Coupled matrix and tensor factorizations have been successfully used in many data fusion scenarios where datasets are assumed to be exactly coupled. However, in the real world, not all the datasets share the same factor matrices, which makes joint analysis of multiple heterogeneous sources challenging. For this reason, approximate coupling or partial coupling is widely used in real-world data fusion, with exact coupling as a special case of these techniques. However, to fully address the challenge of tensor factorization, in this paper, we propose two improved coupled tensor factorization methods: one for approximately coupled datasets and the other for partially coupled datasets. A series of experiments using both simulated data and three real-world datasets demonstrate the improved accuracy of these approaches over existing baselines. In particular, when experiments on MRI data is conducted, the performance of our method is improved even by 12.47% in terms of accuracy compared with traditional methods.