About this Journal Submit a Manuscript Table of Contents
Journal of Applied Mathematics
Volume 2013 (2013), Article ID 178209, 7 pages
http://dx.doi.org/10.1155/2013/178209
Research Article

Fuzzy Approximate Solution of Positive Fully Fuzzy Linear Matrix Equations

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

Received 22 November 2012; Accepted 19 January 2013

Academic Editor: Panayiotis J. Psarrakos

Copyright © 2013 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, “Fuzzy sets,” Information and Computation, vol. 8, pp. 338–353, 1965. View at Zentralblatt MATH · View at MathSciNet
  2. L. A. Zadeh, “The concept of a linguistic variable and its application to approximate reasoning. I,” Information Science, vol. 8, pp. 199–249, 1975. View at Zentralblatt MATH · View at MathSciNet
  3. D. Dubois and H. Prade, “Operations on fuzzy numbers,” International Journal of Systems Science, vol. 9, no. 6, pp. 613–626, 1978. View at Zentralblatt MATH · View at MathSciNet
  4. S. Nahmias, “Fuzzy variables,” Fuzzy Sets and Systems. An International Journal in Information Science and Engineering, vol. 1, no. 2, pp. 97–110, 1978. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. 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 Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. R. Goetschel, Jr. and W. Voxman, “Elementary fuzzy 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
  7. C. X. Wu and M. Ma, “Embedding problem of fuzzy number space. I,” Fuzzy Sets and Systems, vol. 44, no. 1, pp. 33–38, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. C. X. Wu and M. Ma, “Embedding problem of fuzzy number space. III,” Fuzzy Sets and Systems, vol. 46, no. 2, pp. 281–286, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. M. Friedman, M. Ming, and A. Kandel, “Fuzzy linear systems,” Fuzzy Sets and Systems, vol. 96, no. 2, pp. 201–209, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. 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 Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. T. Allahviranloo and M. Ghanbari, “On the algebraic solution of fuzzy linear systems based on interval theory,” Applied Mathematical Modelling, vol. 36, no. 11, pp. 5360–5379, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  12. 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 Zentralblatt MATH · View at MathSciNet
  13. T. Allahviranloo and M. Ghanbari, “A new approach to obtain algebraic solution of interval linear systems,” Soft Computing, vol. 16, no. 1, pp. 121–133, 2012. View at Publisher · View at Google Scholar
  14. 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 Zentralblatt MATH · View at MathSciNet
  15. 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 Zentralblatt MATH · View at MathSciNet
  16. 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 Zentralblatt MATH · View at MathSciNet
  17. R. Nuraei, T. Allahviranloo, and M. Ghanbari, “Finding an inner estimation of the so- lution set of a fuzzy linear system,” Applied Mathematical Modelling, vol. 37, no. 7, pp. 5148–5161, 2013. View at Publisher · View at Google Scholar
  18. 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 Zentralblatt MATH · View at MathSciNet
  19. 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 Zentralblatt MATH · View at MathSciNet
  20. S. Abbasbandy, M. Otadi, and M. Mosleh, “Minimal solution of general dual fuzzy linear systems,” Chaos, Solitons & Fractals, vol. 37, no. 4, pp. 1113–1124, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. 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 Zentralblatt MATH · View at MathSciNet
  22. 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 Zentralblatt MATH · View at MathSciNet
  23. 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 Zentralblatt MATH · View at MathSciNet
  24. 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 Zentralblatt MATH · View at MathSciNet
  25. M. Dehghan, B. Hashemi, and M. Ghatee, “Solution of the fully fuzzy linear systems using iterative techniques,” Chaos, Solitons & Fractals, vol. 34, no. 2, pp. 316–336, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  26. T. Allahviranloo, N. Mikaeilvand, and M. Barkhordary, “Fuzzy linear matrix equation,” Fuzzy Optimization and Decision Making, vol. 8, no. 2, pp. 165–177, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  27. X. Guo and Z. 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 Zentralblatt MATH · View at MathSciNet
  28. Z. Gong and X. 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 Zentralblatt MATH · View at MathSciNet
  29. X. Guo and D. Shang, “Fuzzy symmetric solutions of fuzzy matrix equations,” Advances in Fuzzy Systems, vol. 2012, Article ID 318069, 9 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  30. T. Allahviranloo, M. Ghanbari, A. A. Hosseinzadeh, E. Haghi, and R. Nuraei, “A note on ‘Fuzzy linear systems’,” Fuzzy Sets and Systems, vol. 177, pp. 87–92, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  31. C.-T. Yeh, “Weighted semi-trapezoidal approximations of fuzzy numbers,” Fuzzy Sets and Systems, vol. 165, pp. 61–80, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  32. T. Allahviranloo, F. H. Lotfi, M. K. Kiasari, and M. Khezerloo, “On the fuzzy solution of LR fuzzy linear systems,” Applied Mathematical Modelling, vol. 37, no. 3, pp. 1170–1176, 2013. View at Publisher · View at Google Scholar
  33. M. Otadi and M. Mosleh, “Solving fully fuzzy matrix equations,” Applied Mathematical Modelling, vol. 36, no. 12, pp. 6114–6121, 2012. View at Publisher · View at Google Scholar
  34. X. B. Guo and D. Q. Shang, “Approximate solutions of LR fuzzy Sylvester matrix equations,” Journal of Applied Mathematics. In press.
  35. A. Ben-Israel and T. N. E. Greville, Generalized Inverses: Theory and Applications, Springer-Verlag, New York, NY, USA, 2nd edition, 2003. View at MathSciNet
  36. A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Academic Press, New York, NY, USA, 1979. View at MathSciNet
  37. R. J. Plemmons, “Regular nonnegative matrices,” Proceedings of the American Mathematical Society, vol. 39, pp. 26–32, 1973. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet