Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2013, Article ID 406240, 12 pages
http://dx.doi.org/10.1155/2013/406240
Research Article

Approximate Solution of th-Order Fuzzy Linear Differential 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 29 January 2013; Accepted 19 March 2013

Academic Editor: Ker-Wei Yu

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. S. S. L. Chang and L. A. Zadeh, “On fuzzy mapping and control,” vol. SMC-2, pp. 330–340, 1972. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. D. Dubois and H. Prade, “Operations on fuzzy numbers,” International Journal of Systems Science, vol. 9, no. 6, pp. 613–626, 1978. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. 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
  4. 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
  5. R. P. Agarwal, D. O'Regan, and V. Lakshmikantham, “Viability theory and fuzzy differential equations,” Fuzzy Sets and Systems, vol. 151, no. 3, pp. 563–580, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. V. A. Baĭdosov, “Fuzzy differential inclusions,” Journal of Applied Mathematics and Mechanics, vol. 54, no. 1, pp. 8–13, 1990. View at Publisher · View at Google Scholar · View at MathSciNet
  7. K. Kirkiakidis and A. Tzez, “Fuzzy logic adaptive sliding control design with an application to air-handling systems,” in Proceedings of the European Congress on Intelligent Techniques and Soft Computing (EUFIT '95), pp. 954–959, 1995.
  8. M. T. Mizukoshi, L. C. Barros, Y. Chalco-Cano, H. Román-Flores, and R. C. Bassanezi, “Fuzzy differential equations and the extension principle,” Information Sciences, vol. 177, no. 17, pp. 3627–3635, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. J. J. Nieto and R. Rodríguez-López, “Bounded solutions for fuzzy differential and integral equations,” Chaos, Solitons and Fractals, vol. 27, no. 5, pp. 1376–1386, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  10. J. J. Nieto, R. Rodríguez-López, and D. Franco, “Linear first-order fuzzy differential equations,” International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, vol. 14, no. 6, pp. 687–709, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. R. Rodríguez-López and T. Feuring, “Monotone method for fuzzy differential equations,” Fuzzy Sets and Systems, vol. 159, no. 16, pp. 2047–2076, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. R. Palm and D. Driankov, “Fuzzy inputs,” Fuzzy Sets and Systems, vol. 70, no. 2-3, pp. 315–335, 1995. View at Publisher · View at Google Scholar · View at MathSciNet
  13. B. S. Moon, “A tuning algorithm for the fuzzy logic controllers,” in Proceedings of the European Congress on Intelligent Techniques and Soft Computing (EUFIT '95), pp. 620–624, 1995.
  14. C. X. Wu and S. J Shih, “Existence theorem to the Cauchy problem of fuzzy differential equations under compactness-type conditions,” Information Sciences, vol. 108, no. 1–4, pp. 123–134, 1998. View at Publisher · View at Google Scholar · View at MathSciNet
  15. C. X. Wu and G. Wang, “Convergence of sequences of fuzzy numbers and fixed point theorems for increasing fuzzy mappings and application,” Fuzzy Sets and Systems, vol. 130, no. 3, pp. 383–390, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. A. Kandel and W. J. Byatt, “Fuzzy sets, Fuzzy algebra and fuzzy statistics,” in Proceedings of the IEEE, pp. 1619–1639, 1978. View at MathSciNet
  17. A. Kandel and W. J. Byatt, “Fuzzy differential equations,” in Proceedings of the international Conference on Cybernetics and Society, pp. 1213–1216, Tokyo, Japan, 1987.
  18. A. Kandel and W. J. Byatt, “Fuzzy processes,” Fuzzy Sets and Systems, vol. 4, no. 2, pp. 117–152, 1980. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. A. Kandel, “Fuzzy dynamical systems and the nature of their solutions,” in Fuzzy Sets: Theory and Application To Policy Analysis and Information Systems, P. P. Wang and S. K. Chang, Eds., pp. 93–122, Plenum Press, New York, NY, USA, 1980. View at Google Scholar
  20. 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
  21. O. Kaleva, “The Cauchy problem for fuzzy differential equations,” Fuzzy Sets and Systems, vol. 35, no. 3, pp. 389–396, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. S. Seikkala, “On the fuzzy initial value problem,” Fuzzy Sets and Systems, vol. 24, no. 3, pp. 319–330, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. H. Ouyang and Y. Wu, “On fuzzy differential equations,” Fuzzy Sets and Systems, vol. 32, no. 3, pp. 321–325, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. P. E. Kloeden, “Remarks on Peano-like theorems for fuzzy differential equations,” Fuzzy Sets and Systems, vol. 44, no. 1, pp. 161–164, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. M. D. Wu, “Linear fuzzy differential equation systems on R1,” Journal of Fuzzy Mathematics, vol. 2, pp. 51–56, 1988 (Chinese). View at Google Scholar
  26. J.-P. Aubin, “Fuzzy differential inclusions,” Problems of Control and Information Theory, vol. 19, no. 1, pp. 55–57, 1990. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  27. J.-P. Aubin, “A survey of viability theory,” SIAM Journal on Control and Optimization, vol. 28, no. 4, pp. 749–788, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  28. R. P. Leland, “Fuzzy differential systems and Malliavin calculus,” Fuzzy Sets and Systems, vol. 70, no. 1, pp. 59–73, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  29. G. Colombo and V. Křivan, “Fuzzy differential inclusions and nonprobabilistic likelihood,” Dynamic Systems and Applications, vol. 1, no. 4, pp. 419–439, 1992. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  30. S. Abbasbandy and T. Allahviranloo, “Numerical solutions of fuzzy differential equations by Taylor method,” Computational Methods in Applied Mathematics, vol. 2, no. 2, pp. 113–124, 2002. View at Google Scholar · View at MathSciNet
  31. S. Abbasbandy, T. A. Viranloo, Ó. López-Pouso, and J. J. Nieto, “Numerical methods for fuzzy differential inclusions,” Computers & Mathematics with Applications, vol. 48, no. 10-11, pp. 1633–1641, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  32. T. Allahviranloo, N. Ahmady, and E. Ahmady, “Numerical solution of fuzzy differential equations by predictor-corrector method,” Information Sciences, vol. 177, no. 7, pp. 1633–1647, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  33. T. Allahviranloo, S. Abbasbandy, N. Ahmady, and E. Ahmady, “Improved predictor-corrector method for solving fuzzy initial value problems,” Information Sciencesl, vol. 179, no. 7, pp. 945–955, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  34. J. J. Buckley and T. Feuring, “Fuzzy initial value problem for nth-order linear differential equations,” Fuzzy Sets and Systems, vol. 121, no. 2, pp. 247–255, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  35. T. Allahviranloo, E. Ahmady, and N. Ahmady, “Nth-order fuzzy linear differential equations,” Information Sciences, vol. 178, no. 5, pp. 1309–1324, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  36. P. Diamond, “Stability and periodicity in fuzzy differential equations,” IEEE Transactions on Fuzzy Systems, vol. 8, pp. 583–590, 2000. View at Google Scholar
  37. B. R. Fang, J. D. Zhou, Y. M. Li, and Y. M., Matrix Theory, Tsinghua university and Springer press, BeiJing, China, 2004.