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Top1. Introduction
Fuzzy Support Vector Machine (FSVM) theory was firstly proposed by Lin, etc. (Lin & Wang, 2002). Its main idea is to introduce the concept of fuzzy weights to the original sample, enhancing the noise resistance of this algorithm. Currently, this algorithm is widely applied in the fields of network intrusion detection (Lun, University, & Beijing, 2005; Yang, Yu, Xie, & Zhang, 2011), face recognition (Leng & Wang, 2008; Liu & Chen, 2007), text classification (Wang & Chiang, 2007, 2009) and credit risk evaluation (Wang, Wang, & Lai, 2005).
For the fuzzy support vector machine, the original sample 
is usually expressed as 
, where 
stands for the fuzzy weight of samples. Fuzzy support vector machine weakens the effect of noise samples for classification results through introducing fuzzy weight. Fuzzy support vector machine algorithm can be achieved by solving the following optimization problem:
(1)Different from the traditional support vector machine algorithm, in the fuzzy support vector machine model, the misclassification penalty 
of samples is influenced by fuzzy weight 
and so the effects of noise samples for classification can be reduced by setting reasonable fuzzy weights. The key of fuzzy support vector machine algorithm is to assign the fuzzy weights, and currently the commonly applied approach is the center distance fuzzy weight assignment method. The specific calculation formula is as follows:
(2) where
and
denote the sample center of the two kinds of sample, and
is used to avoid
.
and
denote the radius of the two kinds of samples, and they can be defined as follows:
(3)