Summary: Frequency-based cluster prototypes have been used to cluster categorical objects, based on the simple matching dissimilarity measure. This paper introduces a new generalization called fuzzy \(p\)-mode prototype, of frequency-based prototypes. A fuzzy \(p\)-mode cluster prototype at a categorical feature is expressed as a list of \(p\) labels that have larger frequencies than others in the cluster. This paper also presents a new generalization of the fuzzy C-means clustering algorithm for the objects of mixed features. In the general fuzzy C-means clustering algorithm, any dissimilarity measures at the categorical feature level are assumed, not like other clustering algorithms that use the simple matching dissimilarity. The convergence of the general fuzzy C-means clustering algorithm under the optimization framework is proved. It is also explained through experiments over real object sets that the size of fuzzy \(p\)-mode prototypes and the fuzzification coefficients affect clustering performance.