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In this article, we proposed a new representation of type-2 fuzzy numbers called generalized type-2 fuzzy numbers. Dirichlet, Neumann and Mixed kind of boundary value problem have been considered with the boundary condition as generalized type-2 fuzzy numbers. The theorems have been developed for solving generalized type-2 fuzzy boundary value problems. In every case, suitable examples have also been provided. The solutions graph for fuzzy cases has been plotted and discuss for understanding of the nature of fuzzy solutions.