Boundary valued problem; Fuzzy Partition; Weak Formulation of BVP; Weak Solution of BVP; Hilbert Space; Sobolev Space; Generalized Derivatives

The contribution proposes a new methodology to the construction of an approximate weak solution to the boundary valued problem (BVP). It uses the framework of the Galerkin method and formulates the approximate solution in terms of the inverse fuzzy transform with respect to a uniform fuzzy partition. We proposes technical details of the corresponding approximate solution in the form of a system of linear equation.