Article
Full entry |
PDF
(0.5 MB)
Feedback
PDF
(0.5 MB)
Feedback
Keywords:
fuzzy number; fuzzy random variable; strong law of large numbers
fuzzy number; fuzzy random variable; strong law of large numbers
Summary:
In this paper, a general convergence theorem of fuzzy random variables is considered. Using this result, we can easily prove the recent result of Joo et al, which gives generalization of a strong law of large numbers for sums of stationary and ergodic processes to the case of fuzzy random variables. We also generalize the recent result of Kim, which is a strong law of large numbers for sums of levelwise independent and levelwise identically distributed fuzzy random variables.
References:
[1] Artstein Z., Vitale R. A.: A strong law of large numbers for random compact sets. Ann. Probab. 13 (1985), 307–309 MR 0770645
[2] Goetschel R., Voxman W.: Elementary fuzzy calculus. Fuzzy Sets and Systems 18 (1986), 31–43 DOI 10.1016/0165-0114(86)90026-6 | MR 0825618 | Zbl 0626.26014
[3] Hiai F.: Strong laws of large numbers for multivalued fuzzy random variables (Lecture Notes in Mathematics 1091). Springer–Verlag, Berlin 1984, pp. 160–172 DOI 10.1007/BFb0098809 | MR 0785583
[4] Hong D. H., Kim H. J.: Marcinkiewicz-type law of large numbers for fuzzy random variables. Fuzzy Sets and Systems 64 (1994), 387–393 DOI 10.1016/0165-0114(94)90161-9 | MR 1289544 | Zbl 0859.60003
[5] Inoue H.: A strong law of large numbers for fuzzy random sets. Fuzzy Sets and Systems 41 (1991), 285–291 DOI 10.1016/0165-0114(91)90132-A | MR 1111975 | Zbl 0737.60003
[6] Joo S. Y., Lee S. S., Yoo Y. H.: A strong law of large numbers for stationary fuzzy random variables. J. Korean Statist. Soc. 30 (2001), 153–161 MR 1892638
[7] Joo S. Y., Kim Y. K.: The Skorokhod topology on space of fuzzy numbers. Fuzzy Sets and Systems 111 (2000), 497–501 DOI 10.1016/S0165-0114(98)00185-7 | MR 1748559 | Zbl 0961.54024
[8] Kim Y. K.: A strong law of large numbers for fuzzy random variables. Fuzzy Sets and Systems 111 (2000), 319–323 MR 1748548
[9] Klement E. P., Puri M. L., Ralescu D. A.: Limit theorems for fuzzy random variables. Proc. Roy. Soc. London Ser. A 407 (1986), 171–182 MR 0861082 | Zbl 0605.60038
[10] Kruse R.: The strong law of large numbers for fuzzy random variables. Inform. Sci. 28 (1982), 233–241 DOI 10.1016/0020-0255(82)90049-4 | MR 0717301 | Zbl 0571.60039
[11] Miyakoshi M., Shimbo M.: A strong law of large numbers for fuzzy random variables. Fuzzy Sets and Systems 12 (1984), 133–142 DOI 10.1016/0165-0114(84)90033-2 | MR 0734945 | Zbl 0551.60035
[12] Molchanov I. S.: On strong law of large numbers for fuzzy random upper semi-continuous functions. J. Math. Anal. Appl. 235 (1999), 349–355 DOI 10.1006/jmaa.1999.6403 | MR 1758687
[13] Puri M. L., Ralescu D. A.: Strong law of large numbers for Banach space valued random sets. Ann. Probab. 11 (1983), 222–224 DOI 10.1214/aop/1176993671 | MR 0682812 | Zbl 0508.60021
[14] Puri M. L., Ralescu D. A.: Limit theorems for random compact set in Banach space. Math. Proc. Cambridge Philos. Soc. 97 (1985), 403–409 MR 0764504
[15] Puri M. L., Ralescu D. A.: Fuzzy random variables. J. Math. Anal. Appl. 114 (1986), 402–422 MR 0833596 | Zbl 0605.60038
[16] Rao R. R.: The law of large numbers for $D[0,1]$-valued random variables. Theor. Probab. Appl. 8 (1963), 70–74 DOI 10.1137/1108005 | Zbl 0122.13303
[17] Taylor R. L., Inoue H.: A strong law of large numbers for random sets in Banach spaces. Bull. Inst. Math., Academia Sinica 13 (1985), 403–409 MR 0866575 | Zbl 0585.60014
[18] Uemura T.: A law of large numbers for random sets. Fuzzy Sets and Systems 59 (1993), 181–188 DOI 10.1016/0165-0114(93)90197-P | MR 1253840 | Zbl 0788.60005
Search
Partner of
