Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2014, Article ID 873498, 7 pages
http://dx.doi.org/10.1155/2014/873498
Research Article

Composite Gauss-Legendre Formulas for Solving Fuzzy Integration

1College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China
2Department of Public Courses, Gansu College of Traditional Chinese Medicine, Lanzhou 730000, China
3College of Chemistry and Chemical Engineering, Northwest Normal University, Lanzhou 730070, China

Received 9 December 2013; Revised 6 May 2014; Accepted 6 May 2014; Published 29 May 2014

Academic Editor: Valentina Emilia Balas

Copyright © 2014 Xiaobin Guo et al. 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. P. J. Davis and P. Rabinowitz, Methods of Numerical Integration, Academic Press, Orlando, Fla, USA, 2nd edition, 1984. View at MathSciNet
  2. R. L. Burden and J. Douglas, Numerical Analyisis, Thomson Learning, Boston, Mass, USA, 2001.
  3. B. Q. Liu, “Asymptotic analysis for some numerical integral formulas,” Communication on Applied Mathematics and Computation, vol. 14, no. 2, pp. 83–87, 2000. View at Google Scholar · View at MathSciNet
  4. B. Q. Liu, “Limit properties about a class of Gaussian integration formulas,” Journal of Engineering Mathematics, vol. 20, no. 4, pp. 137–139, 2003. View at Google Scholar · View at MathSciNet
  5. S. F. Qiu and Z. W. Wang, “Asymptotic properties of the intermediate point to numerical integration and its Applications,” Mathematics in Practice and Theory, vol. 36, no. 5, pp. 218–223, 2006. View at Google Scholar · View at MathSciNet
  6. Q. H. Zhao, “Correction formulas for numerical integral,” Mathematics in Practice and Theory, vol. 37, pp. 207–208, 2007. View at Google Scholar · View at Scopus
  7. H. J. Zimmerman, “Fuzzy sets theory and its applications,” Fuzzy Sets and Systems, vol. 24, pp. 319–330, 1987. View at Publisher · View at Google Scholar
  8. T. Allahviranloo, “Newton Cot's methods for integration of fuzzy functions,” Applied Mathematics and Computation, vol. 166, no. 2, pp. 339–348, 2005. View at Publisher · View at Google Scholar · View at Scopus
  9. T. Allahviranloo, “Romberg integration for fuzzy function,” Applied Mathematics and Computation, vol. 168, pp. 886–876, 2005. View at Google Scholar · View at MathSciNet
  10. T. Allahviranloo and M. Otadi, “Gaussian quadratures for approximate of fuzzy integrals,” Applied Mathematics and Computation, vol. 170, no. 2, pp. 874–885, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. T. Allahviranloo and M. Otadi, “Gaussian quadratures for approximate of fuzzy multiple integrals,” Applied Mathematics and Computation, vol. 172, no. 1, pp. 175–187, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. C. X. Wu and M. Ma, “On emdedding problem of fuzzy number space—part I,” Fuzzy Sets and Systems, vol. 44, no. 1, pp. 33–38, 1991. View at Publisher · View at Google Scholar · View at MathSciNet
  13. R. Goetschel, Jr. and W. Voxman, “Elementary calculus,” Fuzzy Sets and Systems, vol. 18, no. 1, pp. 31–43, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. M. L. Puri and D. A. Ralescu, “Fuzzy random variables,” Journal of Mathematical Analysis and Applications, vol. 114, no. 2, pp. 409–422, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. O. Kaleva, “Fuzzy differential equations,” Fuzzy Sets and Systems, vol. 24, no. 3, pp. 301–317, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. M. Matłoka, “On fuzzy integrals,” in Proceedings of the 2nd Polish Symposium on Interval and Fuzzy Mathematics, vol. 18, pp. 167–170, Plite Chnick Poznansk, 1987. View at MathSciNet
  17. J. Stoer and R. Bulirsch, Introduction to Numerical Analysis, Springer, New York, NY, USA, 1980. View at MathSciNet
  18. Q. Y. Li, N. C. Wang, and D. Y. Yi, Numerical Analyisis, Tsuing University Press, Springer, 2003.