Separability for graph convergence of sequences of fuzzy-valued random variables

Fuzzy Sets and Systems

Volumn 123, Issue 1, 2001, Pages 19-27

  Ogura, Yukio ^a   Li, Shoumei ^b  

^a SAGA UNIVERSITY   (Japan)

^b BEIJING UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Convergence in graph; Fuzzy valued random variable; Set valued random variable; The Hausdorff convergence; The Kuratowski Mosco convergence

Indexed keywords

EID: 0035480416     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0165-0114(00)00092-0     Document Type: Article

References (26)

1. Z. Artstein R.A. Vitale A strong law of large numbers for random compact sets Ann. Probab. 3 1975 879 882
2. J. Ban Radon-Nikodym theorem and conditional expectation of fuzzy valued measure Fuzzy Sets and Systems 34 1990 383 392
3. G. Beer Topologies on Closed and Closed Convex Sets, Mathematics and Its Applications 1993 Kluwer Academic Publishers Dordrecht, Holland
4. G. Beer R.T. Rockafellar R. Wets A characterization of epi-convergence in terms of convergence of level sets Proc. Amer. Math. Soc. 116 1992 753 761
5. G. Beer J.M. Borwein Mosco and slice convergence of level sets and graphs of linear functionals J. Math. Anal. Appl. 175 1993 53 67
6. C. Castaing M. Valadier Convex Analysis and Measurable Multifunctions, Lecture Notes in Mathematics Vol. 580 1977 Springer Berlin
7. A. Colubi M. Lopez J.S. Dominguez-Menchero M.A. Gil A generalized strong law of large numbers Probab. Theory Related Fields 114 1999 401 417
8. N. Cressie A strong limit theorem for random sets Suppl. Adv. Appl. Probab. 10 1978 36 46
9. E. Giné H.G. Hahn J. Zinn Limit theorems for random sets: an application of probability in Banach space results A. Beck K. Jacobs Probability in Banach Spaces 4, Lecture Notes in Mathematics Vol. 990 1983 Springer Berlin 112 135
10. C. Hess On multivalued martingales whose values may be unbounded martingale selectors and Mosco convergence J. Multivariate Anal. 39 1991 175 201
11. C. Hess Multivalued strong laws of large numbers in the slice topology, application to integrands Set Valued Anal. 2 1994 183 205
12. C. Hess, On the almost sure convergence of sequences of random sets: martingales and extensions, to appear.
13. F. Hiai H. Umegaki Integrals, conditional expectations and martingales of multivalued functions J. Multivariate Anal. 7 1977 149 182
14. F. Hiai Convergence of conditional expectations and strong laws of large numbers for multivalued random variables Trans. Amer. Math. Soc. 291 1985 613 627
15. H. Inoue R.L. Taylor A SLLN for arrays of rowwise exchangeable fuzzy random variables Stochastic Anal. Appl. 13 1995 461 470
16. E.P. Klement L.M. Puri D.A. Ralescu Limit theorems for fuzzy random variables Proc. Roy. Soc. London 407 1986 171 182
17. E. Klein A.C. Thompson Theory of Correspondences Including Applications to Mathematical Economics 1984 Wiley New York
18. S. Li Y. Ogura Fuzzy random variables, conditional expectations and fuzzy martingales J. Fuzzy Math. 4 1996 905 927
19. S. Li Y. Ogura Convergence of set valued and fuzzy valued martingales Fuzzy Sets and Systems 101 1999 453 461
20. S. Li Y. Ogura Convergence of set valued sub- and super-martingales in the Kuratowski–Mosco sense Ann. Probab. 26 3 1998 1384 1402
21. S. Li, Y. Ogura, Convergence in graph for fuzzy valued martingales and smartingales, in: M.A. Gil, Bertoluzza, D.A. Ralescu (Eds.), Statistical Modeling, Analysis, and Management of Fuzzy Data, to appear.
22. F.N. Proske, M.L. Puri, Limit theorems for fuzzy random variables, to appear.
23. M.L. Puri D.A. Ralescu A strong law of large numbers for Banach space valued random variables Ann. Probab. 11 1983 222 224
24. M.L. Puri D.A. Ralescu Fuzzy random variables J. Math. Anal. Appl. 114 1986 406 422
25. M.L. Puri D.A. Ralescu Convergence theorem for fuzzy martingales J. Math. Anal. Appl. 160 1991 107 121
26. R.L. Taylor H. Inoue A strong law of large numbers for random sets in Banach spaces Bull. Inst. Math. Acad. Sinica 13 1985 403 409