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 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 Multisensor Data Fusion in Testability Evaluation of Equipment

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Peng Di ◽  
Xuan Wang ◽  
Tong Chen ◽  
Bin Hu
Keyword(s):  
Data Fusion ◽  
Test Data ◽  
Evaluation Method ◽  
Evidence Theory ◽  
Uncertain Information ◽  
Fusion Method ◽  
Practical Applications ◽  
Multisensor Data Fusion ◽  
Basic Probability ◽  
Multisensor Data

The multisensor data fusion method has been extensively utilized in many practical applications involving testability evaluation. Due to the flexibility and effectiveness of Dempster–Shafer evidence theory in modeling and processing uncertain information, this theory has been widely used in various fields of multisensor data fusion method. However, it may lead to wrong results when fusing conflicting multisensor data. In order to deal with this problem, a testability evaluation method of equipment based on multisensor data fusion method is proposed. First, a novel multisensor data fusion method, based on the improvement of Dempster–Shafer evidence theory via the Lance distance and the belief entropy, is proposed. Next, based on the analysis of testability multisensor data, such as testability virtual test data, testability test data of replaceable unit, and testability growth test data, the corresponding prior distribution conversion schemes of testability multisensor data are formulated according to their different characteristics. Finally, the testability evaluation method of equipment based on the multisensor data fusion method is proposed. The result of experiment illustrated that the proposed method is feasible and effective in handling the conflicting evidence; besides, the accuracy of fusion of the proposed method is higher and the result of evaluation is more reliable than other testability evaluation methods, which shows that the basic probability assignment of the true target is 94.71%.

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 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 Health Monitoring and Diagnosis of Equipment Based on Multi-sensor Fusion

2018 ◽  
Vol 14 (04) ◽  
pp. 4
Author(s):  
Xuemei Yao ◽  
Shaobo Li ◽  
Yong Yao ◽  
Xiaoting Xie
Keyword(s):  
Evidence Theory ◽  
Sensor Data ◽  
Uncertain Information ◽  
Fusion Algorithm ◽  
Monitoring And Diagnosis ◽  
Multi Sensor Data Fusion ◽  
Basic Probability ◽  
Optimal Fusion ◽  
Single Sensor ◽  
Mechanical Devices

As the information measured by a single sensor cannot reflect the real situation of mechanical devices completely, a multi-sensor data fusion based on evidence theory is introduced. Evidence theory has the advantage of dealing with uncertain information. However, it produces unreasonable conclusions when the evidence conflicts. An improved fusion method is proposed to solve this problem. Basic probability assignment of evidence is corrected according to evidence and sensor weights, and an optimal fusion algorithm is selected by comparing an introduced threshold and a conflict factor. The effectiveness and practicability of the algorithm are tested by simulating the monitoring and diagnosis of rolling bearings. The result shows that the method has better robustness.

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.

A cosine similarity measure for multi-criteria group decision making under neutrosophic soft environment

2020 ◽  
Vol 39 (5) ◽  
pp. 7863-7880
Author(s):  
Yuanxiang Dong ◽  
Xiaoting Cheng ◽  
Weijie Chen ◽  
Hongbo Shi ◽  
Ke Gong
Keyword(s):  
Decision Making ◽  
Similarity Measure ◽  
Group Decision Making ◽  
Group Decision ◽  
Evidence Theory ◽  
Cosine Similarity ◽  
Uncertain Information ◽  
Soft Sets ◽  
Cosine Similarity Measure ◽  
Credibility Degree

In actual life, uncertain and inconsistent information exists widely. How to deal with the information so that it can be better applied is a problem that has to be solved. Neutrosophic soft sets can process uncertain and inconsistent information. Also, Dempster-Shafer evidence theory has the advantage of dealing with uncertain information, and it can synthesize uncertain information and deal with subjective judgments effectively. Therefore, this paper creatively combines the Dempster-Shafer evidence theory with the neutrosophic soft sets, and proposes a cosine similarity measure for multi-criteria group decision making. Different from the previous studies, the proposed similarity measure is utilized to measure the similarity between two objects in the structure of neutrosophic soft set, rather than two neutrosophic soft sets. We also propose the objective degree and credibility degree which reflect the decision makers’ subjective preference based on the similarity measure. Then parameter weights are calculated by the objective degree. Additionally, based on credibility degree and parameter weights, we propose the modified score function, modified accuracy function, and modified certainty function, which can be employed to obtain partial order relation and make decisions. Later, we construct an aggregation algorithm for multi-criteria group decision making based on Dempster’s rule of combination and apply the algorithm to a case of medical diagnosis. Finally, by testing and comparing the algorithm, the results demonstrate that the proposed algorithm can solve the multi-criteria group decision making problems effectively.

