A vector and geometry interpretation of basic probability assignment in Dempster‐Shafer theory

2020 ◽  
Vol 35 (6) ◽  
pp. 944-962 ◽  
Author(s):  
Ziyuan Luo ◽  
Yong Deng
Keyword(s):  
Probability Assignment ◽  
Basic Probability Assignment ◽  
Dempster Shafer Theory ◽  
Basic Probability ◽  
Shafer Theory

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 novel method to determine basic probability assignment in Dempster–Shafer theory and its application in multi-sensor information fusion

2019 ◽  
Vol 15 (7) ◽  
pp. 155014771986587 ◽  
Author(s):  
Liguo Fei ◽  
Jun Xia ◽  
Yuqiang Feng ◽  
Luning Liu
Keyword(s):  
Information Fusion ◽  
Generation Model ◽  
Processing Unit ◽  
K Nearest Neighbor ◽  
Probability Assignment ◽  
Basic Probability Assignment ◽  
Dempster Shafer Theory ◽  
Basic Probability ◽  
Sensor Information ◽  
Shafer Theory

Multi-sensor information fusion occurs in a vast variety of applications, including medical diagnosis, automatic drive, speech recognition, and so on. Often these problems can be modeled by Dempster–Shafer theory. In Dempster–Shafer theory, the most primary processing unit is the basic probability assignment, which is a description of objective information in the real world. How to make this description more effective is a vital but open issue. A novel basic probability assignment generation model is proposed in this article whose objective is to provide perspective with respect to how basic probability assignment can be determined based on learning algorithms. First, the basic probability assignment generation model is constructed based on clustering idea using K-means method, which is employed to determine basic probability assignment with the proposed basic probability assignment generation method. Moreover, the proposed basic probability assignment generation method is extended by K–nearest neighbor (K-NN) algorithm. The detailed implementation of the proposed method is demonstrated by several numerical examples. As an extension, a classifier called KKC is constructed according to the developed approach, and its classification effect is compared with several famous classification algorithms. Experiments manifest desirable results with regard to classification accuracy, which illustrates the applicability of the proposed method to determine basic probability assignment.

scholarly journals Combining Fuzzy Logic and Dempster-Shafer Theory

2015 ◽  
Vol 16 (3) ◽  
pp. 583
Author(s):  
Andino Maseleno ◽  
Md. Mahmud Hasan ◽  
Norjaidi Tuah
Keyword(s):  
Fuzzy Logic ◽  
Membership Function ◽  
Mathematical Theory ◽  
Fuzzy Membership ◽  
Fuzzy Membership Function ◽  
Basic Probability Assignment ◽  
Dempster Shafer Theory ◽  
Basic Probability ◽  
Shafer Theory ◽  
Theory Of Evidence

This research aims to combine the mathematical theory of evidence with the rule based logics to refine the predictable output. Integrating Fuzzy Logic and Dempster-Shafer theory by calculating the similarity between Fuzzy membership function. The novelty aspect of this work is that basic probability assignment is proposed based on the similarity measure between membership function. The similarity between Fuzzy membership function is calculated to get a basic probability assignment. The Dempster-Shafer mathematical theory of evidence has attracted considerable attention as a promising method of dealing with some of the basic problems arising in combination of evidence and data fusion. Dempster-Shafer theory provides the ability to deal with ignorance and missing information. The foundation of Fuzzy logic is natural language which can help to make full use of expert information.

scholarly journals An improved conflicting-evidence combination method based on the redistribution of the basic probability assignment

2021 ◽  
Author(s):  
Zezheng Yan ◽  
Hanping Zhao ◽  
Xiaowen Mei
Keyword(s):  
Evidence Theory ◽  
Combination Method ◽  
Probability Assignment ◽  
Basic Probability Assignment ◽  
Combination Methods ◽  
Conflicting Evidence ◽  
Basic Probability ◽  
The Right ◽  
Conflict Intensity ◽  
Dempster’S Rule Of Combination

AbstractDempster–Shafer evidence theory is widely applied in various fields related to information fusion. However, the results are counterintuitive when highly conflicting evidence is fused with Dempster’s rule of combination. Many improved combination methods have been developed to address conflicting evidence. Nevertheless, all of these approaches have inherent flaws. To solve the existing counterintuitive problem more effectively and less conservatively, an improved combination method for conflicting evidence based on the redistribution of the basic probability assignment is proposed. First, the conflict intensity and the unreliability of the evidence are calculated based on the consistency degree, conflict degree and similarity coefficient among the evidence. Second, the redistribution equation of the basic probability assignment is constructed based on the unreliability and conflict intensity, which realizes the redistribution of the basic probability assignment. Third, to avoid excessive redistribution of the basic probability assignment, the precision degree of the evidence obtained by information entropy is used as the correction factor to modify the basic probability assignment for the second time. Finally, Dempster’s rule of combination is used to fuse the modified basic probability assignment. Several different types of examples and actual data sets are given to illustrate the effectiveness and potential of the proposed method. Furthermore, the comparative analysis reveals the proposed method to be better at obtaining the right results than other related methods.

scholarly journals Conflict Data Fusion in a Multi-Agent System Premised on the Base Basic Probability Assignment and Evidence Distance

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 820
Author(s):  
Jingyu Liu ◽  
Yongchuan Tang
Keyword(s):  
Data Fusion ◽  
Evidence Theory ◽  
Multi Agent System ◽  
Agent System ◽  
Combination Rules ◽  
Probability Assignment ◽  
Basic Probability Assignment ◽  
Reasonable Evidence ◽  
Basic Probability ◽  
Multi Agent

The multi-agent information fusion (MAIF) system can alleviate the limitations of a single expert system in dealing with complex situations, as it allows multiple agents to cooperate in order to solve problems in complex environments. Dempster–Shafer (D-S) evidence theory has important applications in multi-source data fusion, pattern recognition, and other fields. However, the traditional Dempster combination rules may produce counterintuitive results when dealing with highly conflicting data. A conflict data fusion method in a multi-agent system based on the base basic probability assignment (bBPA) and evidence distance is proposed in this paper. Firstly, the new bBPA and reconstructed BPA are used to construct the initial belief degree of each agent. Then, the information volume of each evidence group is obtained by calculating the evidence distance so as to modify the reliability and obtain more reasonable evidence. Lastly, the final evidence is fused with the Dempster combination rule to obtain the result. Numerical examples show the effectiveness and availability of the proposed method, which improves the accuracy of the identification process of the MAIF system.

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