Projection measure is a very suitable tool for dealing with multiple attribute decision making problems. It considers not only the distance but also the included angle between objects evaluated. However, the existing projection formulae are illogical in some cases. To overcome the shortcoming implied in the existing projection measures, this paper developed normalized bidirectional projection method, measuring real vectors and interval numbers and their multiple attribute group decision making method with the hybrid information of crisp values and interval numbers. Through the normalized bidirectional projection measure between each alternative decision matrix and the ideal alternative matrix, all alternatives can be ranked to determine the best matrix. An illustrative example, applied alternative selection in the flexible manufacturing system, demonstrates the effectiveness and advantages of the proposed method through a comparative analysis with the existing projection measures.