About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 820141, 6 pages
http://dx.doi.org/10.1155/2013/820141
Research Article

A New Characterization of Compact Sets in Fuzzy Number Spaces

1Department of Mathematics, Jimei University, Xiamen 361021, China
2Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China

Received 14 August 2013; Accepted 18 October 2013

Academic Editor: Juan Carlos Cortés López

Copyright © 2013 Huan Huang and Congxin Wu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. H. Huang and C. Wu, “Approximation capabilities of multilayer fuzzy neural networks on the set of fuzzy-valued functions,” Information Sciences, vol. 179, no. 16, pp. 2762–2773, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  2. P. Diamond and P. Kloeden, Metric Spaces of Fuzzy Sets—Theory and Applications, World Scientific, River Edge, NJ, USA, 1994. View at MathSciNet
  3. B. M. Ghil, S. Y. Joo, and Y. K. Kim, “A characterization of compact subsets of fuzzy number space,” Fuzzy Sets and Systems, vol. 123, no. 2, pp. 191–195, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  4. O. Kaleva, “On the convergence of fuzzy sets,” Fuzzy Sets and Systems, vol. 17, no. 1, pp. 53–65, 1985. View at Publisher · View at Google Scholar · View at MathSciNet
  5. M. Rojas-Medar and H. Román-Flores, “On the equivalence of convergences of fuzzy sets,” Fuzzy Sets and Systems, vol. 80, no. 2, pp. 217–224, 1996. View at Publisher · View at Google Scholar · View at MathSciNet
  6. J.-X. Fang and H. Huang, “Some properties of the level convergence topology on fuzzy number space En,” Fuzzy Sets and Systems, vol. 140, no. 3, pp. 509–517, 2003, Theme: Topology. View at Publisher · View at Google Scholar · View at MathSciNet
  7. J.-X. Fang and H. Huang, “On the level convergence of a sequence of fuzzy numbers,” Fuzzy Sets and Systems, vol. 147, no. 3, pp. 417–435, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  8. T. Fan, “On the compactness of fuzzy numbers with sendograph metric,” Fuzzy Sets and Systems, vol. 143, no. 3, pp. 471–477, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  9. G. H. Greco and M. P. Moschen, “Supremum metric and relatively compact sets of fuzzy sets,” Nonlinear Analysis. Theory, Methods & Applications, vol. 64, no. 6, pp. 1325–1335, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  10. Ö. Talo and F. Başar, “On the slowly decreasing sequences of fuzzy numbers,” Abstract and Applied Analysis, vol. 2013, Article ID 891986, 7 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  11. H. Huang, “Some notes on Zadeh's extensions,” Information Sciences, vol. 180, no. 19, pp. 3806–3813, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  12. C. Wu and M. Ma, The Basic of Fuzzy Analysis, National Defence Industry Press, Beijing, China, 1991, (Chinese).
  13. H. Huang and C. Wu, “Approximation of fuzzy functions by regular fuzzy neural networks,” Fuzzy Sets and Systems, vol. 177, pp. 60–79, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  14. J.-X. Fang and Q.-Y. Xue, “Some properties of the space of fuzzy-valued continuous functions on a compact set,” Fuzzy Sets and Systems, vol. 160, no. 11, pp. 1620–1631, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  15. M. L. Puri and D. A. Ralescu, “The concept of normality for fuzzy random variables,” The Annals of Probability, vol. 13, no. 4, pp. 1373–1379, 1985. View at MathSciNet
  16. E. Klein and A. C. Thompson, Theory of Correspondences, John Wiley & Sons, New York, NY, USA, 1984. View at MathSciNet
  17. H. Román-Flores, “The compactness of E(X),” Applied Mathematics Letters, vol. 11, no. 2, pp. 13–17, 1998. View at Publisher · View at Google Scholar · View at MathSciNet
  18. J. L. Kelley, General topology, Springer, New York, NY, USA, 1975. View at MathSciNet