Strong Law of Large Numbers for Tight Fuzzy Random Variables

  • Joo, Sang Yeol (Department of Statistics, Kangwon National University)
  • Published : 2002.03.01

Abstract

In this paper, we obtain a strong law of large numbers for convex tight random elements taking values in the space of fuzzy numbers in R.

References

  1. The Annals of Probability v.13 Artstein, Z.; Vitale, R. A. https://doi.org/10.1214/aop/1176993083
  2. Convergence of Probability Measure (Second edition) Billingsley, P.
  3. The Annals of Probability v.7 Laws of large numbers for D〔0,1〕 Daffer, P. Z.; Taylor, R. L. https://doi.org/10.1214/aop/1176995150
  4. Fuzzy Sets and Systems v.123 A characterization of compact subsets of fuzzy number space Ghil, B. M.; Joo, S. Y.; Kim, Y. K. https://doi.org/10.1016/S0165-0114(00)00097-X
  5. Fuzzy Sets and Systems v.18 Elementary fuzzy calculus Goetschel, R.; Voxman, W. https://doi.org/10.1016/0165-0114(86)90026-6
  6. Fuzzy Sets and Systems v.41 A strong law of large numbers for fuzzy random sets Inoue, J. H. https://doi.org/10.1016/0165-0114(91)90132-A
  7. Fuzzy Sets and Systems v.111 The Skorokhod topology on space of fuzzy numbers Joo, S. Y.; Kim, Y. K. https://doi.org/10.1016/S0165-0114(98)00185-7
  8. Fuzzy Sets and Systems v.120 Kolmogorov's strong law of large numbers for fuzzy random variables Joo, S. Y.; Kim, Y. K. https://doi.org/10.1016/S0165-0114(99)00140-2
  9. Journal of the Korean Statistical Society v.30 A strong law of large numbers for stationary fuzzy random variables Joo, S. Y.; Lee, S. S.; Yoo, Y. H.
  10. Fuzzy Sets and Systems v.111 A strong law of large numbers for fuzzy random variables Kim, Y. K. https://doi.org/10.1016/S0165-0114(97)00392-8
  11. Fuzzy Sets and Systems, to appear Measurability of fuzzy valued functions Kim, Y. K.
  12. Proceedings of the Royal Society v.A407 Limit theorems for fuzzy random variables Klement, E. P.; Puri, M. L.; Ralescu, D. A.
  13. Journal of Mathematical Analysis and Applications v.235 On strong law of large numbers for random upper semicontinuous functions Molchanov, I. S. https://doi.org/10.1006/jmaa.1999.6403
  14. The Annals of Probability v.11 Strong law of large numbers for Banach space valued random sets Puri, M. L.; Ralescu, D. A. https://doi.org/10.1214/aop/1176993671
  15. Journal of Mathematical Analysis and Applications v.114 Fuzzy random variables Puri, M. L.; Ralescu, D. A.