References
- Z. Artstein and J. C. Hansen, Convexification in limit laws of random sets in Banach spaces Ann. Probab. 13 (1985), 307-309. https://doi.org/10.1214/aop/1176993083
- Z. Artstein and R. A. Vitale, A strong law of large numbers for random compact sets, Ann. Probab. 3 (1975) 879-882. https://doi.org/10.1214/aop/1176996275
- A. Colubi, J. S. Dominguez-Menchero, M. Lopez-Diaz, and M. A. Gil, A generalized strong law of large numbers, Probab. Theory Related Fields 114 (1999), 401-417. https://doi.org/10.1007/s004400050229
- A. Colubi, J. S. Dominguez-Menchero, M. Lopez-Diaz, and R. Korner, A method to derive strong laws of large numbers for random upper semicontinuous functions, Statist. Probab. Lett. 53 (2001), 269-275. https://doi.org/10.1016/S0167-7152(01)00057-8
-
A. Colubi, J. S. Domingeuz-Menchero, M. Lopez-Diaz and D. Ralescu, A
$D_E$ [0, 1] representation of random upper semicontinuous functions, Proc. Amer. Math. Soc. 130 (2002), 3237-3242. https://doi.org/10.1090/S0002-9939-02-06429-8 - G. Debreu, Integration of correspondences, Proc. 5th Berkeley Symp. Math. Statist. Prob. II 2 (1966), 351-372.
- Y. Feng, An approach to generalize law of large numbers for fuzzy random variables, Fuzzy Sets and Systems 128 (2002), 237-245. https://doi.org/10.1016/S0165-0114(01)00142-7
- K. A. Fu and L. X. Zhang, Strong laws of large numbers for arrays of row-wise independent random compact sets and fuzzy random sets, Fuzzy Sets and Systems 159 (2008), 3360-3368. https://doi.org/10.1016/j.fss.2008.06.012
- G. H. Greco and M. P. Moschen, Supremum metric and relatively compact sets of fuzzy sets, Nonlinear Anal. 64 (2006), 1325-1335. https://doi.org/10.1016/j.na.2005.06.038
- L. Guan and S. Li, Laws of large numbers for weighted sums of fuzzy set valued random variables, Inter. J. Uncertainty Fuzziness Knowl. Based Syst. 12 (2004), 811-825. https://doi.org/10.1142/S0218488504003223
- H. Inoue, A strong law of large numbers for fuzzy random sets, Fuzzy Sets and Systems 41 (1991), 285-291. https://doi.org/10.1016/0165-0114(91)90132-A
- S. Y. Joo, Strong law of large numbers for tight fuzzy random variables, J. Korean Statist. Soc. 31 (2002), 129-140.
- S. Y. Joo and Y. K. Kim, Topological properties on the space of fuzzy sets, J. Math. Anal. Appl. 246 (2000), 576-590. https://doi.org/10.1006/jmaa.2000.6820
- S. Y. Joo, Y. K. Kim and J. S. Kwon, Strong Convergence for weighted sums of fuzzy random sets, Inform. Sci. 176 (2006), 1086-1099. https://doi.org/10.1016/j.ins.2005.02.002
- Y. K. Kim, Strong law of large numbers for random upper-semicontinuous fuzzy sets, Bull. Korean Math. Soc. 39 (2002), 511-526.
- Y. K. Kim, Measurability for fuzzy valued functions, Fuzzy Sets and Systems, 129 (2002), 105-109. 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 407 (1986), 171-182. https://doi.org/10.1098/rspa.1986.0091
- S. Li and Y. Ogura, Strong laws of large numbers for independent fuzzy set valued random variables, Fuzzy Sets and Systems, 157 (2006), 2569-2578. https://doi.org/10.1016/j.fss.2003.06.011
- S. Li, Y. Ogura and V. Kreinovich, Limit theorems and Applications of set valued and fuzzy set valued random variables, Kluwer Academic Publishers, 2002.
- I. S. Molchanov, On strong laws of large numbers for random upper- semicontinuous functions, J. Math. Anal. Appl. 235 (1999), 349-355. https://doi.org/10.1006/jmaa.1999.6403
- F. Proske and M. L. Puri, Strong laws of large numbers for Banach space valued fuzzy random variables, J. Theoret. Probab. 15 (2002), 543-551. https://doi.org/10.1023/A:1014823228848
- M. L. Puri and D. A. Ralescu, A strong law of large numbers for Banach space valued random sets, Ann. Probab. 11 (1983), 222-224. https://doi.org/10.1214/aop/1176993671
- M. L. Puri and D. A. Ralescu, Fuzzy random variables, J. Math. Anal. Appl. 114 (1986), 402-422.
- R. L. Taylor and H. Inoue, A strong law of large numbers for random sets in Banach space, Bull. Inst. Math. Acad. Sin. 13 (1985), 403-409.
- R. L. Taylor and H. Inoue, Laws of large numbers for random sets, Random sets: Theory and Applications, 1985, IMA 97, Springer. New York, 347-366.
- R. L. Taylor and H. Inoue, A strong law of large numbers for random sets in Banach spaces, Bull. Inst. Math. Acad. Sin. 13 (1985), 403-409.
- T. Uemura, A law of large numbers for random sets, Fuzzy Sets and Systems, 59 (1993), 181-188. https://doi.org/10.1016/0165-0114(93)90197-P
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