The performances of standard classifiers, i.e., any method of point prediction for classification, decline in case of imperfect data. In some sensitive domains where these imperfections are present, these classifiers need to be adapted in order to avoid any misclassification that has serious consequences. Recent works proposed to deal with this problem by using cautious classification techniques. This paper is in line with these works, especially with imprecise classifiers, i.e., the output of the classifier for an input sample that is subject to considerable imperfections is a subset of classes. The distinctive feature of our imprecise classification proposition is that it considers that in some applications, data imperfection is not limited to new samples to be classified but can also be present in training data. We therefore propose a relabelling procedure which allows us to identify imperfect samples in the training data and relabel them with an appropriate subset of candidate classes. This approach to imprecise classification is close, in some aspects, to hierarchical classification where a “parent” can be considered as a subset of classes that are the “children” in the leaves. Furthermore, the belief functions framework is considered to represent the uncertainty and imprecision about the class of a new sample where the focal elements are contained in the set of new labels of the training data. A criterion based on a generalised score and the obtained mass function is established to decide which subset of classes should be associated to the new sample. Several options are presented to build our classifier for the relabelling procedure and for the reasoning step. Thus, the performances of each option are presented before comparison with state-of-the-art imprecise classifiers' performances. The comparisons are conducted first on randomly generated data and then on 11 UCI datasets based on five measures of imprecise classification performances. They show that our classifier achieves performances close to, sometimes better than, the best on the five measures.