The theory of fuzzy differential equation has been studied by many researchers. In this paper, the fuzzy differential equation is a different type of differential equations, its fuzziness is not only in the initial conditions and coefficients, but also in the driven process. This paper presents some methods to solve linear complex fuzzy differential equations, and proves some existence and uniqueness theorems of solution for complex fuzzy differential equations based on Lipschitz condition and linear growth condition.
AgarwalR., BaleanuD., NietoJ., TorresD. and ZhouY., A survey on fuzzy fractional differential and optimal control nonlocal evolution equations,, Journal of Computational and Applied Mathematics, In Press, (2017), https://org/10.1016/j.cam.2017.09.039
2.
ChenX. and QinZ., A new existence and uniqueness theorem for fuzzy differential equation, International Journal of Fuzzy Systems13(2) (2011), 148–151.
DingZ., MaM. and KandelA., Exsitence of the solutions of fuzzy differential equations with parameters, Information Sciences99(3-4) (1999), 205–217.
6.
DongS.L., VuH. and PhuD.N., The formulas of the solution for linear-order random fuzzy differential equations, Journal of Intelligent and Fuzzy Systems28(2) (2015), 795–807.
7.
KalevaO., Fuzzy differential equations, Fuzzy Sets and Systems24(3) (1987), 301–317.
8.
KalevaO., The Cauchy problem for fuzzy differential equations, Fuzzy Sets and Systems35(3) (1990), 389–396.
9.
KhastanA., NietoJ. and LópezR., Variation of constant formula for first order fuzzy differential equations, Fuzzy Sets and Systems177(1) (2011), 20–33.
10.
LiX. and LiuB., A sufficient and necessary condition for credibility measures, International Journal of Uncertainty, Fuzziness & Knowledge-Based Systems14(5) (2006), 527–535.
11.
LiuB. and LiuY., Expected value of fuzzy variable and fuzzy expected value models, IEEE Transactions on Fuzzy Systems10(4) (2002), 445–450.
LiuB., Fuzzy process, hybrid process and uncertain process, Journal of Uncertain Systems2(1) (2008), 3–16.
15.
PrakashP., NietoJ., SenthilvelavanS. and PriyaG., Fuzzy fractional initial value problem, Journal of Intelligent and Fuzzy Systems28(6) (2015), 2691–2704.
QinZ. and WenM., On analytic functions of complex Liu process, Journal of Intelligent and Fuzzy Systems28(4) (2015), 1627–1633.
18.
YiX., MiaoY., ZhouJ. and WangY., Some novel inequalities for fuzzy variables on the variance and its rational upper bound,Journal of Inequalities and Applications2016(41) (2016)18. doi:10.1186/s13660-016-0975-6
19.
YouC. and WangG., Properties of a new kind of fuzzy integral, Journal of Hebei University (Natural Science Edition)31(4) (2011), 337–340.
20.
YouC., MaH. and HuoH., A new kind of generalized fuzzy integrals, Journal of Nonlinear Science and Applications3(9) (2016), 1396–1402.
21.
YouC., WangW. and HuoH., Existence and uniqueness theorems for fuzzy differential equations, Journal of Uncertain Systems7(4) (2013), 303–315.
22.
YouC., HuoH. and WangW., Multi-dimensional Liu process, differential and integral, East Asian Mathematical Journal29(1) (2013), 13–22.
23.
YouC. and WangW., Some properties of complex fuzzy integral, Mathematical Problems in Engineering2015(Artical ID 290539) (2015), 7.
24.
YouC. and JiaoX., The credibility of Liu process arrives A before arrives B, Journal of Uncertain Systems10(2) (2016), 124–129.
25.
ZadehL.A., Fuzzy set, Information and Control8(3) (1965), 338–353.
