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The interval multi-attribute decision making (IMADM) problems are investigated, in which the information about attribute weights is known partly and the decision maker has preference information on alternatives in the form of interval numbers reciprocal judgment matrix. The relation between the interval numbers reciprocal judgment matrix and its weight vector is established. A minimizing the maximum difference model is introduced to assess the weights of attributes in the IMADM problem, which integrate subjective interval preference relations and objective information. The additive weighting method is used to obtain the interval overall values of alternatives. By using the priority formula of interval numbers, the decision alternatives are then ranked. Finally, a numerical example is given to show the feasibility and effectiveness of the developed method.