DOI QR코드

DOI QR Code

MULTI-DIMENSIONAL LIU PROCESS, INTEGRAL AND DIFFERENTIAL

  • You, Cuilian (College of Mathematics and Computer Science, Hebei University) ;
  • Huo, Huae (College of Mathematics and Computer Science, Hebei University) ;
  • Wang, Weiqing (College of Mathematics and Computer Science, Hebei University)
  • Received : 2012.03.30
  • Accepted : 2012.12.17
  • Published : 2013.01.31

Abstract

As a fuzzy counterpart of stochastic calculus, fuzzy calculus including Liu integral and Liu formula were introduced. In order to deal with the problems with several fuzzy dynamic factors, Liu process, Liu integral and Liu formula are extended to the case of multi-dimensional in this paper.

Keywords

References

  1. J. J. Buckley, and T. Feuring, Fuzzy differential equations, Fuzzy Sets and Systems 110(2000), 43-54. https://doi.org/10.1016/S0165-0114(98)00141-9
  2. W. Dai, Re-ection principle of Liu process, http://orsc.edu.cn/process/071110.pdf.
  3. Z. Ding, M. Ma and A. Kandel, Existence of the solutions of fuzzy differential equations with parameters, Information Sciences 99(1999), no. 3-4, 1205-1217.
  4. J Gao, Credibiltistic option pricing: A new model, http://orsc.edu.cn/process/071124.pdf.
  5. X Gao, Option pricing formula for Gao's stock model, http://orsc.edu.cn/ process/080326.pdf.
  6. X Gao X, and X Chen, Option pricing formula for generalized stock models, http://orsc.edu.cn/process/080317.pdf.
  7. O. Kaleva, Fuzzy differential equations, Fuzzy Sets and Systems, 24(1987), no. 3, 301-317. https://doi.org/10.1016/0165-0114(87)90029-7
  8. O. Kaleva, The Cauchy problem for fuzzy differential equations, Fuzzy Sets and Systems 35(1987), no. 3, 389-396.
  9. O. Kaleva, A note on fuzzy differential equations, Nonlinear Analysis 64(2006), no. 5, 895-900. https://doi.org/10.1016/j.na.2005.01.003
  10. X. Li, and B. Liu, A sufficent and necessary condition for credibility measures, International Journal of Uncertainty, Fuzziness & Knowledge-Based Systems 14(2006), no. 5, 527-535. https://doi.org/10.1142/S0218488506004175
  11. B. Liu, Uncertainty Theory, Springer-Verlag, Berlin, 2004.
  12. B. Liu, Uncertainty Theory, 2nd ed., Springer-Verlag, Berlin, 2007.
  13. B. Liu, Fuzzy process, hybrid process and uncertain process, Journal of Uncertain Systems 2(2008), no. 1, 3-16.
  14. B. Liu B, and Y. K. Liu, Expected value of fuzzy variable and fuzzy expected value models, IEEE Transactions on Fuzzy Systems 10(2002), no. 4, 445-450. https://doi.org/10.1109/TFUZZ.2002.800692
  15. V. Lakshmikantham, and R. N. Mohapatra, Theory of fuzzy differentials equations and inclusions, Taylor & Francis, London, 2003.
  16. Pearson DW, A property of linear fuzzy differential equations, Applied Mathematics Letters 14(1997), no. 3, 99-103.
  17. Peng J, A general stock model for fuzzy markets, Journal of uncertain Systems 2(2008), no. 4, 248-254.
  18. Qin Z, On analytic functions of complx Liu process, http://orsc.edu.cn/process /071026.pdf.
  19. Qin Z, A new fuzzy control system with application to production planning problem, http://orsc.edu.cn/process/080412.pdf.
  20. Qin Z, and Li X, Option pricing formula for fuzzy financial market, Journal of uncertain Systems 2(2008), no. 1, 17-21.
  21. Qin Z, and Li X, Expected payoff of trading strategies iInvolving European options for fuzzy financial market, http://orsc.edu.cn/process/080407.pdf.
  22. L. A. Zadeh, Fuzzy sets, Information and Control 8(1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
  23. Y. Zhu, Fuzzy optimal control with application to portfolio selection, http://orsc.edu.cn/process /080117.pdf.

Cited by

  1. The Mean Value Theorem of a New Kind of Fuzzy Integral vol.614, pp.1662-7482, 2014, https://doi.org/10.4028/www.scientific.net/AMM.614.401
  2. Properties of Reflected Liu Process at the Origin vol.614, pp.1662-7482, 2014, https://doi.org/10.4028/www.scientific.net/AMM.614.421
  3. Some Properties of Complex Fuzzy Process vol.614, pp.1662-7482, 2014, https://doi.org/10.4028/www.scientific.net/AMM.614.425
  4. Option Pricing Formula for a New Stock Model vol.07, pp.10, 2018, https://doi.org/10.12677/AAM.2018.710142
  5. Some Properties of Complex Fuzzy Integral vol.2015, pp.None, 2015, https://doi.org/10.1155/2015/290539
  6. Existence and uniqueness theorems for complex fuzzy differential equation vol.34, pp.4, 2013, https://doi.org/10.3233/jifs-171231
  7. Stability in credibility for fuzzy differential equation vol.36, pp.1, 2013, https://doi.org/10.3233/jifs-181150
  8. Convergence of numerical methods for fuzzy differential equations vol.38, pp.4, 2013, https://doi.org/10.3233/jifs-191856