A Comparative Study of Evidence Theories in the Modeling, Analysis, and Design of Engineering Systems

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
S. S. Rao ◽  
K. K. Annamdas
Keyword(s):  
Evidence Theory ◽  
Engineering Systems ◽  
Combination Rule ◽  
Multiple Sources ◽  
Combination Rules ◽  
Analysis And Design ◽  
Modeling Analysis ◽  
Evidence Combination ◽  
Different Types ◽  
Shafer Theory

The application of different types of evidence theories in the modeling, analysis and design of engineering systems is explored. In most studies dealing with evidence theory, the Dempster–Shafer theory (DST) has been used as the framework not only for the characterization and representation of uncertainty but also for combining evidence. The versatility of the theory is the motivation for selecting DST to represent and combine different types of evidence obtained from multiple sources. In this work, five evidence combination rules, namely, Dempster–Shafer, Yager, Inagaki, Zhang, and Murrphy combination rules, are considered. The limitations and sensitivity of the DST rule in the case of conflicting evidence are illustrated with examples. The application of all the five evidence combination rules for the modeling, analysis and design of engineering systems is illustrated using a power plant failure example and a welded beam problem. The aim is to understand the basic characteristics of each rule and develop preliminary guidelines or criteria for selecting an evidence combination rule that is most appropriate based on the nature and characteristics of the available evidence. Since this work is the first one aimed at developing the guidelines or criteria for selecting the most suitable evidence combination rule, further studies are required to refine the guidelines and criteria developed in this work.

scholarly journals Analysis of “mixing” combination rules and Smet’s combination rule

2019 ◽  
pp. 4-8
Author(s):  
Sofiia Alpert
Keyword(s):  
Satellite Images ◽  
Probability Distributions ◽  
Evidence Theory ◽  
Combination Rule ◽  
Multiple Sources ◽  
Combination Rules ◽  
Spectral Bands ◽  
Basic Probability ◽  
Shafer Theory ◽  
Theory Of Evidence

The process of solution of different practical and ecological problems, using hyperspectral satellite images usually includes a procedure of classification. Classification is one of the most difficult and important procedures. Some image classification methods were considered and analyzed in this work. These methods are based on the theory of evidence. Evidence theory can simulate uncertainty and process imprecise and incomplete information. It were considered such combination rules in this paper: “mixing” combination rule (or averaging), convolutive x-averaging (or c-averaging) and Smet’s combination rule. It was shown, that these methods can process the data from multiple sources or spectral bands, that provide different assessments for the same hypotheses. It was noted, that the purpose of aggregation of information is to simplify data, whether the data is coming from multiple sources or different spectral bands. It was shown, that Smet’s rule is unnormalized version of Dempster rule, that applied in Smet’s Transferable Belief Model. It also processes imprecise and incomplete data. Smet’s combination rule entails a slightly different formulation of Dempster-Shafer theory. Mixing (or averaging) rule was considered in this paper too. It is the averaging operation that is used for probability distributions. This rule uses basic probability assignments from different sources (spectral bands) and weighs assigned according to the reliability of the sources. Convolutive x-averaging (or c-averaging) rule was considered in this paper too. This combination rule is a generalization of the average for scalar numbers. This rule is commutative and not associative. It also was noted, that convolutive x-averaging (c-averaging) rule can include any number of basic probability assignments. It were also considered examples, where these proposed combination rules were used. Mixing, convolutive x-averaging (c-averaging) rule and Smet’s combination rule can be applied for analysis of hyperspectral satellite images, in remote searching for minerals and oil, solving different environmental and thematic problems.

Modified Interval Dempster-Shafer Theory and its Application for Target Identification

2012 ◽  
Vol 190-191 ◽  
pp. 1153-1156
Author(s):  
Hai Jun Liu ◽  
Hong Shan Nie ◽  
Hong Qi Yu ◽  
Hong Hu Hua ◽  
Zheng Liu
Keyword(s):  
Measurement Uncertainty ◽  
Target Identification ◽  
Identification Algorithm ◽  
Combination Rules ◽  
Feature Measurement ◽  
Dempster Shafer Theory ◽  
Evidence Combination ◽  
Shafer Theory

To deal with the problem of target identification caused by the achieved reliability of multi sensors and the feature measurement uncertainty of the target, this paper proposes a new identification algorithm based on Modified Interval Dempster-Shafer Theory (MIDST), which models sensor’s reliability as scalar value and identification outputs of each sensor as interval values, and then combines the actual interval outputs through interval evidence combination rules. At last, one simulation is presented to demonstrate the identification capability of the MIDST algorithm.

scholarly journals A Self-Adaptive Combination Method in Evidence Theory Based on the Power Pignistic Probability Distance

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 526
Author(s):  
Jian Wang ◽  
Jing-wei Zhu ◽  
Yafei Song
Keyword(s):  
Evidence Theory ◽  
Weighted Average ◽  
Combination Method ◽  
Multiple Sources ◽  
Adaptive Combination ◽  
Conflicting Evidence ◽  
Different Types ◽  
Fusion Methods ◽  
Temporal And Spatial ◽  
Probability Distance

