The fuzzy support vector machines (FSVMs) can be used to deal with multiclass classification problems where the key issue is to solve a quadratic programming problem. This paper introduces a new fuzzy multiclass support vector machines (FMSVMs) based on compact description of data, which extends the exiting support vector machine method to the case of k-class problem in one optimization task (quadratic programming) by considering the relative location of samples to the origin and the knowledge of ambiguity associated with the membership of samples for a given class. The fuzzy membership is defined by not only the relation between a sample and its cluster center, but also by the affinity among samples. Compared with the existing SVMs, our new proposed FMSVMs have the improvement in aspects of classification accuracy and reducing the effects of noises and outliers.