  The theoretical analysis of multi-class classification has proved that the
existing multi-class classification methods can train a classifier with high
classification accuracy on the test set, when the instances are precise in the
training and test sets with same distribution and enough instances can be
collected in the training set. However, one limitation with multi-class
classification has not been solved: how to improve the classification accuracy
of multi-class classification problems when only imprecise observations are
available. Hence, in this paper, we propose a novel framework to address a new
realistic problem called multi-class classification with imprecise observations
(MCIMO), where we need to train a classifier with fuzzy-feature observations.
Firstly, we give the theoretical analysis of the MCIMO problem based on fuzzy
Rademacher complexity. Then, two practical algorithms based on support vector
machine and neural networks are constructed to solve the proposed new problem.
Experiments on both synthetic and real-world datasets verify the rationality of
our theoretical analysis and the efficacy of the proposed algorithms.
