MODIFIED K-STEP METHOD FOR SOLVING FUZZY INITIAL VALUE PROBLEMS

bibitem{abb1} S. Abbasbandy, J. J. Nieto and M. Alavi, {it Tuning of reachable set in one dimensional fuzzy differential inclusions}, Chaos, Solitons Fractals, {bf 26} (2005), 1337-1341.

bibitem{abb2} S. Abbasbandy, T. Allahviranloo, O. López-Pouso and J. J. Nieto, {it Numerical methods for fuzzy differential inclusions}, Comput. Math. Appl., {bf 48} (2004), 1633-1641.

bibitem{abb3} S. Abbasbandy and T. Allahviranloo, {it Numerical solutions of fuzzy differential equations by Taylor method}, , Journal of Computational Methods in Applied Mathematics, {bf 2} (2002), 113-124.

bibitem{alh1} T. Allahviranloo, N. Ahmady and E. Ahmady, {it Numerical solution of fuzzy differential equations by predictor-–corrector method}, Information Sciences, {bf 177} (2007), 1633-1647.

bibitem{alh2} T. Allahviranloo, N. Ahmady and E. Ahmady, {it Improved predictor–corrector method for solving fuzzy initial
value problems}, Information Sciences, {bf 179} (2009), 945-955.

bibitem{bede1} B. Bede, {it Note on "Numerical solutions of fuzzy differential equations by predictor-–corrector method"}, Information Sciences, {bf 178} (2008), 1917-1922.
bibitem{bede2} B. Bede and S. G. Gal, {it Generalizations of the differentiability of fuzzy umber valued functions with applications to fuzzy differential equation}, Fuzzy Sets and Systems, {bf 151} (2005), 581-599.

bibitem{bede3} B. Bede, J. Imre, C. Rudas and L. Attila, {it First order linear fuzzy differential equations under generalized differentiability}, Information Sciences, {bf 177} (2007), 3627-3635.

bibitem{buk1} J. J. Buckley and T. Feuring, {it Fuzzy differential equations}, Fuzzy Sets and Systems, {bf 110} (2000), 43-54.

bibitem{can1} Y. Chalco-Cano and H. Roman-Flores, {it On new solutions of fuzzy differential equations}, Chaos, Solitons and Fractals, {bf 38} (2008), 112-119.

bibitem{can2} Y. Chalco-Cano, H. Roman-Flores, M. A. Rojas-Medar, O. Saavedra and M. Jiménez-Gamero, {it The extension principle and a decomposition of
fuzzy sets}, Information Sciences, {bf 177} (2007), 5394-5403.

bibitem{chen1} C. K. Chen and S. H. Ho, {it Solving partial differential equations by two-dimensional differential transform method}, Applied Mathematics and Computation, {bf 106} (1999), 171-179.

bibitem{cho} Y. J. Cho and H. Y. Lan, {it The existence of solutions for the nonlinear first order fuzzy differential equations with discontinuous conditions}, Dynamics Continuous Discrete Inpulsive Systems Ser. AMath. Anal., {bf 14} (2007), 873-884.

bibitem{con} W. Congxin and S. Shiji, {it Exitance theorem to the Cauchy problem of fuzzy differential equations under compactance-type conditions}, Information Sciences, {bf 108} (1993), 123-134.

bibitem{dia1} P. Diamond, {it Time-dependent differential inclusions, cocycle attractors and fuzzy differential equations}, IEEE Trans. Fuzzy Systems, {bf 7} (1999), 734-740.

bibitem{dia2} P. Diamond, {it Brief note on the variation of constants formula for fuzzy differential equations}, Fuzzy Sets and Systems, {bf 129} (2002), 65-71.

bibitem{ding} Z. Ding, M. Ma and A. Kandel, {it Existence of solutions of fuzzy differential equations with parameters}, Information Sciences, {bf 99} (1997), 205-217.
bibitem{dub} D. Dubois and H. Prade, {it Towards fuzzy differential calculus: part 3, differentiation}, Fuzzy Sets and Systems, {bf 8} (1982), 225-233.

bibitem{fei} W. Fei, {it Existence and uniqueness of solution for fuzzy random differential equations with non-Lipschitz coefficients}, Information Sciences, {bf 177} (2007), 329-4337.

bibitem{geo1} R. Goetschel and W. Voxman, {it Topological properties of fuzzy number}, Fuzzy Sets and Systems, {bf 10} (1983), 87-99.

