Table of Contents Author Guidelines Submit a Manuscript
Advances in Fuzzy Systems
Volume 2012, Article ID 318069, 9 pages
http://dx.doi.org/10.1155/2012/318069
Research Article

Fuzzy Symmetric Solutions of Fuzzy Matrix Equations

1College of Mathematics and Information Science, Northwest Normal University, Lanzhou 730070, China
2Department of Public Courses, Gansu College of Chinese Medicine, Lanzhou 730000, China

Received 3 April 2012; Accepted 29 April 2012

Academic Editor: F. Herrera

Copyright © 2012 Xiaobin Guo and Dequan Shang. 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. L. A. Zadeh, “The concept of a linguistic variable and its application to approximate reasoning-I,” Information Sciences, vol. 8, no. 3, pp. 199–249, 1975. View at Google Scholar · View at Scopus
  2. D. Dubois and H. Prade, “Operations on fuzzy numbers,” Journal of Systems Science, vol. 9, no. 6, pp. 613–626, 1978. View at Google Scholar
  3. S. Nahmias, “Fuzzy variables,” Fuzzy Sets and Systems, vol. 1, no. 2, pp. 97–110, 1978. View at Google Scholar · View at Scopus
  4. M. L. Puri and D. A. Ralescu, “Differentials of fuzzy functions,” Journal of Mathematical Analysis and Applications, vol. 91, no. 2, pp. 552–558, 1983. View at Google Scholar · View at Scopus
  5. R. Goetschel and W. Voxman, “Elementary fuzzy calculus,” Fuzzy Sets and Systems, vol. 18, no. 1, pp. 31–43, 1986. View at Google Scholar · View at Scopus
  6. C.-X. Wu and M. Ming, “Embedding problem of fuzzy number space: part I,” Fuzzy Sets and Systems, vol. 44, no. 1, pp. 33–38, 1991. View at Google Scholar · View at Scopus
  7. C. X. Wu and M. Ming, “Embedding problem of fuzzy number space: part III,” Fuzzy Sets and Systems, vol. 46, no. 2, pp. 281–286, 1992. View at Google Scholar · View at Scopus
  8. M. Friedman, M. Ming, and A. Kandel, “Fuzzy linear systems,” Fuzzy Sets and Systems, vol. 96, no. 2, pp. 201–209, 1998. View at Google Scholar · View at Scopus
  9. M. Ma, M. Friedman, and A. Kandel, “Duality in fuzzy linear systems,” Fuzzy Sets and Systems, vol. 109, no. 1, pp. 55–58, 2000. View at Google Scholar · View at Scopus
  10. T. Allahviranloo, M. Friedman, M. Ma, and A. Kandel, “A comment on fuzzy linear systems (multiple letters),” Fuzzy Sets and Systems, vol. 140, no. 3, pp. 559–561, 2003. View at Publisher · View at Google Scholar · View at Scopus
  11. T. Allahviranloo, “Numerical methods for fuzzy system of linear equations,” Applied Mathematics and Computation, vol. 155, no. 2, pp. 493–502, 2004. View at Publisher · View at Google Scholar · View at Scopus
  12. T. Allahviranloo, “Successive over relaxation iterative method for fuzzy system of linear equations,” Applied Mathematics and Computation, vol. 162, no. 1, pp. 189–196, 2005. View at Publisher · View at Google Scholar · View at Scopus
  13. T. Allahviranloo, “The Adomian decomposition method for fuzzy system of linear equations,” Applied Mathematics and Computation, vol. 163, no. 2, pp. 553–563, 2005. View at Publisher · View at Google Scholar · View at Scopus
  14. S. Abbasbandy, R. Ezzati, and A. Jafarian, “LU decomposition method for solving fuzzy system of linear equations,” Applied Mathematics and Computation, vol. 172, no. 1, pp. 633–643, 2006. View at Publisher · View at Google Scholar · View at Scopus
  15. S. Abbasbandy, A. Jafarian, and R. Ezzati, “Conjugate gradient method for fuzzy symmetric positive definite system of linear equations,” Applied Mathematics and Computation, vol. 171, no. 2, pp. 1184–1191, 2005. View at Publisher · View at Google Scholar · View at Scopus
  16. S. Abbasbandy, M. Otadi, and M. Mosleh, “Minimal solution of general dual fuzzy linear systems,” Chaos, Solitons and Fractals, vol. 37, no. 4, pp. 1113–1124, 2008. View at Publisher · View at Google Scholar · View at Scopus
  17. B. Asady, S. Abbasbandy, and M. Alavi, “Fuzzy general linear systems,” Applied Mathematics and Computation, vol. 169, no. 1, pp. 34–40, 2005. View at Publisher · View at Google Scholar · View at Scopus
  18. K. Wang and B. Zheng, “Inconsistent fuzzy linear systems,” Applied Mathematics and Computation, vol. 181, no. 2, pp. 973–981, 2006. View at Publisher · View at Google Scholar · View at Scopus
  19. B. Zheng and K. Wang, “General fuzzy linear systems,” Applied Mathematics and Computation, vol. 181, no. 2, pp. 1276–1286, 2006. View at Publisher · View at Google Scholar · View at Scopus
  20. M. Dehghan and B. Hashemi, “Iterative solution of fuzzy linear systems,” Applied Mathematics and Computation, vol. 175, no. 1, pp. 645–674, 2006. View at Publisher · View at Google Scholar · View at Scopus
  21. M. Dehghan, B. Hashemi, and M. Ghatee, “Solution of the fully fuzzy linear systems using iterative techniques,” Chaos, Solitons and Fractals, vol. 34, no. 2, pp. 316–336, 2007. View at Publisher · View at Google Scholar · View at Scopus
  22. X. B. Guo and Z. T. Gong, “Block gaussian elimination methods for fuzzy matrix equations,” International Journal of Pure and Applied Mathematics, vol. 58, no. 2, pp. 157–168, 2010. View at Google Scholar · View at Scopus
  23. X. B. Guo and Z. T. Gong, “Undetermined coefficients method for solving semi-fuzzy matrix equations,” in Proceedings of 8th InternationalConference on Machine Learning and Cybernetics (ICMLC '10), pp. 596–600, Qingdao, China, July 2010. View at Publisher · View at Google Scholar · View at Scopus
  24. Z. T. Gong and X. B. Guo, “Inconsistent fuzzy matrix equations and its fuzzy least squares solutions,” Applied Mathematical Modelling, vol. 35, no. 3, pp. 1456–1469, 2011. View at Publisher · View at Google Scholar · View at Scopus
  25. T. Allahviranloo and S. Salahshour, “Fuzzy symmetric solutions of fuzzy linear systems,” Journal of Computational and Applied Mathematics, vol. 235, no. 16, pp. 4545–4553, 2011. View at Publisher · View at Google Scholar · View at Scopus
  26. T. Allahviranloo, S. Salahshour, and M. Khezerloo, “Maximal- and minimal symmetric solutions of fully fuzzy linear systems,” Journal of Computational and Applied Mathematics, vol. 235, no. 16, pp. 4652–4662, 2011. View at Publisher · View at Google Scholar · View at Scopus
  27. X. D. Zhang, Matrix Analysis and Applications, Tsinghua and Springer Press, Beijing, China, 2004.
  28. R. B. Kearfott, Regorous Global Search: Continuous Problems, Kluwer Academic Publishers, Amsterdam, The Netherlands, 1996.