Uncertain information modeled by linguistic arguments and fuzzy memberships, a new multiple attribute decision making method, has been proposed with partly known attribute weight information. First we use linguistic arguments and fuzzy memberships to model uncertain information, then a linear programming by using the maximum deviation method is set up to determine the attribute weights, and next the TOPSIS is used to rank the alternatives. We apply the proposed methods to evaluating paintings in Xi'an subway to illustrate its efficiency and practical advantages. Numerical example substantiates the effectiveness of the proposed method.