bibitem{geo2} R. Goetschel and W. Voxman, {it Elementary fuzzy calculus}, Fuzzy sets and Systems, {bf 18} (1986), 31-43.

bibitem{ijfs1} M. S. Hashemi, M. K. Mirnia and S. Shahmorad, {it Solving fuzzy linear systems by using the Schur complement when coefficient matrix is an M-matrix}, Iranian Journal of Fuzzy Systems, {bf 5}textbf{(3)} (2008), 15-30.

bibitem{ijfs2}H. Hassanpour, H. R. Maleki and M. A. Yaghoobi, {it A note on evaluation of fuzzy linear regression models by comparing membership functions}, Iranian Journal of Fuzzy Systems, {bf 6}textbf{(2)} (2009), 1-8.

bibitem{hen} P. Henrici, {it Discrete vatiablr methods in ordinary differential equations}, Wiley, New York, 1962.

bibitem{jang} M. J. Jang, C. L. Chen and Y. C. Liy, {it On solving the initial-value problems using the differential transformation method}, Applied Mathematics and Computation, {bf 115} (2000), 145-160.

bibitem{kal1} O. Kaleva, {it Fuzzy differential equations}, Fuzzy Sets and Systems, {bf 24} (1987), 301-317.

bibitem{kal2} O. Kaleva, {it The Cauchy problem for fuzzy differential equations}, Fuzzy Sets and Systems, {bf 35} (1990), 389-396.

bibitem{kal3} O. Kaleva, {it A note on fuzzy differential equations}, Nonlinear Analysis, {bf 64} (2006), 895-900.

bibitem{lak} V. Lakshmikantham and S. Leela, {it Differential and integral inequalities}, Academic Press, New York, {bf1} (1969).

bibitem{lo1} R. R. Lopez, {it Comparison results for fuzzy differential equations}, Information Sciences, {bf 178} (2008), 1756-1779.

bibitem{ma} M. Ma, M. Friedman and A. Kandel, {it Numerical solutions of fuzzy differential equations}, Fuzzy Sets and Systems, {bf 105} (1999) 133–-138.

bibitem{ma1} M. Ma, M. Friedman and A. Kandel, {it A new approach for defuzzification}, Fuzzy Sets and Systems, {bf 111} (2000), 351-356.

bibitem{org} D. '{O}Regan, V. Lakshmikantham and J. Nieto, {it Initial and boundary value problems for fuzzy differential equations}, Nonlinear Anal., {bf 54} (2003), 405-415.

bibitem{miz} M. T. Mizukoshi, L. C. Barros, Y. Chalco-Cano, H. Roman-Flores and R. C. Bassanezi, {it Fuzzy differential equations and the extension principle}, Information Sciences, {bf 177} (2007), 3627-3635.

bibitem{pall} S. C. Palligkinis, G. Stefanidou and P. Efraimidi, {it Runge-Kutta methods for fuzzy differential equations}, Applied Mathematics and Computation, {bf 209} (2009), 97-105.

bibitem{pap} G. Papaschinopoulos, G. Stefanidou and P. Efraimidi, {it Existence uniqueness and asymptotic behavior of the solutions of a fuzzy differential equation with piecewise constant argument}, Information Sciences, {bf 177} (2007), 3855-3870.

bibitem{pur} M. L. Puri and D. A. Ralescu, {it Differentials of fuzzy functions}, Journal of Mathematical Analysis and Applications, {bf 91} (1983), 552-558.

bibitem{ijfs3} R. Saadati, S. Sedghi and H. Zhou, {it A common fixed point theorem for $psi$-weakly commuting maps in L-fuzzy metric spaces}, Iranian Journal of Fuzzy Systems, {bf 5}textbf{(1)} (2008), 47-54.

bibitem{ijfs4} M. R. Safi, H. R. Maleki and E. Zaeimazad, {it A note on Zimmermann method for solving fuzzy linear programming problems}, Iranian Journal of Fuzzy Systems, {bf 4}textbf{(2)} (2007), 31-46.

bibitem{sei} S. Seikkala, {it On the fuzzy initial value problem}, Fuzzy Sets and Systems, {bf 24} (1987), 319-330.

bibitem{ijfs5} A. K. Shaymal and M. Pal, {it Triangular fuzzy matrices}, Iranian Journal of Fuzzy Systems, {bf 4}textbf{(1)} (2007), 75-87.

bibitem{song} S. Song, L. Guo and C. Feng, {it Global existence of solutions to fuzzy differential equations}, Fuzzy Sets and Systems, {bf 115} (2000), 371-376.