References
- P. Billingsley, Convergence of probability measures, Second Edition, Wiley, New York, 1999
-
A. Colubi, J. S. Domingeuz-Menchero, M. L
$\acute{o}$$\acute{i}$$D_{E}$ [0, 1] representation of random upper semicontinuous functions", Proc. Amer. Math. Soc. vol. 130, pp. 3237-3242, 2002 https://doi.org/10.1090/S0002-9939-02-06429-8 - G. Debreu, "Integration of correspondences", Proc. 5th Berkeley Symp. Math. Statist. Prob. vol. 2, pp. 351-372, 1966
- P. Diamond and P. Kloeden, "Metric space of fuzzy sets", Fuzzy Sets and Systems vol. 35, pp. 241-249, 1990 https://doi.org/10.1016/0165-0114(90)90197-E
- P. Diamond and P. Kloeden, Metric spaces of fuzzy sets: Theory and Applications, World Scientific, Singapore, 1994
- T. Fan, "On the compactness of fuzzy numbers with sendograph metric", Fuzzy Sets and Systems vol. 143, pp. 471-477, 2004 https://doi.org/10.1016/S0165-0114(03)00142-8
- G. H. Greco, "Sendograph metric and relatively compact sets of fuzzy sets", Fuzzy Sets and Systems vol. 157, pp. 286-291, 2006 https://doi.org/10.1016/j.fss.2005.07.003
- G. H. Greco and M. P. Moschen, "Supremum metric and relatively compact sets of fuzzy sets", Nonlinear Anal. vol. 64, pp. 1325-1335, 2006 https://doi.org/10.1016/j.na.2005.06.038
- H. Inoue, "A strong law of large numbers for fuzzy random sets", Fuzzy Sets and Systems vol. 41, pp. 285-291, 1991 https://doi.org/10.1016/0165-0114(91)90132-A
- S. Y. Joo and Y. K. Kim, "Topological properties on the space of fuzzy sets", J. Math. Anal. Appl. vol. 246, pp. 576-590, 2000 https://doi.org/10.1006/jmaa.2000.6820
- S. Y. Joo and Y. K. Kim, "Weak convergence and tightness for fuzzy random variables", Indian J. Pure Appl. Math. vol. 35, pp. 793-809, 2004
- S. Y. Joo, G. S. Choi, J. S. Kwon and Y. K. Kim, "Some results on convergence in distribution for fuzzy random sets", J. Korean Math. Soc. vol. 42, pp.171-189, 2005 https://doi.org/10.4134/JKMS.2005.42.1.171
- S. Y. Joo, Y. K. Kim, J. S. Kwon and G. S. Choi, "Convergence in distribution for level-continuous fuzzy random sets", Fuzzy Sets and Systems vol. 157, pp. 243-255, 2006 https://doi.org/10.1016/j.fss.2005.07.001
- D.S. Kim and Y. K. Kim, "Some properties of a new metric on the space of fuzzy numbers", Fuzzy Sets and Systems vol. 145, pp. 395-410, 2004 https://doi.org/10.1016/S0165-0114(03)00281-1
- Y. K. Kim, "Measurability for fuzzy valued functions", Fuzzy Sets and Systems vol. 129, pp. 105-109, 2002 https://doi.org/10.1016/S0165-0114(01)00121-X
- E. P. Klement, M. L. Puri and D. A. Ralescu, "Limit theorems for fuzzy random variables", Proc. Roy. Soc. Lond. Ser. A vol.407, pp. 171-182, 1986 https://doi.org/10.1098/rspa.1986.0091
- S. Li, Y. Ogura and V. Kreinovich, Limit Theorems and Applications of Set-valued and Fuzzy Setvalued Random Variables, Kluwer Academic Publishers, Dordrecht, 2002
-
M. Ming, "Some notes on the characterization of compact sets in (
$E^{n}$ ,$d_{p}$ )", Fuzzy Sets and Systems vol. 56, pp. 297-301, 1993 https://doi.org/10.1016/0165-0114(93)90209-Z - Yu. V. Prokhorov, "Convergence of random processes and limit theorems in probability theory", Theory Probab. Appl. vol. 1, pp. 157-214, 1956 https://doi.org/10.1137/1101016
- M. L. Puri and D. A. Ralescu, "Fuzzy random variables", J. Math. Anal. Appl. vol. 114, pp. 402-422, 1986
-
C.Wu and Z. Zhao, "Some notes on the characterization of compact sets of fuzzy sets with
$L_{p}$ metric", Fuzzy Sets and Systems vol. 159, pp. 2104-2115, 2008 https://doi.org/10.1016/j.fss.2007.11.010