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research-article

Generalized evidence theory

Author:

Yong DengAuthors Info & Claims

Applied Intelligence, Volume 43, Issue 3

Pages 530 - 543

https://doi.org/10.1007/s10489-015-0661-2

Published: 01 October 2015 Publication History

Abstract

Dempster-Shafer evidence theory is an efficient tool in knowledge reasoning and decision-making under uncertain environments. Conflict management is an open issue in Dempster-Shafer evidence theory. In past decades, a large amount of research has been conducted on this issue. In this paper, we propose a new theory called generalized evidence theory (GET). In comparison with classical evidence theory, GET addresses conflict management in an open world, where the frame of discernment is incomplete because of uncertainty and incomplete knowledge. Within the presented GET, we define a novel concept called generalized basic probability assignment (GBPA) to model uncertain information, and provide a generalized combination rule (GCR) for the combination of GBPAs, and build a generalized conflict model to measure conflict among evidences. Conflicting evidence can be effectively handled using the GET framework. We present many numerical examples that demonstrate that the proposed GET can explain and deal with conflicting evidence more reasonably than existing methods.

References

[1]

Ayoun A and Smets PData association in multi-target detection using the transferable belief modelInt J Intell Syst200116101167-11820988.68170

[2]

Cuzzolin F Two new bayesian approximations of belief functions based on convex geometry IEEE Trans Syst Man Cybern B 2007 37 4 993-1008

[3]

Cuzzolin F A geometric approach to the theory of evidence IEEE Trans Syst Man Cybern Part C Appl Rev 2008 38 4 522-534

[4]

Cuzzolin FLp consonant approximations of belief functionsIEEE Trans Fuzzy Syst2014222420-4363206152

[5]

Delgrande JPRevising beliefs on the basis of evidenceInt J Approx Reason2012533396-41229024021258.03022

[6]

Dempster AUpper and lower probabilities induced by a multivalued mappingAnn Math Stat1967382325-3392070010168.17501

[7]

Dempster AP (2008) A generalization of Bayesian inference. In: Classic works of the dempster-shafer theory of belief functions, pp 73–104

[8]

Dempster AP and Chiu WFDempster-Shafer models for object recognition and classificationInt J Intell Syst2006213283-2971096.62065

[9]

Deng X, Hu Y, Deng Y, and Mahadevan S Environmental impact assessment based on D numbers Expert Syst Appl 2014 41 2 635-643

[10]

Deng X, Hu Y, Deng Y, and Mahadevan S Supplier selection using AHP methodology extended by D numbers Expert Syst Appl 2014 41 1 156-167

[11]

Deng X, Chan FT, Sadiq R, Mahadevan S, and Deng Y D-CFPR: D numbers extended consistent fuzzy preference relations Knowl-Based Syst 2015 73 1 61-68

[12]

Deng Y D numbers: Theory and applications J Inf Comput Sci 2012 9 9 2421-2428

[13]

Deng Y and Chan FT A new fuzzy dempster mcdm method and its application in supplier selection Expert Syst Appl 2011 38 8 9854-9861

[14]

Deng Y, Shi W, Zhu Z, and Liu Q Combining belief functions based on distance of evidence Decis Support Syst 2004 38 3 489-493

[15]

Denœux T and Masson MH EVCLUS: evidential clustering of proximity data IEEE Trans Syst Man Cybern B Cybern 2004 34 1 95-109

[16]

Denoeux T and Masson MHEvidential reasoning in large partially ordered setsAnn Oper Res20121951135-16129090461251.68240

[17]

Destercke S and Burger T Toward an axiomatic definition of conflict between belief functions IEEE Trans Cybern 2013 43 2 585-596

[18]

Dezert J, Smarandache F (2006) Dsmt: A new paradigm shift for information fusion. arXiv:cs/0610175

[19]

Dezert J, Han D, Liu Z, Tacnet JM (2012) Hierarchical proportional redistribution for bba approximation. In: Belief functions: theory and applications. Springer, pp 275–283

