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The focus of this paper is on two kinds of parametric linear programming with fuzzy variables (PFVLP) which can describe the behaviors of the optimal value under parametric perturbations of the objective function coefficients and the right-hand side of constraint equations in a FVLP, respectively. Firstly, for these two kinds of PFVLP, we investigate how to obtain an optimal basis of them from an optimal basis of their corresponding FVLP based on the parameters in them. Then, two algorithms are proposed to solve these two problems. 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