When fuzzy measures are upper envelopes of probability measures

Fuzzy Sets and Systems

Volumn 138, Issue 3, 2003, Pages 455-468

  Krätschmer, Volker ^a  

^a SAARLAND UNIVERSITY   (Germany)

Author keywords

Coherent upper probability; Fuzzy measures; Inner extensions; Inner premeasures; Inner regularity; Semiregularity

Indexed keywords

ALGEBRA; NUMERICAL ANALYSIS; PROBABILITY;

INNER REGULARITY;

FUZZY SETS;

EID: 0042121449     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0165-0114(02)00463-3     Document Type: Article

References (21)

1. Adamski W. Capacitylike set functions and upper envelopes of measures. Math. Ann. 229:1977;237-244.
2. Bauer H. Maß- und Integrationstheorie. 2nd Edition:1992;de Gruyter, Berlin, New York.
3. Cohn D.L. Measure Theory. 1997;Birkhäuser, Boston.
4. Denneberg D. Non-additive Measure and Integral. 1994;Kluwer Academic Publishers, Dordrecht.
5. Dubois D., Prade H. When upper probabilities are possibility measures. Fuzzy Sets and Systems. 49:1992;65-74.
6. Dubois D., Prade H. Bayesian conditioning in possibility theory. Fuzzy Sets and Systems. 92:1997;223-240.
7. Goodman I.R., Nguyen H.T. Uncertainty Models for Knowledge-based Systems. 1985;North-Holland, Amsterdam.
8. Huber P.J., Strassen V. Minimax tests and the Neyman-Pearson lemma for capacities. Ann. Statist. 1:1973;252-263.
9. Kindler J. A Mazur-Orlicz type theorem for submodular set functions. J. Math. Anal. Appl. 120:1986;533-546.
10. Kisynski J. On the generation of tight measures. Studia Math. 30:1968;141-151.
11. König H. Measure and Integration. 1997;Springer, Berlin.
12. König H. Measure and integration. mutual generation of outer and inner premeasures Ann. Univ. Sarav. 9:1998;99-122.
13. H. König, Ausgewählte Kapitel aus Mass und Integral: Nicht-additive Integration, Lecture at University of Saarland, Winter Term 1998/99.
14. König H. Upper envelopes of inner premeasures. Ann. Inst. Fourier, Grenoble. 50(2):2000;401-422.
15. Oxtoby J.C. Maß und Kategorie. 1971;Springer, Berlin, Heidelberg, New York.
16. Parthasarathy K.R. Probability Measures on Metric Spaces. 1967;Academic Press, New York, London.
17. Tops ø e F. Compactness in spaces of measures. Studia Math. 36:1970;195-212.
18. Tops ø e F. Topology and Measure. Lecture Notes in Mathematics. Vol. 133:1970;Springer, Berlin, Heidelberg, New York.
19. F. Tops ø e, On construction of measures, in: Proceedings of the Conference on Topology and Measure I (Zinnowitz 1974) Part 2, Ernst-Moritz-Arndt Universität Greifswald, 1978, pp. 343-381.
20. Walley P. Statistical Reasoning with Imprecise Probabilities. 1991;Chapman & Hall, London.
21. Wang Z., Klir G.J. Fuzzy Measure Theory. 1992;Plenum, New York, London.