后验概率加权的模糊隶属度函数

模糊支持向量机(FSVM)中的模糊隶属度函数确定一直是一个难点问题。针对支持向量分类机对噪声数据或孤立点非常敏感的问题，受贝叶斯决策理论的启发，结合样本密度特性，研究样本点相对于同类和异类的关系，对各样本点分布的紧密程度给出了描述，构造了样本点的后验概率与样本密度的加权方法，提出了一种新的加权模糊隶属度函数构造。该方法避免了对噪声数据和孤立点的检测。通过建立基于提出模糊隶属函数的FSVM进行仿真，实验表明，提出的模糊隶属度函数构造的后验概率加权方法的有效性。

Design fuzzy membership functions based on the posterior probability weighting

The determination of fuzzy membership function in the fuzzy support vector machine (FSVM) is a difficult problem. To solve the problem of being sensitive to the noises and outliers in support vector machine, by the inspiration of Bayesian decision theory, combining with sample density characteristics, sample points relation between same class and other class is researched, and the tightness on each sample points is described. Based on that, method of posterior probability and sample density weight are given to each sample, and new fuzzy membership function is proposed. The detection of the noises and outliers is avoided by this method. Numerical simulation shows that the improved fuzzy membership function method is effective.