Evidential matrix metrics as distances between meta-data dependent bodies of evidence

IEEE Transactions on Cybernetics

Volumn 46, Issue 1, 2016, Pages 109-122

  Loudahi, Mehena ^a   Klein, John ^a   Vannobel, Jean Marc ^a   Colot, Olivier ^a  

^a UNIV LILLE   (France)

Author keywords

Combination rules; Distance; Evidence theory; Information source meta data; Theory of belief functions

Indexed keywords

COMPUTATION THEORY; METADATA; UNCERTAINTY ANALYSIS;

BELIEF FUNCTION; COMBINATION RULES; INFORMATION SOURCES; MATHEMATICAL OBJECTS; MATRIX NORMS; META-KNOWLEDGE; POSET STRUCTURES; THEORY OF BELIEF FUNCTIONS;

MATRIX ALGEBRA;

EID: 84960396045     PISSN: 21682267     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCYB.2015.2395877     Document Type: Article

References (34)

1. A. Dempster, "Upper and lower probabilities induced by a multiple valued mapping," Ann. Math. Statist., vol. 38, no. 2, pp. 325-339, 1967.
2. G. Shafer, A Mathematical Theory of Evidence. Princeton, NJ, USA: Princeton Univ. Press, 1976.
3. A.-L. Jousselme, D. Grenier, and E. Bossé, "A new distance between two bodies of evidence," Inf. Fusion, vol. 2, pp. 91-101, Jun. 2001.
4. H. Stephanou and S.-Y. Lu, "Measuring consensus effectiveness by a generalized entropy criterion," IEEE Trans. Pattern Anal. Mach. Intell., vol. 10, no. 4, pp. 544-554, Jul. 1988.
5. W. Perry and H. Stephanou, "Belief function divergence as a classifier," in Proc. IEEE Int. Symp. Intell. Control, Arlington, VA, USA, Aug. 1991, pp. 280-285.
6. L. M. Zouhal and T. Denoeux, "An evidence-theoretic k-NN rule with parameter optimisation," IEEE Trans. Syst., Man, Cybern. C, Appl. Rev., vol. 28, no. 2, pp. 263-271, May 1998.
7. B. Tessem, "Approximations for efficient computation in the theory of evidence," Artif. Intell., vol. 61, pp. 315-329, Jun. 1993.
8. D. Fixen and R. Mahler, "The modified Dempster-Shafer approach to classification," IEEE Trans. Syst., Man, Cybern. A, Syst., Humans, vol. 27, no. 1, pp. 96-104, Jan. 1997.
9. M. Bauer, "Approximation algorithms and decision making in the Dempster-Shafer theory of evidence - An empirical study," Int. J. Approx. Reason., vol. 17, nos. 2-3, pp. 217-237, 1997.
10. D. Harmanec, "Faithful approximations of belief functions," in Proc. Uncertain. Artif. Intell. (UAI), Stockholm, Sweden, 1999, pp. 271-278.
11. G. J. Klir and M. J. Wierman, Uncertainty-Based Information: Elements of Generalized Information Theory, Berlin, Germany: Physica-Verlag, 1999.
12. J. Diaz, M. Rifqi, and B. Bouchon-Meunier, "A similarity measure between basic belief assignments," in Proc. 9th Int. Conf. Inf. Fusion (FUSION), Florence, Italy, 2006, pp. 1-6.
13. Z. Elouedi, K. Mellouli, and P. Smets, "Assessing sensor reliability for multisensor data fusion within the transferable belief model," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 34, no. 1, pp. 782-787, Feb. 2004.
14. Z. Sunberg and J. Rogers, "A belief function distance metric for orderable sets," Inf. Fusion, vol. 14, pp. 361-373, Oct. 2013.
15. T. Weiler and U. Bodenhofer, "Approximation of belief functions by minimizing Euclidean distances," Int. J. Uncertain. Fuzz. Knowl.-Based Syst., vol. 11, no. 6, pp. 170-177, 2003.
16. F. Cuzzolin, "Two new Bayesian approximations of belief functions based on convex geometry," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 37, no. 4, pp. 993-1008, Aug. 2007.
