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The problem of the fuzzy multi-attribute decision making (FMADM) is studied, in which the information about attribute weights is known partly and the decision maker has preference information on alternatives in the form of fuzzy complementary judgment matrix. The attribute values and the preference values given by the decision maker(s) are in the form of triangular fuzzy numbers. A minimizing the maximum difference model is introduced to assess the weights of attributes in a FMADM problem, which integrate subjective fuzzy preference relations and objective fuzzy decision information. The additive weighting method is used to obtain the fuzzy overall values of alternatives. By using the priority formula of triangular fuzzy numbers, the decision alternatives are then ranked. Finally, a numerical example is given to show the feasibility and effectiveness of the developed method.