Basic probability assignment to probability distribution function based on the Shapley value approach

2021 ◽  
Author(s):  
Chongru Huang ◽  
Xiangjun Mi ◽  
Bingyi Kang
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Shapley Value ◽  
Probability Distribution Function ◽  
Probability Assignment ◽  
Basic Probability Assignment ◽  
The Shapley Value ◽  
Basic Probability

The Method of Probabilistic Nodes Combination in Decision Making and Risk Analysis

2016 ◽  
pp. 32-60
Author(s):  
Dariusz Jacek Jakóbczak
Keyword(s):  
Decision Making ◽  
Distribution Function ◽  
Probability Distribution ◽  
Risk Analysis ◽  
Probability Distribution Function ◽  
Linear Interpolation ◽  
Distribution Functions ◽  
Probability Distribution Functions ◽  
Characteristic Points ◽  
Basic Probability

Proposed method, called Probabilistic Nodes Combination (PNC), is the method of 2D curve interpolation and extrapolation using the set of key points (knots or nodes). Nodes can be treated as characteristic points of data for modeling and analyzing. The model of data can be built by choice of probability distribution function and nodes combination. PNC modeling via nodes combination and parameter ? as probability distribution function enables value anticipation in risk analysis and decision making. Two-dimensional curve is extrapolated and interpolated via nodes combination and different functions as discrete or continuous probability distribution functions: polynomial, sine, cosine, tangent, cotangent, logarithm, exponent, arc sin, arc cos, arc tan, arc cot or power function. Novelty of the paper consists of two generalizations: generalization of previous MHR method with various nodes combinations and generalization of linear interpolation with different (no basic) probability distribution functions and nodes combinations.

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 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 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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