17. F. Cuzzolin, "Lp consonant approximation of belief functions in the mass space," in Proc. 7th Int. Symp. Imprecise Probab.: Theories Appl., Innsbruck, Austria, 2011, pp. 1-10.
18. F. Cuzzolin, "On consistent approximations of belief functions in the mass space," in Symbolic and Quantitative Approaches to Reasoning With Uncertainty (Lecture Notes in Computer Science) vol. 6717, W. Liu, Ed. Berlin, Germany: Springer, 2011, pp. 287-298.
19. A.-L. Jousselme and P. Maupin, "Distances in evidence theory: Comprehensive survey and generalizations," Int. J. Approx. Reason., vol. 53, pp. 118-145, Feb. 2012.
20. M. Loudahi, J. Klein, J.-M. Vannobel, and O. Colot, "New distances between bodies of evidence based on dempsterian specialization matrices and their consistency with the conjunctive combination rule," Int. J. Approx. Reason., vol. 55, no. 5, pp. 1093-1112, 2014.
21. F. Cuzzolin, Visions of a Generalized Probability Theory. London, U.K.: Lambert Academic, 2014.
22. F. Cuzzolin, "A geometric approach to the theory of evidence," IEEE Trans. Syst., Man, Cybern. C, Appl. Rev., vol. 38, no. 4, pp. 522-534, Jul. 2008.
23. P. Smets and R. Kennes, "The transferable belief model," Artif. Intell., vol. 66, no. 2, pp. 191-234, 1994.
24. P. Smets, "The alpha-junctions: Combination operators applicable to belief functions," in Qualitative and Quantitative Practical Reasoning (Lecture Notes in Computer Sciences), vol. 1244. Berlin, Germany: Springer, 1997, pp. 131-153.
25. F. Pichon and T. Denoeux, "Interpretation and computation of α-junctions for combining belief functions," in Proc. 6th Int. Symp. Imprecise Probab. Theories Appl. (ISIPTA), Durham, U.K., Jul. 2009, pp. 1-10.
26. F. Pichon, "On the α-conjunctions for combining belief functions," in Belief Functions: Theory and Applications (Advances in Intelligent and Soft Computing), vol. 164, T. Denoeux and M.-H. Masson, Eds. Berlin, Germany: Springer, 2012, pp. 285-292.
27. F. Pichon, D. Dubois, and T. Denoeux, "Relevance and truthfulness in information correction and fusion," Int. J. Approx. Reason., vol. 53, no. 2, pp. 159-175, 2012.
28. P. Smets, "The application of the matrix calculus to belief functions," Int. J. Approx. Reason., vol. 31, pp. 1-30, Oct. 2002.
29. F. Cuzzolin, "Geometry of Dempster's rule of combination," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 34, no. 2, pp. 961-977, Apr. 2004.
30. M. Fréchet, "Sur quelques points du calcul fonctionnel," Ph.D. dissertation, Facultés des sciences de Paris, Paris, France, 1906.
31. W. Liu, "Analysing the degree of conflict among belief functions," Artif. Intell., vol. 170, no. 11, pp. 909-924, 2006.
32. D. Han, J. Dezert, C. Han, and Y. Yang, "New dissimilarity measure in evidence theory," in Proc. 14th Int. Conf. Inf. Fusion (FUSION), Chicago, IL, USA, 2011, pp. 1-7.
33. T. Burger and S. Destercke, "How to randomly generate mass functions," Int. J. Uncertain. Fuzz. Knowl.-Based Syst., vol. 21, no. 5, pp. 645-673, 2013.
34. J. Klein, M. Loudahi, J.-M. Vannobel, and O. Colot, "α-junctions of categorical mass functions," in Belief Functions: Theory and Applications (Lecture Notes in Artificial Intelligence) vol. 8764, F. Cuzzolin, Ed. Berlin, Germany: Springer, 2014, pp. 1-10.