How to process multi-class problem with SVM is one of the present research focuses.We propose a fuzzy multi-class SVM model referred as FMSVM.It is constructed by introducing a fuzzy membership function to the penalty in the quadratic problem of Weston and Watkins

the membership function acquire different values for each input data according to their different affects on the classification results.Hence

we can ignore the data

which affect the classification result a little.Therefore different input points can make different contributions to the learning of the decision surface

i.e.

the optimal separating hyper-plane.Both theoretical analysis and digital experiment results show that the model proposed here works very well on benchmark data sets and also has the property of robustness.