[20]

Dezert J, Tchamova A, Han D, Tacnet JM (2013a) Why dempster’s fusion rule is not a generalization of bayes fusion rule. In: 2013 16th International Conference on Information fusion (FUSION), IEEE, pp 1127–1134

[21]

Dezert J, Tchamova A, Han D, Tacnet JM (2013b) Why dempster’s rule doesn’t behave as bayes rule with informative priors. In: Innovations in Intelligent Systems and Applications (INISTA), 2013 IEEE International Symposium on IEEE, pp 1–5

[22]

Dubois D and Prade H Representation and combination of uncertainty with belief functions and possibility measures Comput Intell 1988 4 3 244-264

[23]

Elouedi Z, Mellouli K, and Smets P Assessing sensor reliability for multisensor data fusion within the transferable belief model IEEE Trans Syst Man Cybern B Cybern 2004 34 1 782-787

[24]

Haenni R Are alternatives to dempster’s rule of combination real alternatives?: Comments on about the belief function combination and the conflict management problem—lefevre et al Inf Fusion 2002 3 3 237-239

[25]

Haenni R (2005) Shedding new light on Zadeh’s criticism of Dempster’s rule of combination. In: 2005 7th International conference on information fusion, vol 2, pp 879–884

[26]

Haenni R and Lehmann NResource bounded and anytime approximation of belief function computationsInt J Approx Reason2002311103-15419406111033.68116

[27]

Huang S, Su X, Hu Y, Mahadevan S, and Deng Y A new decision-making method by incomplete preferences based on evidence distance Knowl-Based Syst 2014 56 264-272

[28]

Jousselme AL, Grenier D, and Bossé É A new distance between two bodies of evidence Inf Fusion 2001 2 2 91-101

[29]

Jousselme AL, Liu C, Grenier D, and Bosse E Measuring ambiguity in the evidence theory IEEE Trans Syst Man Cybern Syst Hum 2006 36 5 890-903

[30]

Kang B, Deng Y, Sadiq R, and Mahadevan S Evidential cognitive maps Knowl-Based Syst 2012 35 77-86

[31]

Klir GJ and Lewis H Remarks on “Measuring ambiguity in the evidence theory” IEEE Trans Syst Man Cybern Syst Hum 2008 38 4 995-999

[32]

Lefèvre E and Elouedi Z How to preserve the conflict as an alarm in the combination of belief functions? Decis Support Syst 2013 56 326-333

[33]

Lefevre E, Colot O, and Vannoorenberghe P Belief function combination and conflict management Inf fusion 2002 3 2 149-162

[34]

Liu H, You J, Fan X, and Lin Q Failure mode and effects analysis using d numbers and grey relational projection method Expert Syst Appl 2014 41 10 4670-4679

[35]

Liu WAnalyzing the degree of conflict among belief functionsArtif Intell200617011909-9241131.68539

[36]

Liu Z, Pan Q, and Dezert J Evidential classifier for imprecise data based on belief functions Knowl-Based Syst 2013 52 246-257

[37]

Liu Z, Pan Q, and Dezert J A belief classification rule for imprecise data Appl Intell 2014 40 2 214-228

[38]

Liu Z, Pan Q, Dezert J, and Mercier G Credal classification rule for uncertain data based on belief functions Pattern Recog 2014 47 7 2532-2541

[39]

Masson MH and Denoeux TEnsemble clustering in the belief functions frameworkInt J Approx Reason201152192-10927490581213.68501

[40]

Murphy CK Combining belief functions when evidence conflicts Decis Support Syst 2000 29 1 1-9

[41]

Nguyen HT (2012) On belief functions and random sets. In: Belief functions: theory and applications. Springer, pp 1–19

[42]

Roquel A, Le Hégarat-Mascle S, Bloch I, Vincke B (2012) A new local measure of disagreement between belief functions–application to localization. In: Belief functions: theory and applications. Springer, pp 335–342

[43]

