Browse > Article
http://dx.doi.org/10.5351/CKSS.2009.16.3.529

Weak Laws of Large Numbers for Weighted Sums of Fuzzy Random Variables  

Hyun, Young-Nam (Ministry for Health Welfare and Family Affairs)
Kim, Yun-Kyong (Department of Information & Communication Engineering, Dongshin University)
Kim, Young-Ju (Department of Statistics, Kangwon National University)
Joo, Sang-Yeol (Department of Statistics, Kangwon National University)
Publication Information
Communications for Statistical Applications and Methods / v.16, no.3, 2009 , pp. 529-540 More about this Journal
Abstract
In this paper, we present some results on weak laws of large numbers for weighted sums of fuzzy random variables taking values in the space of fuzzy numbers of the real line R. We first give improvements of WLLN for weighted sums of convex-compactly uniformly integrable fuzzy random variables obtained by Joo and Hyun (2005). And then, we consider the case that the averages of expectations of fuzzy random variables converges. As results, WLLN for weighted sums of convexly tight or identically distributed case is obtained.
Keywords
Fuzzy random variables; fuzzy numbers; weak laws of large numbers; tightness;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
연도 인용수 순위
1 Proske, F. N. and Puri, M. L. (2002). Strong law of large numbers for Banach space valued fuzzy random variables, Journal of Theoretical Probability, 15, 543-551   DOI
2 Colubi, A., Dominguez-Menchero, J. S., Lopez-Diaz, M. and Gil, M. A. (1999). A generalized strong law of large numbers, Probability Theory and Related Fields, 114, 401-417   DOI
3 Colubi, A., Dominguez-Menchero, J. S., Lopez-Diaz, M. and Korner, R. (2001). A method to derive strong laws of large numbers for random upper semicontinuous functions, Statistics & Probability Letters, 53, 269-275   DOI   ScienceOn
4 Feng, Y. (2002). An approach to generalize laws of large numbers for fuzzy random variables, Fuzzy Sets and Systems, 128, 237-245   DOI   ScienceOn
5 Guan, L. and Li, S. (2004). Laws of large numbers for weighted sums of fuzzy set-valued random variables, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 12, 811-825   DOI   ScienceOn
6 Goetschel, R. and Voxman, W. (1986). Elementary fuzzy calculus, Fuzzy Sets and Systems, 18, 31-43   DOI   ScienceOn
7 lnoue, H. (1991). A strong law of large numbers for fuzzy random sets, Fuzzy Sets and Systems, 41, 285-291   DOI   ScienceOn
8 Joo, S. Y. (2002). Strong law of large numbers for tight fuzzy random variables, Journal of the Korean Statistical Society, 31, 129-140   과학기술학회마을
9 Uemura, T. (1993). A law of large numbers for random sets, Fuzzy Sets and Systems, 59, 181-188   DOI   ScienceOn
10 Taylor, R. L., Seymour, L. and Chen, Y. (2001). Weak laws of large numbers for fuzzy random sets, Nonlinear Analysis, 47, 1245-1256   DOI   ScienceOn
11 Joo, S. Y. and Kim, Y. K. (2001). Kolmogorov's strong law of large numbers for fuzzy random variables, Fuzzy Sets and Systems, 120, 499-503   DOI   ScienceOn
12 Joo, S. Y. (2004). Weak laws of large numbers for fuzzy random variables, Fuzzy Sets and Systems, 147, 453-464   DOI   ScienceOn
13 Joo, S. Y. and Hyun, Y. N. (2005). Convergence in probability for weighted sums of fuzzy random variables, The Korean Communications in Statistics, 12, 275-283   과학기술학회마을   DOI
14 Joo, S. Y. and Kim, Y. K. (2000). The Skorokhod topology on the space of fuzzy numbers, Fuzzy Sets and Systems, 111, 497-501   DOI   ScienceOn
15 Joo, S. Y., Kim, Y. K. and Kwon, J. S. (2006). Strong convergence for weighted sums of fuzzy random sets, Infomation Sciences, 176, 1086-1099   DOI   ScienceOn
16 Kim, Y. K. (2002). Measurability for fuzzy valued functions, Fuzzy Sets and Systems, 129, 105-109   DOI   ScienceOn
17 Kim, Y. K. (2004). Compactness and convexity on the space of fuzzy sets Ⅱ, Nonlinear Analysis, 57, 639-653   DOI   ScienceOn
18 Kiement, E. P., Pun, M. L. and Ralescu, D. A. (1986). Limit theorems for fuzzy random variables, in Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 407, 171-182   DOI
19 Molchanov, I. (1999). On strong law of large numbers for random upper semicontinuous functions, Journal of Mathematical Analysis and Applications, 235, 349-355   DOI   ScienceOn