Lower previsions induced by multi-valued mappings

Journal of Statistical Planning and Inference

Volumn 133, Issue 1, 2005, Pages 173-197

  Miranda, Enrique ^a   de Cooman, Gert ^b   Couso, Inés ^c  

^a UNIVERSIDAD REY JUAN CARLOS   (Spain)

^b GHENT UNIVERSITY   (Belgium)

^c UNIVERSITY OF OVIEDO   (Spain)

Author keywords

Coherence; Conditioning; Evidence theory; Imprecise probabilities; Lower inverse; Lower prevision; Multi valued mapping; Natural extension; Random set

Indexed keywords

EID: 17844390652     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jspi.2004.03.005     Document Type: Article

References (28)

1. Th. Augustin Modelling weak information with generalised probability assignments in: H.H. Bock W. Polasek (Eds.), Data Analysis and Information Systems - Statistical and Conceptual Approaches 1996 Springer Heidelberg 101-113
2. Augustin, Th., 2004. Generalized basic probability assignaments. Internat. J. Gen. Systems, conditionally accepted for publication.
3. J.O. Berger The robust Bayesian viewpoint in: J.B. Kadane (Ed.), Robustness of Bayesian Analyses 1984 Elsevier Science Amsterdam 63-144
4. G. Choquet Theory of capacities Ann. Inst. Fourier 5 1953-1954 131-295
5. I. Couso S. Moral P. Walley Examples of independence for imprecise probabilities Risk Decision Policy 5 2 2000 165-181
6. G. Debreu Integration of correspondences In: Proceedings of the Fifth Berkeley Symposium of Mathematical Statistics and Probability 1965 Berkeley 351-372
7. G. de Cooman D. Aeyels A random set description of a possibility measure and its natural extension IEEE Trans. Systems Man Cybernet. - Part A: Systems Humans 30 2 2000 124-130
8. B. de Finetti Theory of Probability 1974-1975 Wiley Chichester (English Translation of Teoria delle Probabilità)
9. A.P. Dempster Upper and lower probabilities induced by a multivalued mapping Ann. Math. Statist. 38 1967 325-339
10. A.P. Dempster Upper and lower probabilities generated by a random closed interval Ann. Math. Statist. 39 1968 957-966
11. D. Denneberg Non-Additive Measure and Integral 1994 Kluwer Academic Dordrecht
12. F.J. Giron S. Rios Quasi-Bayesian behaviour: A more realistic approach to decision making? in: J.M. Bernardo M.H. DeGroot D.V. Lindley A.F.M. Smith (Eds.), Bayesian Statistics 1980 Valencia University Press Valencia 17-38
13. I.R. Goodman H.T. Nguyen E.A. Walker Conditional Inference and Logic for Intelligent Systems 1991 North-Holland Amsterdam
14. M. Grabisch H.T. Nguyen E.A. Walker Fundamentals of Uncertainty Calculi with Applications to Fuzzy Inference 1995 Kluwer Academic Publishers Dordrecht
15. C.J. Himmelberg Measurable relations Fund. Mathe. 87 1975 53-72
16. D.G. Kendall Foundations of a theory of random sets in: E.F. Harding D.G. Kendall (Eds.), Stochastic Geometry 1974 Wiley New York 322-376
17. A.N. Kolmogorov Grundbegriffe der Wahrscheinlichkeitsrechnung 1933 Springer Berlin
18. R. Kruse K.D. Meyer Statistics with Vague Data 1987 D. Reidel Publishing Company Dordrecht
19. I. Levi The Enterprise of Knowledge 1980 MIT Press London
20. G. Matheron Random Sets and Integral Geometry 1975 Wiley New York
21. Miranda, E., de Cooman, G., Couso, I. 2002. Imprecise probabilities induced by multi-valued mappings. In: Proceedings of the Ninth International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2002, Annecy, France, July 1-5, 2002, Gutenberg, pp. 1061-1068.
22. Miranda, E., Couso, I., Gil, P., 2004. A random set characterization of possibility measures. Inform. Sci., accepted for publication.
23. H.T. Nguyen On random sets and belief functions J. Math. Anal. Appl. 65 3 1978 531-542
24. G. Shafer A Mathematical Theory of Evidence 1976 Princeton University Press Princeton, NJ
25. V. Strassen Meßfehler und Information Z. Wahrscheinlichkeitstheorie Verwandte Gebiete 2 1964 273-305
26. Sugeno, M., 1974. The theory of fuzzy integrals and its applications. Ph.D. Thesis, Tokyo Institute of Technology, Tokyo.
27. Walley, P., 1981. Coherent lower (and upper) probabilities. Statistics Research Report 22, University of Warwick, Coventry.
28. P. Walley Statistical Reasoning with Imprecise Probabilities 1991 Chapman & Hall London