Existing methods employed for combining temporal and spatial evidence derived from multiple sources into a single coherent description of objects and their environments lack versatility in various applications such as multi-sensor target recognition. This is addressed in the present study by proposing an adaptive evidence fusion method based on the power pignistic probability distance. This method classifies evidence sets into non-conflicting and conflicting evidence sets based on the maximum power pignistic probability distance obtained between evidence pairs in the evidence set. Non-conflicting evidence sets are fused using Dempster’s rule, while conflicting evidence sets are fused using a weighted average combination method based on the power pignistic probability distance. The superior evidence fusion performance of the proposed method is demonstrated by comparisons with the performances of seven other fusion methods based on numerical examples with four different evidence conflict scenarios. The results show that the method proposed in this paper not only can properly fuse different types of evidence, but also provides an excellent focus on the components of evidence sets with high confidence, which is conducive to timely and accurate decisions.

Predicting the remaining useful life in the presence of the regime-switching behaviour of health index using distance-based evidence theory

2021 ◽  
Vol 63 (1) ◽  
pp. 37-46
Author(s):  
S Ramezani ◽  
A Moini ◽  
M Riahi ◽  
A C Marquez
Keyword(s):  
Condition Monitoring ◽  
Regime Switching ◽  
Evidence Theory ◽  
Remaining Useful Life ◽  
Monitoring Data ◽  
Sources Of Information ◽  
Combination Rules ◽  
Useful Life ◽  
Shafer Theory ◽  
Degradation State

With the development of new maintenance techniques based on condition monitoring, diagnostic and prognostic methods are also being extended. In the process of estimating the remaining useful life (RUL) using the data-driven approach, it is difficult to determine the degradation state of the equipment with several sources of information and to predict the remaining useful life with non-smooth data that have sudden changes inherent in the monitoring data. In this paper, a procedure is presented to address these two issues in which the degradation state of the equipment is determined in the presence of several information sources using a combination of the fuzzy c-means clustering and the combination rules of the Dempster-Shafer theory, and the prediction of the data for the estimation of the remaining useful life is carried out using an autoregressive Markov regime-switching (ARMRS) model that is capable of dealing with sudden changes in condition monitoring data. To evaluate the proposed model, the bearing dataset of the FEMTO-ST Institute is used. The experimental results show the high competitiveness of the proposed procedure compared to similar methods.

scholarly journals A novel weighted evidence combination rule based on improved entropy function with a diagnosis application

2019 ◽  
Vol 15 (1) ◽  
pp. 155014771882399 ◽  
Author(s):  
Lei Chen ◽  
Ling Diao ◽  
Jun Sang
Keyword(s):  
Medical Diagnosis ◽  
Real Life ◽  
Entropy Function ◽  
New Method ◽  
Combination Rule ◽  
Initial Weight ◽  
Rule Based ◽  
Dempster Shafer Theory ◽  
Evidence Combination ◽  
Shafer Theory

Managing conflict in Dempster–Shafer theory is a popular topic. In this article, we propose a novel weighted evidence combination rule based on improved entropy function. This newly proposed approach can be mainly divided into two steps. First, the initial weight will be determined on the basis of the distance of evidence. Then, this initial weight will be modified using improved entropy function. This new method converges faster when handling high conflicting evidences and greatly reduces uncertainty of decisions, which can be demonstrated by a numerical example where the belief degree is raised up to 0.9939 when five evidences are in conflict, an application in faulty diagnosis where belief degree is increased hugely from 0.8899 to 0.9416 when compared with our previous works, and a real-life medical diagnosis application where the uncertainty of decision is reduced to nearly 0 and the belief degree is raised up to 0.9989.

scholarly journals Trust evaluation based on evidence theory in online social networks

2018 ◽  
Vol 14 (10) ◽  
pp. 155014771879462 ◽  
Author(s):  
Jian Wang ◽  
Kuoyuan Qiao ◽  
Zhiyong Zhang
Keyword(s):  
Social Networks ◽  
Online Social Networks ◽  
Privacy Preservation ◽  
Evidence Theory ◽  
Trust Evaluation ◽  
Combination Rule ◽  
Privacy Leakage ◽  
Evidence Combination ◽  
Fixed Model ◽  
The Mean

Trust is an important criterion for access control in the field of online social networks privacy preservation. In the present methods, the subjectivity and individualization of the trust is ignored and a fixed model is built for all the users. In fact, different users probably take different trust features into their considerations when making trust decisions. Besides, in the present schemes, only users’ static features are mapped into trust values, without the risk of privacy leakage. In this article, the features that each user cares about when making trust decisions are mined by machine learning to be User-Will. The privacy leakage risk of the evaluated user is estimated through information flow predicting. Then the User-Will and the privacy leakage risk are all mapped into trust evidence to be combined by an improved evidence combination rule of the evidence theory. In the end, several typical methods and the proposed scheme are implemented to compare the performance on dataset Epinions. Our scheme is verified to be more advanced than the others by comparing the F-Score and the Mean Error of the trust evaluation results.

