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The aim of this paper is to develop a method to determine the weights of attributes objectively under intuitionistic fuzzy environment. Based on the mean deviation, we establish an optimization model in which the information about attribute weights is completely unknown. By solving the model, we get a simple and exact formula which can be used to determine the attribute weights. After that, we utilize the intuitionistic fuzzy weighted average (IFWA) operator to aggregate the given intuitionistic fuzzy information corresponding to each alternative, and then select the most desirable alternative according to the score function and accuracy function. Finally, a practical example is given to verify the developed method and to demonstrate its practicality and effectiveness.