Extensions of belief functions and possibility distributions by using the imprecise Dirichlet model

Fuzzy Sets and Systems

Volumn 154, Issue 3, 2005, Pages 413-431

  Utkin, Lev V ^a  

^a SAINT PETERSBURG STATE FOREST TECHNICAL UNIVERSITY   (Russian Federation)

Author keywords

Approximate reasoning; Belief measures; Dempster Shafer theory; Dirichlet distribution; Imprecise probability theory; Multinomial model; Possibility theory

Indexed keywords

APPROXIMATION THEORY; FUZZY SETS; MATHEMATICAL MODELS; PROBABILISTIC LOGICS; PROBABILITY DISTRIBUTIONS; RELIABILITY THEORY; STATISTICAL METHODS;

APPROXIMATE REASONING; BELIEF MEASURES; DEMPSTER SHAFER THEORY; DIRICHLET DISTRIBUTION; IMPRECISE PROBABILITY THEORY; MULTINOMIAL MODELS; POSSIBILITY THEORY;

PROBABILITY DENSITY FUNCTION;

EID: 21744462473     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fss.2005.03.012     Document Type: Article

References (29)

1. J.-M. Bernard, Non-parametric inference about an unknown mean using the imprecise Dirichlet model, in: G. de Cooman, T.L. Fine, T. Seidenfeld (Eds.), Imprecise Probabilities and Their Applications. Proc. Second Int. Symp., ISIPTA'01, June 2001, Ithaca, USA, Shaker Publishing, pp. 40-50.
2. J.-M. Bernard Implicative analysis for multivariate binary data using an imprecise Dirichlet model J. Stat. Planning Infererence 105 1 2002 83 104
3. J.-M. Bernard, An introduction to the imprecise Dirichlet model for multinomial data, Reprint No. IdmInt04, Universite de Paris 5, Laboratoire de Psychologie Environnementale, France, December 2004.
4. A. Bernardini What are the random and fuzzy sets and how to use them for uncertainty modelling in engineering systems I. Elishakoff Whys and Hows in Uncertainty Analysis: Probability, Fuzziness and Anti-optimization 1999 Springer Vienna 63 125
5. J.M. Bernardo, and A.F.M. Smith Bayesian Theory 1994 Wiley Chichester
6. F.P.A. Coolen An imprecise Dirichlet model for Bayesian analysis of failure data including right-censored observations Reliab. Eng. System Safe. 56 1997 61 68
7. G. de Cooman, and M. Zaffalon Updating beliefs with incomplete observations Artif. Intell. 159 1-2 2004 75 125
8. M. DeGroot Optimal Statistical Decisions 1970 McGraw-Hill New York
9. A.P. Dempster Upper and lower probabilities induced by a multi-valued mapping Ann. Math. Stat. 38 1967 325 339
10. D. Dubois, and H. Prade Possibility Theory: An Approach to Computerized Processing of Uncertainty 1988 Plenum Press New York
11. D. Dubois, and H. Prade Possibility theory and data fusion in poorly informed environments Control. Eng. Pract. 2 5 1994 811 823
12. S. Ferson, V. Kreinovich, L. Ginzburg, D.S. Myers, K. Sentz, Constructing probability boxes and Dempster-Shafer structures, Report SAND2002-4015, Sandia National Laboratories, January 2003.
13. J.Y. Halpern, and R. Fagin Two views of belief: belief as generalized probability and belief as evidence Artif. Intell. 54 1992 275 317
14. P.J. Huber Robust Statistics 1981 Wiley New York
15. M. Hutter, Robust estimators under the imprecise Dirichlet model, in: J.-M. Bernard, T. Seidenfeld, M. Zaffalon (Eds.), Proc. Third Int. Symp. on Imprecise Probabilities and Their Applications, ISIPTA'03, July 2003, Lugano, Switzerland, Carleton Scientific, pp. 274-289.
16. G.J. Klir, and M.J. Wierman Uncertainty-Based Information: Elements of Generalized Information Theory 1998 Physica-Verlag Heidelberg
17. V.P. Kuznetsov Interval Statistical Models 1991 Radio and Communication Moscow in Russian
18. E. Quaeghebeur, G. de Cooman, Game-theoretic learning using the imprecise Dirichlet model, in: J.-M. Bernard, T. Seidenfeld, M. Zaffalon (Eds.), Proc. Third Int. Symp. on Imprecise Probabilities and Their Applications, ISIPTA'03, July 2003, Lugano, Switzerland, Carleton Scientific, pp. 450-464.
19. M. Ramoni, and P. Sebastiani Robust learning with missing data Mach. Learn. 45 2 2001 147 170
20. K. Sentz, S. Ferson, Combination of evidence in Dempster-Shafer theory, Report SAND2002-0835, Sandia National Laboratories, April 2002.
21. G. Shafer A Mathematical Theory of Evidence 1976 Princeton University Press Princeton
22. P. Smets, Belief induced by the knowledge of the probabilities, Tech. report 94-4.1, Institut de Recherches Interdisciplinaires et de Developpements en Intelligence Artificielle, Brussels, 1994.
23. M. Smithson, T. Bartos, K. Takemura, Human judgment under sample space ignorance, in: G. de Cooman, F.G. Cozman, S. Moral, P. Walley (Eds.), Proc. First Int. Symp. on Imprecise Probabilities and Their Applications, ISIPTA '99, June 1999, Zwijnaarde, Belgium, pp. 324-332.
24. F. Tonon, A. Bernardini, and A. Mammino Determination of parameters range in rock engineering by means of random set theory Reliab. Eng. System Safe. 70 2000 241 261
25. P. Walley Statistical Reasoning with Imprecise Probabilities 1991 Chapman & Hall London
26. P. Walley Inferences from multinomial data: learning about a bag of marbles J. Roy. Stat. Soc. B 58 1996 3 57 with discussion
27. K. Weichselberger, Elementare Grundbegriffe einer allgemeineren Wahrscheinlichkeitsrechnung, vol. I, Intervallwahrscheinlichkeit als umfassendes Konzept, Physika, Heidelberg, 2001.
28. S. Wilks Mathematical Statistics 1962 Wiley New York
29. M. Zaffalon Exact credal treatment of missing data J. Stat. Planning Inference 105 1 2002 105 122