| Title:
|
A convergence of fuzzy random variables (English) |
| Author:
|
Hong, Dug Hun |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
39 |
| Issue:
|
3 |
| Year:
|
2003 |
| Pages:
|
[275]-280 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
fuzzy number |
| Keyword:
|
fuzzy random variable |
| Keyword:
|
strong law of large numbers |
| MSC:
|
60B12 |
| idZBL:
|
Zbl 1249.60007 |
| idMR:
|
MR1995730 |
| . |
| Date available:
|
2009-09-24T19:53:32Z |
| Last updated:
|
2015-03-23 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135528 |
| . |
| Reference:
|
[1] Artstein Z., Vitale R. A.: A strong law of large numbers for random compact sets.Ann. Probab. 13 (1985), 307–309 MR 0770645 |
| Reference:
|
[2] Goetschel R., Voxman W.: Elementary fuzzy calculus.Fuzzy Sets and Systems 18 (1986), 31–43 Zbl 0626.26014, MR 0825618, 10.1016/0165-0114(86)90026-6 |
| Reference:
|
[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 MR 0785583, 10.1007/BFb0098809 |
| Reference:
|
[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 Zbl 0859.60003, MR 1289544, 10.1016/0165-0114(94)90161-9 |
| Reference:
|
[5] Inoue H.: A strong law of large numbers for fuzzy random sets.Fuzzy Sets and Systems 41 (1991), 285–291 Zbl 0737.60003, MR 1111975, 10.1016/0165-0114(91)90132-A |
| Reference:
|
[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 |
| Reference:
|
[7] Joo S. Y., Kim Y. K.: The Skorokhod topology on space of fuzzy numbers.Fuzzy Sets and Systems 111 (2000), 497–501 Zbl 0961.54024, MR 1748559, 10.1016/S0165-0114(98)00185-7 |
| Reference:
|
[8] Kim Y. K.: A strong law of large numbers for fuzzy random variables.Fuzzy Sets and Systems 111 (2000), 319–323 MR 1748548 |
| Reference:
|
[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 Zbl 0605.60038, MR 0861082 |
| Reference:
|
[10] Kruse R.: The strong law of large numbers for fuzzy random variables.Inform. Sci. 28 (1982), 233–241 Zbl 0571.60039, MR 0717301, 10.1016/0020-0255(82)90049-4 |
| Reference:
|
[11] Miyakoshi M., Shimbo M.: A strong law of large numbers for fuzzy random variables.Fuzzy Sets and Systems 12 (1984), 133–142 Zbl 0551.60035, MR 0734945, 10.1016/0165-0114(84)90033-2 |
| Reference:
|
[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 MR 1758687, 10.1006/jmaa.1999.6403 |
| Reference:
|
[13] Puri M. L., Ralescu D. A.: Strong law of large numbers for Banach space valued random sets.Ann. Probab. 11 (1983), 222–224 Zbl 0508.60021, MR 0682812, 10.1214/aop/1176993671 |
| Reference:
|
[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 |
| Reference:
|
[15] Puri M. L., Ralescu D. A.: Fuzzy random variables.J. Math. Anal. Appl. 114 (1986), 402–422 Zbl 0605.60038, MR 0833596 |
| Reference:
|
[16] Rao R. R.: The law of large numbers for $D[0,1]$-valued random variables.Theor. Probab. Appl. 8 (1963), 70–74 Zbl 0122.13303, 10.1137/1108005 |
| Reference:
|
[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 Zbl 0585.60014, MR 0866575 |
| Reference:
|
[18] Uemura T.: A law of large numbers for random sets.Fuzzy Sets and Systems 59 (1993), 181–188 Zbl 0788.60005, MR 1253840, 10.1016/0165-0114(93)90197-P |
| . |