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The main objective of this paper is to introduce interval two-points fuzzy boundary value problems, in which the fuzziness course when the coefficients of the governing ordinary differential equation and/or the boundary conditions includes fuzzy numbers of either triangular or trapezoidal types. Such equations will be solved by introducing the concept of α – level sets, α ∈ [0,1] to treat the fuzzy ordinary differential equation into two nonfuzzy ordinary differential equations, which are corresponds to the lower and upper solutions of the interval fuzzy solution. The shooting method is applied to solve the resultant equations in both cases, linear and nonlinear. [ABSTRACT FROM AUTHOR]