Existing clustering ensemble algorithms for partitioning categorical data only apply to know the generating process of clustering members very well. In order to broaden the application of clustering ensemble, a fuzzy clustering ensemble algorithm for partitioning categorical data is proposed in this paper. The proposed algorithm makes use of relationship degree between different attributes for pruning a part of attributes (features). According to the distribution of clustering members, Descartes subset and relationship degree between objects are used for establishing the relationships between objects under unsupervised circumstances and get the minimum value of objective function of clustering and corresponding partitions. Then, numbers of clusters satisfying the difference and differential rate of objective function local maximum are the optimal numbers of clusters and its corresponding partitions are optimal clustering. Finally, the proposed algorithm is applied in Fellow-small dataset and Zoo dataset and results show the algorithm is effective and feasible.