Set-value classification allows the classifiers to output a set of plausible labels rather than a single label. In particular, a set-valued classifier divide the feature space into regions, which may have overlaps, corresponding to the class label. An observation is predicted to a class if it falls in that class's region. By introducing a new type of functional margin, we propose a multi-class support vector classifier that, with high probability, can guarantee a user-defined coverage rate for each class. Fisher consistency of the new classifier is showed and an efficient algorithm is developed.