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We investigate multiattribute decision-making problems, where the attribute values are intuitionistic fuzzy values, and the weight information on attributes cannot be known completely. We first define the concepts of the overall attribute ideal solution and the overall attribute negative ideal solution of alternatives. Based on these two solutions, we define the satisfaction degree of each alternative. After that, we establish a multiobjective optimization model and then transform it into a single-objective optimization model. Furthermore, we establish an interactive method for multiattribute decision making with intuitionistic fuzzy information. A numerical example is also given to illustrate the solution processes of our methods. Finally, the extended results in interval-valued intuitionistic fuzzy situations are also pointed out.