基于模糊相似测量和模糊映射改进的模糊支持向量机对不确定性信息处理

针对传统模糊支持向量机(FSVM)对于不确定性信息处理的局限性，提出一种基于模糊相似测量和高维空间模糊映射的改进模糊支持向量机方法。首先，构建不确定信息集的模糊相似测量函数, 从不确定性信息本质出发，利用Gregson相似度，构建具有模糊特征的相似测量函数；然后，根据空间映射理论，将模糊相似测量函数应用于FSVM，构建满足Mercer理论的FSVM相似内核；最后，利用该方法对旋转超声加工中材料切屑率(MRR)中的不确信性信息进行建模。对比具有传统内核的FSVM，所提方法能够利用较少的运算步骤完成较好的不确定性信息处理，有效提高不确定信息处理的准确性，且计算复杂度低。

Uncertainty data processing by fuzzy support vector machine with fuzzy similarity measure and fuzzy mapping

In order to improve the processing ability for uncertainty data using the traditional Fuzzy Support Vector Machine (FSVM), FSVM with fuzzy similarity measure and high dimensional space fuzzy mapping was proposed. Firstly, by using Gregson similarity measure, the fuzzy similarity measure function was established, which was effective to explain the uncertainty information. And then, using the theory of mapping and Mercer, fuzzy similarity kernel learning was formulated and used in the algorithm of the FSVM. Finally, this algorithm was used to the modeling of the material removal rate in the rotary ultrasonic machining with uncertainty data. Compared to the results using traditional FSVM methods, the current approach can better process uncertainty data with less operation steps. And the proposed method has higher accuracy in processing uncertainty data with lower computational complexity.