scholarly journals Fractional Deng Entropy and Extropy and Some Applications

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 623
Author(s):  
Mohammad Reza Kazemi ◽  
Saeid Tahmasebi ◽  
Francesco Buono ◽  
Maria Longobardi
Keyword(s):  
Pattern Recognition ◽  
Evidence Theory ◽  
Two Measures ◽  
Deng Entropy

Deng entropy and extropy are two measures useful in the Dempster–Shafer evidence theory (DST) to study uncertainty, following the idea that extropy is the dual concept of entropy. In this paper, we present their fractional versions named fractional Deng entropy and extropy and compare them to other measures in the framework of DST. Here, we study the maximum for both of them and give several examples. Finally, we analyze a problem of classification in pattern recognition in order to highlight the importance of these new measures.

scholarly journals A Dual Measure of Uncertainty: The Deng Extropy

Entropy ◽  
2020 ◽  
Vol 22 (5) ◽  
pp. 582
Author(s):  
Francesco Buono ◽  
Maria Longobardi
Keyword(s):  
Pattern Recognition ◽  
Evidence Theory ◽  
Characterization Result ◽  
Numerical Example ◽  
Measure Of Discrimination ◽  
Measure Of Uncertainty ◽  
Deng Entropy

The extropy has recently been introduced as the dual concept of entropy. Moreover, in the context of the Dempster–Shafer evidence theory, Deng studied a new measure of discrimination, named the Deng entropy. In this paper, we define the Deng extropy and study its relation with Deng entropy, and examples are proposed in order to compare them. The behaviour of Deng extropy is studied under changes of focal elements. A characterization result is given for the maximum Deng extropy and, finally, a numerical example in pattern recognition is discussed in order to highlight the relevance of the new measure.

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 Deng Entropy Weighted Risk Priority Number Model for Failure Mode and Effects Analysis

Entropy ◽  
2020 ◽  
Vol 22 (3) ◽  
pp. 280 ◽  
Author(s):  
Haixia Zheng ◽  
Yongchuan Tang
Keyword(s):  
Risk Factors ◽  
Risk Factor ◽  
Failure Mode ◽  
Evidence Theory ◽  
Relative Weight ◽  
Relative Importance ◽  
Risk Priority Number ◽  
Domain Experts ◽  
Entropy Weighted ◽  
Deng Entropy

Failure mode and effects analysis (FMEA), as a commonly used risk management method, has been extensively applied to the engineering domain. A vital parameter in FMEA is the risk priority number (RPN), which is the product of occurrence (O), severity (S), and detection (D) of a failure mode. To deal with the uncertainty in the assessments given by domain experts, a novel Deng entropy weighted risk priority number (DEWRPN) for FMEA is proposed in the framework of Dempster–Shafer evidence theory (DST). DEWRPN takes into consideration the relative importance in both risk factors and FMEA experts. The uncertain degree of objective assessments coming from experts are measured by the Deng entropy. An expert’s weight is comprised of the three risk factors’ weights obtained independently from expert’s assessments. In DEWRPN, the strategy of assigning weight for each expert is flexible and compatible to the real decision-making situation. The entropy-based relative weight symbolizes the relative importance. In detail, the higher the uncertain degree of a risk factor from an expert is, the lower the weight of the corresponding risk factor will be and vice versa. We utilize Deng entropy to construct the exponential weight of each risk factor as well as an expert’s relative importance on an FMEA item in a state-of-the-art way. A case study is adopted to verify the practicability and effectiveness of the proposed model.

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 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 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 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.

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