We describe and compare two fuzzy clustering algorithms based on optimizing penalty functions of relational data. More specifically, the AP algorithm of Windham is contrasted with the relational fuzzy c-means approach through a numerical example on a small artificial data set defined by Windham. Our results indicate that while the two algorithms seem to cluster objects using very different mathematical criteria, the numerical results can be quite similar. However, a second numerical example using a slightly distorted version of Windham's data seems to exhibit real differences between clusterings obtained by the two approaches