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An approximate homotopy direct reduction method is proposed and applied to two perturbed modified Korteweg-de Vries (mKdV) equations with fourth-order dispersion and second-order dissipation. The similarity reduction equations are derived to arbitrary orders. The method is valid not only for single soliton solutions but also for the Painleve Ⅱ waves and periodic waves expressed by Jacobi elliptic functions for both fourth-order dispersion and second-order dissipation. The method is also valid for strong perturbations.