scholarly journals A new divergence measure of interval-valued pythagorean fuzzy sets and its application

2021 ◽  
Vol 5 (2) ◽  
pp. 9-24
Author(s):  
Arthi N ◽  
Mohana K
Keyword(s):  
Fuzzy Sets ◽  
Distance Measure ◽  
Evidence Theory ◽  
Belief Function ◽  
Divergence Measure ◽  
Pythagorean Fuzzy Sets ◽  
Practical Applications ◽  
Basic Probability ◽  
Jensen Shannon Divergence ◽  
Interval Valued

As the extension of the Fuzzy sets (FSs) theory, the Interval-valued Pythagorean Fuzzy Sets (IVPFS) was introduced which play an important role in handling the uncertainty. The Pythagorean fuzzy sets (PFSs) proposed by Yager in 2013 can deal with more uncertain situations than intuitionistic fuzzy sets because of its larger range of describing the membership grades. How to measure the distance of Interval-valued Pythagorean fuzzy sets is still an open issue. Jensen–Shannon divergence is a useful distance measure in the probability distribution space. In order to efficiently deal with uncertainty in practical applications, this paper proposes a new divergence measure of Interval-valued Pythagorean fuzzy sets,which is based on the belief function in Dempster–Shafer evidence theory, and is called IVPFSDM distance. It describes the Interval-Valued Pythagorean fuzzy sets in the form of basic probability assignments (BPAs) and calculates the divergence of BPAs to get the divergence of IVPFSs, which is the step in establishing a link between the IVPFSs and BPAs. Since the proposed method combines the characters of belief function and divergence, it has a more powerful resolution than other existing methods.

scholarly journals An improved method to determine basic probability assignment with interval number and its application in classification

2019 ◽  
Vol 15 (1) ◽  
pp. 155014771882052 ◽  
Author(s):  
Bowen Qin ◽  
Fuyuan Xiao
Keyword(s):  
Evidence Theory ◽  
Classification Problem ◽  
Interval Number ◽  
Training Data ◽  
Cluster Method ◽  
Uncertain Information ◽  
Data Set ◽  
Probability Assignment ◽  
Basic Probability Assignment ◽  
Basic Probability

Due to its efficiency to handle uncertain information, Dempster–Shafer evidence theory has become the most important tool in many information fusion systems. However, how to determine basic probability assignment, which is the first step in evidence theory, is still an open issue. In this article, a new method integrating interval number theory and k-means++ cluster method is proposed to determine basic probability assignment. At first, k-means++ clustering method is used to calculate lower and upper bound values of interval number with training data. Then, the differentiation degree based on distance and similarity of interval number between the test sample and constructed models are defined to generate basic probability assignment. Finally, Dempster’s combination rule is used to combine multiple basic probability assignments to get the final basic probability assignment. The experiments on Iris data set that is widely used in classification problem illustrated that the proposed method is effective in determining basic probability assignment and classification problem, and the proposed method shows more accurate results in which the classification accuracy reaches 96.7%.

scholarly journals A Novel Uncertainty Management Approach for Air Combat Situation Assessment Based on Improved Belief Entropy

Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 495 ◽  
Author(s):  
Ying Zhou ◽  
Yongchuan Tang ◽  
Xiaozhe Zhao
Keyword(s):  
Information Fusion ◽  
Evidence Theory ◽  
Uncertainty Management ◽  
Management Approach ◽  
Uncertain Information ◽  
Improved Method ◽  
Situation Assessment ◽  
Air Combat ◽  
Belief Entropy ◽  
Dempster’S Rule Of Combination

Uncertain information exists in each procedure of an air combat situation assessment. To address this issue, this paper proposes an improved method to address the uncertain information fusion of air combat situation assessment in the Dempster–Shafer evidence theory (DST) framework. A better fusion result regarding the prediction of military intention can be helpful for decision-making in an air combat situation. To obtain a more accurate fusion result of situation assessment, an improved belief entropy (IBE) is applied to preprocess the uncertainty of situation assessment information. Data fusion of assessment information after preprocessing will be based on the classical Dempster’s rule of combination. The illustrative example result validates the rationality and the effectiveness of the proposed method.

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