The fuzzy c-means (FCM) and possibilistic c-means (PCM) algorithms have been utilized in a wide variety of fields and applications. Although many methods are derived from the FCM and PCM for clustering various types of spatial data, relational clustering has received much less attention. Most fuzzy clustering methods can only process the spatial data (e.g., in Euclidean space) instead of the nonspatial data (e.g., where the Pearson's correlation coefficient is used as similarity measure). In this paper, we propose a novel clustering method, similarity-based PCM (SPCM), which is fitted for clustering nonspatial data without requesting users to specify the cluster number. The main idea behind the SPCM is to extend the PCM for similarity-based clustering applications by integration with the mountain method. The SPCM has the merit that it can automatically generate clustering results without requesting users to specify the cluster number. Through performance evaluation on real and synthetic data sets, the SPCM method is shown to perform excellently for similarity-based clustering in clustering quality, even in a noisy environment with outliers. This complements the deficiency of other fuzzy clustering methods when applied to similarity-based clustering applications.