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http://dx.doi.org/10.7858/eamj.2011.27.3.289

EXISTENCE AND UNIQUENESS THEOREM FOR LINEAR FUZZY DIFFERENTIAL EQUATIONS  

You, Cuilian (College of Mathematics and Computer Science Hebei University)
Wang, Gensen (Hebei Jitie Group Company)
Publication Information
East Asian mathematical journal / v.27, no.3, 2011 , pp. 289-297 More about this Journal
Abstract
The introduction of fuzzy differential equation is to deal wit fuzzy dynamic systems. As classical differential equations, it is difficult to find the solutions to all fuzzy differential equations. In this paper an existence and uniqueness theorem for linear fuzzy differential equations is obtained. Moreover, the exact solution to linear fuzzy differential equation is given.
Keywords
fuzzy variable; fuzzy process; fuzzy integral;
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  • Reference
1 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.   DOI   ScienceOn
2 W. Dai, Reflection 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 O. Kaleva, Fuzzy differential equations, Fuzzy Sets and Systems 24(1987), no. 3, 301-317.   DOI   ScienceOn
5 O. Kaleva, The Cauchy problem for fuzzy differential equations, Fuzzy Sets and Systems 35(1987), no. 3, 389-396.
6 V. Lakshmikantham, and R. N. Mohapatra, Theory of fuzzy differentials equations and inclusions, Taylor & Francis, London, 2003.
7 Z. Qin, and X. Li, Option pricing formula for fuzzy financial market, Journal of uncertain Systems 2(2008), no. 1, 17-21.
8 C. You, Multi-dimensional Liu process, differential and integral, http://orsc.edu.cn/process/071015.pdf.
9 L. A. Zadeh, Fuzzy sets, Information and Control 8(1965), 338-353, 1965.   DOI
10 Y. Zhu, Fuzzy optimal control with application to portfolio selection, http://orsc.edu.cn/process/080117.pdf.
11 D.W. Pearson, A property of linear fuzzy differential equations, Applied Mathematics Letters 10(1997), no. 3, 99-103.   DOI   ScienceOn
12 B. Liu, Uncertainty Theory, Springer-Verlag, Berlin, 2004.
13 Z. Qin, On analytic functions of complx Liu process, http://orsc.edu.cn/process/071026.pdf.
14 O. Kaleva, A note on fuzzy differential equations, Nonlinear Analysis 64(2006), no. 5, 895-900.   DOI   ScienceOn
15 X. Li, and B. Liu, A suffcent and necessary condition for credibility measures, International Journal of Uncertainty, Fuzziness & Knowledge-Based Systems 14(2006), no. 5, 527-535.   DOI   ScienceOn
16 B. Liu, Uncertainty Theory, 2nd ed., Springer-Verlag, Berlin, 2007.
17 B. Liu, Fuzzy process, hybrid process and uncertain process, Journal of Uncertain Systems 2(2008), no. 1, 3-16.