Table of Contents Author Guidelines Submit a Manuscript
The Scientific World Journal
Volume 2014, Article ID 156203, 6 pages
http://dx.doi.org/10.1155/2014/156203
Research Article

The Solution of Fully Fuzzy Quadratic Equation Based on Optimization Theory

Department of Mathematics, Islamic Azad University, Science and Research Branch, Tehran, Iran

Received 16 April 2014; Accepted 17 May 2014; Published 9 June 2014

Academic Editor: Mohsen Vaez-ghasemi

Copyright © 2014 T. Allahviranloo and L. Gerami Moazam. 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. J. J. Buckley, “The fuzzy mathematics of finance,” Fuzzy Sets and Systems, vol. 21, no. 3, pp. 257–273, 1987. View at Google Scholar · View at Scopus
  2. M. Li Calzi, “Towards a general setting for the fuzzy mathematics of finance,” Fuzzy Sets and Systems, vol. 35, no. 3, pp. 265–280, 1990. View at Google Scholar · View at Scopus
  3. J. J. Buckley, “Solving fuzzy equations in economics and finance,” Fuzzy Sets and Systems, vol. 48, no. 3, pp. 289–296, 1992. View at Google Scholar · View at Scopus
  4. J. J. Buckley and Y. Qu, “Solving systems of linear fuzzy equations,” Fuzzy Sets and Systems, vol. 43, no. 1, pp. 33–43, 1991. View at Google Scholar · View at Scopus
  5. Q.-X. Li and S.-F. Liu, “The foundation of the grey matrix and the grey input-output analysis,” Applied Mathematical Modelling, vol. 32, no. 3, pp. 267–291, 2008. View at Publisher · View at Google Scholar · View at Scopus
  6. C. C. Wu and N. B. Chang, “Grey input-output analysis and its application for environmental cost allocation,” European Journal of Operational Research, vol. 145, no. 1, pp. 175–201, 2003. View at Publisher · View at Google Scholar · View at Scopus
  7. S.-H. Chen and X.-W. Yang, “Interval finite element method for beam structures,” Finite Elements in Analysis and Design, vol. 34, no. 1, pp. 75–88, 2000. View at Publisher · View at Google Scholar · View at Scopus
  8. P. Sevastjanov and L. Dymova, “A new method for solving interval and fuzzy equations: linear case,” Information Sciences, vol. 179, no. 7, pp. 925–937, 2009. View at Publisher · View at Google Scholar · View at Scopus
  9. J. J. Buckley and Y. Qu, “Solving linear and quadratic fuzzy equations,” Fuzzy Sets and Systems, vol. 38, no. 1, pp. 43–59, 1990. View at Google Scholar · View at Scopus
  10. J. J. Buckley and Y. Qu, “On using α-cuts to evaluate fuzzy equations,” Fuzzy Sets and Systems, vol. 38, no. 3, pp. 309–312, 1990. View at Google Scholar · View at Scopus
  11. J. J. Buckley and Y. Qu, “Solving fuzzy equations: a new solution concept,” Fuzzy Sets and Systems, vol. 39, no. 3, pp. 291–301, 1991. View at Google Scholar · View at Scopus
  12. S. Abbasbandy and M. Otadi, “Numerical solution of fuzzy polynomials by fuzzy neural network,” Applied Mathematics and Computation, vol. 181, no. 2, pp. 1084–1089, 2006. View at Publisher · View at Google Scholar · View at Scopus
  13. S. Abbasbandy and B. Asady, “Newton's method for solving fuzzy nonlinear equations,” Applied Mathematics and Computation, vol. 159, no. 2, pp. 349–356, 2004. View at Publisher · View at Google Scholar · View at Scopus
  14. T. Allahviranloo, M. Otadi, and M. Mosleh, “Iterative method for fuzzy equations,” Soft Computing, vol. 12, no. 10, pp. 935–939, 2008. View at Publisher · View at Google Scholar · View at Scopus
  15. J. J. Buckley and E. Eslami, “Neural net solutions to fuzzy problems: the quadratic equation,” Fuzzy Sets and Systems, vol. 86, no. 3, pp. 289–298, 1997. View at Google Scholar · View at Scopus
  16. J. J. Buckley, E. Eslami, and Y. Hayashi, “Solving fuzzy equations using neural nets,” Fuzzy Sets and Systems, vol. 86, no. 3, pp. 271–278, 1997. View at Google Scholar · View at Scopus
  17. D. Dubois and H. Prade, “Operations on fuzzy numbers,” Journal of Systems Sience, vol. 9, pp. 613–626, 1978. View at Google Scholar
  18. D. Dubois and H. Prade, Theory and Application, Fuzzy Sets and Systems, Academic Press, 1980.
  19. L. A. Zadeh, “Fuzzy sets,” Information and Control, vol. 8, no. 3, pp. 338–353, 1965. View at Google Scholar · View at Scopus
  20. H. J. Zimmermann, Fuzzy Set Theory and Its Applications, Kluwer Academic Press, Dordrecht, The Netherlands, 1991.
  21. W. Cong-Xin 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
  22. R. Goetschel Jr. 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
  23. L. Jaulin, M. Kieffir, O. Didrit, and E. Walter, Applied Interval Analysis, Springer, London, UK, 2001.
  24. R. E. Moore, Interval Analysis, Prentice-Hall, Englewood Cliffs, NJ, USA, 1966.
  25. P. Diamond and P. Kloeden, Metric Space of Fuzzy Sets, WordScientific, Singapore, 1994.