Supremum preserving upper probabilities

Information sciences

Volumn 118, Issue 1, 1999, Pages 173-212

  De Cooman, Gert ^a   Aeyels, Dirk ^a  

^a GHENT UNIVERSITY   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

FUNCTIONS; INTEGRAL EQUATIONS; PROBABILITY DISTRIBUTIONS; RANDOM PROCESSES;

CHOQUET INTEGRAL; UPPER PROBABILITY;

PROBABILITY;

EID: 0033321331     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-0255(99)00007-9     Document Type: Article

References (33)

1. Birkhoff G. Lattice Theory. 1967;A.M.S. Colloquium Publications, Providence, RI.
2. L. Boyen, G. de Cooman, E.E. Kerre, On the extension of P-consistent mappings, in: G. de Cooman, D. Ruan, E.E. Kerre (Eds.), Foundations and Applications of Possibility Theory, Proceedings of FAPT 95, World Scientific, Singapore, 1995, pp. 88-98.
3. G. Choquet, Theory of capacities, Annales de l'Institut Fourier 5 (1953)-(1954) 131-295.
4. Davey B.A., Priestley H.A. Introduction to Lattices and Order. 1990;Cambridge University Press, Cambridge.
5. B. De Baets, E.E. Kerre, A primer on solving fuzzy relational equations on the unit interval, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 2 (1994) 205-225.
6. G. de Cooman, Describing linguistic information in a behavioural framework: possible or not? in: J. Albus, A. Meystel, R. Quintero (Eds.), Intelligent Systems: A Semiotic Perspective, Proceedings of the 1996 International Multidisciplinary Conference, Gaithersburg, MD, 20-23 October 1996, pp. 141-150.
7. de Cooman G. Possibility theory I: The measure- and integral-theoretic groundwork. International Journal of General Systems. 25:1997;291-323.
8. de Cooman G. Possibility theory II: conditional possibility. International Journal of General Systems. 25:1997;325-351.
9. de Cooman G. Possibility theory III: possibilistic independence. International Journal of General Systems. 25:1997;353-371.
10. G. de Cooman, D. Aeyels, A random set description of a possibility measure and its natural extension, (1997), submitted for publication.
11. de Cooman G., Kerre E.E. Ample fields. Simon Stevin. 67:1993;235-244.
12. de Cooman G., Kerre E.E. Order norms on bounded partially ordered sets. The Journal of Fuzzy Mathematics. 2:1994;281-310.
13. de Cooman G., Kerre E.E. Possibility and necessity integrals. Fuzzy Sets and Systems. 77:1996;207-227.
14. G. de Cooman, D. Ruan, E.E. Kerre (Eds.), Foundations and Applications of Possibility Theory - Proceedings of FAPT '95, Ghent, 13-15 December 1995, World Scientific, Singapore, 1995.
15. B. de Finetti, Theory of Probability, English Translation of Teoria delle Probabilità, vol. 1, Wiley, Chichester, 1974.
16. Denneberg D. Non-additive measure and integral. 1994;Kluwer Academic Publishers, Dordrecht.
17. D. Dubois, J. Lang, H. Prade, Possibilistic logic, in: D.M. Gabbay, C.J. Hogger, J.A. Robinson (Eds.), Handbook of Logic in Artificial Intelligence and Logic Programming, vol. 3, Oxford University Press, Oxford, 1994, pp. 439-513.
18. Dubois D., Moral S., Prade H. A semantics for possibility theory based on likelihoods. Journal of Mathematical Analysis and Applications. 205:1997;359-380.
19. Dubois D., Prade H. Théorie des possibilités. 1985;Masson, Paris.
20. Dubois D., Prade H. When upper probabilities are possibility measures. Fuzzy Sets and Systems. 49:1992;65-74.
21. D. Dubois, H. Prade, Possibility theory: qualitative and quantitative aspects, in: Ph. Smets (Ed.), Handbook of Defeasible Reasoning and Uncertainty Management Systems, vol. 1, Kluwer Academic Publishers, Dordrecht, 1998, pp. 169-226.
22. Schechter E. Handbook of Analysis and Its Foundations. 1996;Academic Press, San Diego, CA.
23. Shackle G.L.S. Decision, Order and Time in Human Affairs. 1961;Cambridge University Press, Cambridge.
24. Shafer G. A Mathematical Theory of Evidence. 1976;Princeton University Press, Princeton, NJ.
25. Shilkret N. Maxitive measures and integration. Indagationes Mathematicae. 33:1971;109-116.
26. Sugeno M. The Theory of Fuzzy Integrals and Its Applications, PhD thesis. 1974;Tokyo Institute of Technology, Tokyo.
27. P. Walley, Coherent lower (and upper) probabilities, Statistics Research Report 22, University of Warwick, Coventry, 1981.
28. Walley P. Statistical Reasoning with Imprecise Probabilities. 1991;Chapman and Hall, London.
29. Walley P. Measures of uncertainty in expert systems. Artificial Intelligence. 83:1996;1-58.
30. P. Walley, G.de Cooman, A behavioural model for linguistic uncertainty, in: P.P. Wang (Ed.), Computing with Words, Wiley, New York, 1998, accepted for publication.
31. Wang P.-Z. Fuzzy contactability and fuzzy variables. Fuzzy Sets and Systems. 8:1982;81-92.
32. Wang Z., Klir G.J. Fuzzy Measure Theory. 1992;Plenum Press, New York, NY.
33. Zadeh L.A. Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems. 1:1978;3-28.