A random set characterization of possibility measures

Information Sciences

Volumn 168, Issue 1-4, 2004, Pages 51-75

  Miranda, Enrique ^a   Couso, Inés ^b   Gil, Pedro ^b  

^a UNIVERSIDAD REY JUAN CARLOS   (Spain)

^b UNIVERSITY OF OVIEDO   (Spain)

Author keywords

Condensability; Maxitive measures; Nested random sets; Possibility measures; Upper probabilities

Indexed keywords

COMPUTATIONAL METHODS; FINITE ELEMENT METHOD; FUNCTIONS; KNOWLEDGE BASED SYSTEMS; LINGUISTICS; PROBABILITY; RANDOM PROCESSES;

CONDENSABILITY; MAXITIVE MEASURES; NESTED RANDOM SETS; POSSIBILITY MEASURES; UPPER PROBABILITIES;

SET THEORY;

EID: 9544230691     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ins.2003.09.028     Document Type: Article

References (32)

1. Z. Arstein, Distribution of random sets and random selections, Israel Journal of Mathematics 46 (1983) 313-324.
2. I. Couso, S. Montes, P. Gil, The necessity of the strong α-cuts of a fuzzy set, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 9 (2001) 249-262.
3. G. de Cooman, Possibility theory I-III, International Journal of General Systems 25 (1997) 291-371.
4. G. de Cooman, D. Aeyels, Supremum preserving upper probabilities, Information Sciences 118 (1999) 173-212.
5. G. de Cooman, D. Aeyels, A random set description of a possibility measure and its natural extension, IEEE Transactions on Systems, Man and Cybernetics 30 (2000) 124-130.
6. A.P. Dempster, Upper and lower probabilities induced by a multivalued mapping, Annals of Mathematical Statistics 38 (1967) 325-339.
7. D. Denneberg, Non-additive measure and integral, Kluwer Academic, Dordrecht, 1994.
8. D. Dubois, S. Moral, H. Prade, A semantics for possibility theory based on likelihoods, Journal of Mathematical Analysis and Applications 305 (1997) 359-380.
9. D. Dubois, H. Prade, The mean value of a fuzzy number, Fuzzy Sets and Systems 24 (1987) 279-300.
10. D. Dubois, H. Prade, Possibility Theory, Plenum, New York, 1988.
11. D. Dubois, H. Prade, When upper probabilities are possibility measures, Fuzzy Sets and Systems 49 (1992) 65-74.
12. A.B. El Rayes, N. Morsi, Generalized possibility measures, Information Sciences 79 (1994) 201-222.
13. I.R. Goodman, Fuzzy sets as equivalence classes of possibility random sets, in: R.R. Yager (Ed.), Fuzzy Sets and Possibility Theory: Recent Developments, Pergamon, Oxford, 1982, pp. 327-343.
14. C. Hess, The distribution of unbounded random sets and the multivalued strong law of large numbers in nonreflexive banach spaces, Journal of Convex Analysis 6 (1999) 163-182.
15. C.J. Himmelberg, Measurable relations, Fundamenta Mathematicae 87 (1975) 53-72.
16. P.J. Huber, V. Strassen, Minimax tests and the Neyman-Pearson lemma for capacities, Annals of Statistics 1 (1973) 251-263.
17. A.S. Kechris, Classical Descriptive Set Theory, Springer Verlag, New York, 1995.
18. G. Mathèron, Random sets and integral geometry, Wiley, New York, 1975.
19. P.A. Meyer, Probabilitès et potentiel, Herrman, Paris, 1966.
20. E. Miranda, T. Couso, P. Gil, Relationships between possibility measures and nested random sets, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 10 (2002) 1-15.
21. Y.N. Moschovakis, Descriptive Set Theory, North-Holland, Amsterdam, 1980.
22. H.T. Nguyen, On random sets and belief functions, Journal of Mathematical Analysis and Applications 65 (1978) 531-542.
23. H.T. Nguyen, On modeling of linguistic information using random sets, Information Sciences 34 (1984) 265-274.
24. H.T. Nguyen, Some mathematical structures for computational information, Information Sciences 128 (2000) 67-89.
25. H.T. Nguyen, N.T. Nguyen, T. Wang, On capacity functionals in interval probabilities, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 5 (1997) 359-377.
26. T. Norberg, Random capacities and their distributions, Probability Theory and Related Fields 73 (1986) 281-297.
27. G.L.S. Shackle, Decision, Order and Time in Human Affairs, Cambridge University, Cambridge, 1961.
28. G. Shafer, A mathematical theory of evidence, Princeton University, New Jersey, 1976.
29. G. Shafer, Allocations of probability, Annals of Probability 7 (1979) 827-839.
30. N. Shilkret, Maxitive measures and integration, Indagationes Mathematicae 33 (1971) 109-116.
31. M. Sugeno, Theory of fuzzy integrals and its applications, Ph.D. Thesis, Tokyo Institute of Technology, 1974.
32. L.A. Zadeh, Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems 1 (1978) 3-28.