scholarly journals An Uncertainty Measure for Interval-valued Evidences

2017 ◽  
Vol 12 (5) ◽  
pp. 631 ◽  
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. 

scholarly journals The Pseudo-Pascal Triangle of Maximum Deng Entropy

2020 ◽  
Vol 15 (1) ◽  
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.

scholarly journals Probability Transform Based on the Ordered Weighted Averaging and Entropy Difference

2020 ◽  
Vol 15 (4) ◽  
Author(s):  
Lipeng Pan ◽  
Yong Deng
Keyword(s):  
Probability Distribution ◽  
Evidence Theory ◽  
Mass Function ◽  
New Method ◽  
Weighted Averaging ◽  
Minimum Entropy ◽  
Transform Method ◽  
Numerical Examples ◽  
Ordered Weighted Averaging ◽  
Open Issue

Dempster-Shafer evidence theory can handle imprecise and unknown information, which has attracted many people. In most cases, the mass function can be translated into the probability, which is useful to expand the applications of the D-S evidence theory. However, how to reasonably transfer the mass function to the probability distribution is still an open issue. Hence, the paper proposed a new probability transform method based on the ordered weighted averaging and entropy difference. The new method calculates weights by ordered weighted averaging, and adds entropy difference as one of the measurement indicators. Then achieved the transformation of the minimum entropy difference by adjusting the parameter r of the weight function. Finally, some numerical examples are given to prove that new method is more reasonable and effective.

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 An Improved Total Uncertainty Measure in the Evidence Theory and Its Application in Decision Making

Entropy ◽  
2020 ◽  
Vol 22 (4) ◽  
pp. 487 ◽  
Author(s):  
Miao Qin ◽  
Yongchuan Tang ◽  
Junhao Wen
Keyword(s):  
Decision Making ◽  
Evidence Theory ◽  
Uncertain Information ◽  
Uncertainty Measure ◽  
Total Uncertainty ◽  
Practical Applications ◽  
Basic Probability ◽  
Belief Entropy ◽  
Element Number ◽  
Theory Framework

Dempster–Shafer evidence theory (DS theory) has some superiorities in uncertain information processing for a large variety of applications. However, the problem of how to quantify the uncertainty of basic probability assignment (BPA) in DS theory framework remain unresolved. The goal of this paper is to define a new belief entropy for measuring uncertainty of BPA with desirable properties. The new entropy can be helpful for uncertainty management in practical applications such as decision making. The proposed uncertainty measure has two components. The first component is an improved version of Dubois–Prade entropy, which aims to capture the non-specificity portion of uncertainty with a consideration of the element number in frame of discernment (FOD). The second component is adopted from Nguyen entropy, which captures conflict in BPA. We prove that the proposed entropy satisfies some desired properties proposed in the literature. In addition, the proposed entropy can be reduced to Shannon entropy if the BPA is a probability distribution. Numerical examples are presented to show the efficiency and superiority of the proposed measure as well as an application in decision making.

scholarly journals Complex Entropy and Its Application in Decision-Making for Medical Diagnosis

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Fuyuan Xiao ◽  
Xiao-Guang Yue
Keyword(s):  
Decision Making ◽  
Information Fusion ◽  
Medical Diagnosis ◽  
Uncertain Information ◽  
Fusion Algorithm ◽  
Numerical Examples ◽  
Open Issue ◽  
Complex Planes ◽  
Complex Valued ◽  
Complex Entropy

In decision-making systems, how to measure uncertain information remains an open issue, especially for information processing modeled on complex planes. In this paper, a new complex entropy is proposed to measure the uncertainty of a complex-valued distribution (CvD). The proposed complex entropy is a generalization of Gini entropy that has a powerful capability to measure uncertainty. In particular, when a CvD reduces to a probability distribution, the complex entropy will degrade into Gini entropy. In addition, the properties of complex entropy, including the nonnegativity, maximum and minimum entropies, and boundedness, are analyzed and discussed. Several numerical examples illuminate the superiority of the newly defined complex entropy. Based on the newly defined complex entropy, a multisource information fusion algorithm for decision-making is developed. Finally, we apply the decision-making algorithm in a medical diagnosis problem to validate its practicability.

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

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.

scholarly journals An Improved Belief Entropy and Its Application in Decision-Making

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-15 ◽  
Author(s):  
Deyun Zhou ◽  
Yongchuan Tang ◽  
Wen Jiang
Keyword(s):  
Decision Making ◽  
Mass Function ◽  
The Body ◽  
Uncertain Information ◽  
Uncertainty Measure ◽  
Numerical Examples ◽  
Fusion Applications ◽  
Belief Entropy ◽  
The Difference ◽  
Available Information

Uncertainty measure in data fusion applications is a hot topic; quite a few methods have been proposed to measure the degree of uncertainty in Dempster-Shafer framework. However, the existing methods pay little attention to the scale of the frame of discernment (FOD), which means a loss of information. Due to this reason, the existing methods cannot measure the difference of uncertain degree among different FODs. In this paper, an improved belief entropy is proposed in Dempster-Shafer framework. The proposed belief entropy takes into consideration more available information in the body of evidence (BOE), including the uncertain information modeled by the mass function, the cardinality of the proposition, and the scale of the FOD. The improved belief entropy is a new method for uncertainty measure in Dempster-Shafer framework. Based on the new belief entropy, a decision-making approach is designed. The validity of the new belief entropy is verified according to some numerical examples and the proposed decision-making approach.

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 New Belief Entropy Based on Deng Entropy

Entropy ◽  
2019 ◽  
Vol 21 (10) ◽  
pp. 987 ◽  
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.

Sign in / Sign up

Export Citation Format

Share Document