In this paper, we are interested in the label ranking problem. We are more specifically interested in the recent trend consisting in predicting partial but more accurate (i. e. , making less incorrect statements) orders rather than complete ones. To do so, we propose a ranking method based on label-wise decomposition. We estimate an imprecise probabilistic model over each label rank and we infer a partial order from it using optimisation techniques. This leads to new results concerning a particular bilinear assignment problem. Finally, we provide some experiments showing the feasibility of our method.