Sankararaman S and Mahadevan S Model validation under epistemic uncertainty Reliab Eng Syst Saf 2011 96 9 1232-1241

[44]

Sarabi-Jamab A, Araabi BN, and Augustin T Information-based dissimilarity assessment in dempster–shafer theory Knowl-Based Syst 2013 54 114-127

[45]

Schubert JConflict management in Dempster-Shafer theory using the degree of falsityInt J Approx Reason2011523449-4602771971

[46]

Shafer G A mathematical theory of evidence 1976 Princeton Princeton University Press

[47]

Smets PDecision making in the tbm: the necessity of the pignistic transformationInt J Approx Reason2005382133-14721167811065.68098

[48]

Smets P and Kennes RThe transferable belief modelArtif Intell1994662191-23412678090807.68087

[49]

Smets P and Kennes RThe transferable belief modelArtif Intell1994662191-23412678090807.68087

[50]

Utkin L and Destercke SComputing expectations with continuous p-boxes: Univariate caseInt J Approx Reason2009505778-79825528081195.60027

[51]

Voorbraak FA computationally efficient approximation of dempster-shafer theoryInt J Man Mach Stud1989305525-5360684.68105

[52]

Wei D, Deng X, Zhang X, Deng Y, and Mahadevan S Identifying influential nodes in weighted networks based on evidence theory Physica A: Statistical Mechanics and its Applications 2013 392 10 2564-2575

[53]

Xu P, Su X, Mahadevan S, Li C, and Deng Y A non-parametric method to determine basic probability assignment for classification problems Appl Intell 2014 41 3 681-693

[54]

Yager RROn the Dempster-Shafer framework and new combination rulesInf Sci198741293-1378867860629.68092

[55]

Yager RR On the aggregation of prioritized belief structures IEEE Trans Syst Man Cybern Syst Hum 1996 26 6 708-717

[56]

Yager RRDempster-Shafer structures with general measuresInt J Gen Syst2012414395-40829135621277.93076

[57]

Yang BS and Kim KJApplication of Dempster-Shafer theory in fault diagnosis of induction motors using vibration and current signalsMech Syst Signal Process2006202403-4201815108

[58]

Yang J and Singh MG An evidential reasoning approach for multiple-attribute decision making with uncertainty IEEE Trans Syst Man Cybern 1994 24 1 1-18

[59]

Yang J and Xu D Evidential reasoning rule for evidence combination AArtif Intell 2013 205 1-29

[60]

Yang J, Wang Y, Xu D, and Chin KSThe evidential reasoning approach for mada under both probabilistic and fuzzy uncertaintiesEur J Oper Res20061711309-34321834781091.90525

[61]

Yang Y, Han D, and Han C Discounted combination of unreliable evidence using degree of disagreement Int J Approx Reason 2013 54 8 1197-1216

[62]

Zadeh LA A simple view of the Dempster-Shafer theory of evidence and its implication for the rule of combination AI Mag 1986 7 2 85

[63]

Zhang Y, Deng X, Wei D, and Deng Y Assessment of E-Commerce security using AHP and evidential reasoning Expert Syst Appl 2012 39 3 3611-3623

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Published In

Applied Intelligence Volume 43, Issue 3

Oct 2015

234 pages

ISSN:0924-669X

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© Springer Science+Business Media New York 2015.

Publisher

Kluwer Academic Publishers

United States

Publication History

Published: 01 October 2015

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Cited By

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Parmar JChouhan SRaychoudhury VRathore S(2023)Open-world Machine Learning: Applications, Challenges, and OpportunitiesACM Computing Surveys10.1145/356138155:10(1-37)Online publication date: 2-Feb-2023
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Yang QHan GGao WYang ZZhu SDeng Y(2023)A Robust Learning Membership Scaling Fuzzy C-Means Algorithm Based on New Belief PeakIEEE Transactions on Fuzzy Systems10.1109/TFUZZ.2023.328691031:12(4486-4500)Online publication date: 1-Dec-2023
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