Online social networks have been used for a variety of rich activities in recent years, such as investigating potential employees and seeking recommendations of high quality services and service providers. In such activities, trust is one of the most critical factors for the decision-making of users. In the literature, the state-of-the-art trust prediction approaches focus on either dispositional trust tendency and propagated trust of the pair-wise trust relationships along a path or the similarity of trust rating values. However, there are other influential factors that should be taken into account, such as the similarity of the trust rating distributions. In addition, tendency, propagated trust and similarity are of different types, as either personal properties or interpersonal properties. But the difference has been neglected in existing models. Therefore, in trust prediction, it is necessary to take all the above factors into consideration in modeling, and process them separately and differently. In this paper we propose a new trust prediction model based on trust decomposition and matrix factorization, considering all the above influential factors and differentiating both personal and interpersonal properties. In this model, we first decompose trust into trust tendency and tendency-reduced trust. Then, based on tendency-reduced trust ratings, matrix factorization with a regularization term is leveraged to predict the tendency-reduced values of missing trust ratings, incorporating both propagated trust and the similarity of users' rating habits. In the end, the missing trust ratings are composed with predicted tendency-reduced values and trust tendency values. Experiments conducted on a real-world dataset illustrate significant improvement delivered by our approach in trust prediction accuracy over the state-of-the-art approaches.