Many methods have been proposed for managing of fuzzy numbers. How ever, these methods just can apply to compare some types of fuzzy numbers and other comparing cases can just rank by their graph, intuitively. Therefore, using proper methods is important in proper conditions constructing ranking indexes since the centroid of fuzzy numbers is an important case. In this study, we present a modified method for ordering fuzzy numbers. Some applications, which constitute a step in the evaluation of the evolution of Reims during the domination of the Roman Empire, illustrate the use of the anteriority index.