Most of existing fuzzy clustering approaches cluster objects based on the vector representation or their pairwise relation. In this paper, we propose a new approach called LinkFCM to make use of both types of data by adding an additional term into fuzzy c-means type objective functions. This new term measures the total within cluster association. The LinkFCM is useful for clustering many real-world data, such as Webpages, where together with the content of each Webpage, we may also know the inter-links. Moreover, when the relational data is the user specified pairwise constraints, the proposed approach becomes a semi-supervised fuzzy clustering. We will show that the term measuring the violation of constraints in some existing semi-supervised fuzzy clustering approaches is a special case of the second term in LinkFCM. Experimental study is conducted on real-word data where the relation matrix is constructed under two scenarios: in the first scenario, the relation matrix records the link information between each pair of objects, and in the second scenario, the relation matrix records user specified pairwise constraints. The experimental results show the effectiveness of the proposed LinkFCM in both cases.