For multi-attribute decision making problems including quantitative and fuzzy criteria, a new method with incomplete information for functional requirements based-on information axiom was proposed. When several alternatives satisfy the FRs, the satisfactory degree of users are taken into account in the process of multi-attribute decision making. When the design range of the criterion is unknown, the acceptable range is defined and considered as the design range. The definition and formulation of information content with incomplete information for multi-attribute decision making was developed. All alternatives can be ranked by the total information content, and a final decision was made for the best alternative. Finally, an example on punching machines’ evaluation and selection was used to illustrate the proposed method.