Parametric regression analysis of imprecise and uncertain data in the fuzzy belief function framework

International Journal of Approximate Reasoning

Volumn 54, Issue 8, 2013, Pages 1217-1242

  Su, Zhi Gang ^a   Wang, Yi Fan ^b   Wang, Pei Hong ^a  

^a Southeast University   (China)

^b CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

EM algorithm; Evidence theory; Fuzzy belief function; Fuzzy data; Regression analysis; Uncertain data

Indexed keywords

BELIEF FUNCTION; EM ALGORITHMS; EVIDENCE THEORIES; FUZZY DATA; UNCERTAIN DATAS;

ALGORITHMS; LINEAR REGRESSION; MATHEMATICAL MODELS; REGRESSION ANALYSIS; STATISTICS;

UNCERTAINTY ANALYSIS;

EID: 84879602390     PISSN: 0888613X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijar.2013.02.008     Document Type: Article

References (41)

1. H. Akaike A new look at the statistical model identification IEEE Transactions on Automatic Control 19 6 1974 716 723
2. E. Alpaydin Introduction to Machine Learning 2004 MIT press
3. A. Bargiela, W. Pedrycz, and T. Nakashima Multiple regression with fuzzy data Fuzzy Sets and Systems 158 19 2007 2169 2188
4. Marco E.G.V. Cattaneo Belief functions combination without assumption of independence of the information sources International Journal of Approximate Reasoning 52 3 2011 299 315
5. M. Chebbah, A. Martin, B. Ben Yaghlane, About sources dependence in the theory of belief functions, in: The 2nd International Conference on Belief Functions, May 11-12, 2012, France, pp. 239-246.
6. I. Couso, and S. Moral Independence concepts in evidence theory International Journal of Approximate Reasoning 51 7 2010 748 758
7. A.P. Dempster Upper and lower probabilities induced by a multivalued mapping Annals of Mathematical Statistics 38 2 1967 325 339
8. A.P. Dempster Upper and lower probabilities generated by a random closed interval Annals of Mathematical Statistics 39 3 1968 957 966
9. A.P. Dempster, N.M. Laird, and D.B. Rubin Maximum likelihood from incomplete data via the EM algorithm Journal of the Royal Statistical Society B 39 1 1977 1 38
10. T. Denoeux A k-nearest neighbor classification rule based on Dempster-Shafer theory IEEE Transactions on Systems, Man and Cybernetics 25 5 1995 804 813
11. T. Denoeux Modeling vague beliefs using fuzzy-valued belief structures Fuzzy Sets and Systems 116 2 2000 167 199
12. T. Denoeux Maximum likelihood from evidential data: an extension of the EM algorithm C. Borgelt, Combining Soft Computing and Statistical Methods in Data Analysis (Proceedings of SMPS) Advances in Intelligent and Soft Computing 2010 Springer Oviedeo, Spain 181 188
13. T. Denoeux Maximum likelihood estimation from uncertain data in the belief framework IEEE Transactions on Knowledge and Data Engineering 25 1 2013 119 130
14. T. Denoeux Maximum likelihood estimation from fuzzy data using the EM algorithm Fuzzy Sets and Systems 183 1 2011 72 91
15. T. Denoeux, and Ph. Smets Classification using belief functions: the relationship between the case-based and model-based approaches IEEE Transactions on Systems, Man and Cybernetics B 36 6 2006 1395 1406
16. T. Denoeux, and L.M. Zouhal Handling possibilistic labels in pattern classification using evidential reasoning Fuzzy Sets and Systems 122 3 2001 47 62
17. D. Dubois, and H. Prade Possibility Theory: An Approach to Computerized Processing of Uncertainty 1988 Plenum Press New York
18. P. D'Urso, R. Mssari, and A. Santoro Robust fuzzy regression analysis Information Sciences 181 19 2011 4154 4174
19. T. Hastie, R. Tibshirani, and J. Friedman The Elements of Statistical Learning 2001 Springer New York
20. J.S.R. Jang, C.T. Sun, and E. Mizutani Neuro-Fuzzy and Soft Computing 1997 Prentice-Hall Upper Saddle River, NJ
21. R. Kohavi A study of cross-validation and bootstrap for accuracy estimation and model selection Proceedings of the Fourteenth International Joint Conference on Artificial Intelligence 2 12 1995 1137 1143
22. J. Shawe-Taylor, and N. Cristianini Kernel Methods for Pattern Analysis 2004 Cambridge University Press Cambridge, UK
23. S. Petit-Renaud, and T. Denoeux Nonparametric regression analysis of uncertain and imprecise data using belief functions International Journal of Approximate Reasoning 35 1 2004 1 28
24. Gideon E. Schwarz Estimating the dimension of a model Annals of Statistics 6 2 1978 461 464
25. G. Shafer A Mathematical Theory of Evidence 1976 Princeton University Press Princeton, NJ
26. Ph. Smets The degree of belief in a fuzzy event Information Sciences 25 1 1981 1 19
27. Ph. Smets The combination of evidence in the transferable belief model IEEE Transactions on Pattern Analysis and Machine Intelligence 12 5 1990 447 458
28. Ph. Smets Varieties of ignorance Information Sciences 57-58 1991 135 144
29. Ph. Smets Belief functions on real numbers International Journal of Approximate Reasoning 40 3 2005 181 223
30. Ph. Smets, and R. Kennes The transferable belief model Artificial Intelligence 66 1994 191 243
31. Z.G. Su, and P.H. Wang Improved adaptive evidential k-NN rule and its application for monitoring level of coal powder filling ball mill Journal of Process Control 19 10 2009 1751 1762
32. Z.G. Su, P.H. Wang, Z.L. Song, and Kernel based nonlinear fuzzy regression model Engineering Applications of Artificial Intelligence 26 2 2013 724 738
33. T. Takagi, and M. Sugeno Fuzzy identification of systems and its applications to modeling and control IEEE Transactions on Systems, Man and Cybernetics 15 1 1985 116 132
34. H. Tanaka, S. Uejima, and K. Asai Linear regression analysis with fuzzy model IEEE Transactions on Systems Man Cybernetics 12 6 1982 903 907
35. H. Varian Bootstrap tutorial Mathematica Journal 9 2005 768 775
36. R.R. Yager Generalized probabilities of fuzzy events from fuzzy belief structures Information Sciences 28 1 1982 45 62
37. R.R. Yager On the normalization of fuzzy belief structure International Journal of Approximate Reasoning 14 2-3 1996 127 153
38. R.R. Yager, and D.P. Filev Including probabilistic uncertainty in fuzzy logic controller modeling using Dempster-Shafer theory IEEE Transactions on Systems, Man and Cybernetics 25 8 1995 1221 1230
39. B. Ben Yaghlane, Ph. Smets, and K. Mellouli Belief function independence: 1. The marginal case International Journal of Approximate Reasoning 29 1 2002 47 70
40. J. Yen Generalizing the Dempster-Shafer theory to fuzzy sets IEEE Transactions on Systems, Man and Cybernetics 20 3 1990 559 569
41. L.A. Zadeh Probability measures of fuzzy events Journal of Mathematical Analysis and Applications 23 2 1968 421 427