Critical path assessment plays an important role in production project management in order to schedule and control of the projects. In fuzzy sets theory, it is often difficult for an expert to accurately quantify his or her opinion as a number in interval [0,1]. Therefore, it is more appropriate to indicate this degree of certainty by an interval that is why interval-valued fuzzy sets (IVSs) are used to better address the uncertainty of real world production projects. Also, a new multi-criteria decision making (MCDM) method based on fuzzy preference relation under IVFSs is developed. Moreover, entropy method is extended by means of distance between each point from nearer and farther point among ideal points under IVFSs. Finally, an application about production project is solved to better illustrate the calculation and capability of the proposed method.