effectiveness of the proposed </div><div>method. </div>

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