Abstract: Clustering, as an unsupervised learning method, is a hot topic in data mining and has been widely used. Fuzzy clustering is an important branch of clustering. Many representative fuzzy clustering algorithms have been proposed, such as fuzzy c-means. Fuzzy c-means clustering algorithm and its improved versions are absolutely probability constrained clustering algorithms, which adapt the membership forms that represent the absolutely subordinative extent of the data. Some complex data distribution would make this absolutely subordinative extent invalid, for data objects perhaps can not be judged to belong to some cluster absolutely. It has been demonstrated that these problems deteriorate the clustering performance greatly. To solve these problems, uncertainty membership relationship are proposed. On the basis of uncertainty theory, a new possibility fuzzy clustering algorithm based on uncertainty membership （UMPFCA） is developed by applying two relative subordinative degree based judgment criterion parameters. UMPFCA introduces the possibility membership and uncertainty membership of data sets to the corresponding clusters into objective function during each iteration, which is possibility membership degree and uncertainty membership degree. Meanwhile, the algorithm based on new theories is implemented in which clustering process can be performed efficiently. Theoretical analysis and experimented results testify that UMPFCA has higher accuracy of clustering compared with K-means algorithm and fuzzy c-means algorithm.