scholarly journals An Improved Multi-Source Data Fusion Method Based on the Belief Entropy and Divergence Measure

Entropy ◽  
2019 ◽  
Vol 21 (6) ◽  
pp. 611 ◽  
Author(s):  
Zhe Wang ◽  
Fuyuan Xiao
Keyword(s):  
Data Fusion ◽  
Evidence Theory ◽  
Weighted Average ◽  
Weights Of Evidence ◽  
Experimental Result ◽  
Fusion Method ◽  
Combination Rule ◽  
Combination Rules ◽  
Source Data ◽  
Belief Entropy

Dempster–Shafer (DS) evidence theory is widely applied in multi-source data fusion technology. However, classical DS combination rule fails to deal with the situation when evidence is highly in conflict. To address this problem, a novel multi-source data fusion method is proposed in this paper. The main steps of the proposed method are presented as follows. Firstly, the credibility weight of each piece of evidence is obtained after transforming the belief Jenson–Shannon divergence into belief similarities. Next, the belief entropy of each piece of evidence is calculated and the information volume weights of evidence are generated. Then, both credibility weights and information volume weights of evidence are unified to generate the final weight of each piece of evidence before the weighted average evidence is calculated. Then, the classical DS combination rule is used multiple times on the modified evidence to generate the fusing results. A numerical example compares the fusing result of the proposed method with that of other existing combination rules. Further, a practical application of fault diagnosis is presented to illustrate the plausibility and efficiency of the proposed method. The experimental result shows that the targeted type of fault is recognized most accurately by the proposed method in comparing with other combination rules.

scholarly journals An Evidence Combination Rule Based on New Weight Assignment Scheme

2022 ◽  
Author(s):  
yucui wang ◽  
Jian Wang ◽  
Mengjie Huang ◽  
Minghui Wang
Keyword(s):  
Evidence Theory ◽  
Wasserstein Distance ◽  
Combination Rule ◽  
Assignment Method ◽  
Weight Assignment ◽  
Conflicting Evidence ◽  
Evidence Combination ◽  
Reference Index ◽  
The Impact ◽  
Assignment Scheme

Abstract Conflicting evidence and fuzzy evidence have a significant impact on the results of evidence combination in the application of evidence theory. However, the existing weight assignment methods can hardly reflect the significant influence of fuzzy evidence on the combination results. Therefore, a new method for assigning evidence weights and the corresponding combination rule are proposed. The proposed weight assignment method strengthens the consideration of fuzzy evidence and introduces the Wasserstein distance to compute the clarity degree of evidence which is an important reference index for weight assignment in the proposed combination rule and can weaken the effect of ambiguous evidence effectively. In the experiments, it's firstly verified that the impact of fuzzy evidence on the combination results is significant; therefore it should be fully considered in the weight assignment process. Then, the proposed combination rule with new weight assignment method is tested on a set of numerical arithmetic and Iris datasets. Compared with four existing methods, the results show that the proposed method has higher decision accuracy, F1 score, better computational convergence, and more reliable fusion results as well.

Analysis and Improvement of Combination Rule in D-S Theory

2014 ◽  
Vol 556-562 ◽  
pp. 3930-3934
Author(s):  
Ruo Cheng Wang
Keyword(s):  
Evidence Theory ◽  
Combination Rule ◽  
Effective Combination ◽  
Evidence Combination ◽  
Combination Principle

In this paper, the evidence combination principle of Dempster-Shafer (D-S) evidence theory is analyzed in detail. And the method of evidence combination is improved because of the deficiency of D-S evidence theory. Considering the principle“the minority should be subordinate to the majority”, based on Yager’s rule, we put forward a new effective combination rule which works more reasonably.

scholarly journals Weighted Evidence Combination Rule Based on Evidence Distance and Uncertainty Measure: An Application in Fault Diagnosis

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Lei Chen ◽  
Ling Diao ◽  
Jun Sang
Keyword(s):  
Fault Diagnosis ◽  
Conflict Management ◽  
Information Fusion ◽  
Uncertainty Measure ◽  
Combination Rule ◽  
Rule Based ◽  
Dempster Shafer Theory ◽  
Evidence Combination ◽  
Weight Value ◽  
Shafer Theory

Conflict management in Dempster-Shafer theory (D-S theory) is a hot topic in information fusion. In this paper, a novel weighted evidence combination rule based on evidence distance and uncertainty measure is proposed. The proposed approach consists of two steps. First, the weight is determined based on the evidence distance. Then, the weight value obtained in first step is modified by taking advantage of uncertainty. Our proposed method can efficiently handle high conflicting evidences with better performance of convergence. A numerical example and an application based on sensor fusion in fault diagnosis are given to demonstrate the efficiency of our proposed method.

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