Decision making problems always puzzled managers and decision makers in enterprises or organizations. There are many useful soft operation research methods could solve the complicated problem. The paper raises two classic approaches ANP (Analytical network process) and FCM (Fuzzy cognitive map). Those two methods have some similarities and differences. In thus, according to different decision problems, people could compare the two approaches’ characteristics and choose the best tool to deal with the problems. At the end of the paper, a case study has been given for us.