摘要： 研究了当训练点的输出为模糊数时支持向量分类机的构建问题。对于线性模糊分类问题,首先将其转化为模糊系数规划。利用模糊系数规划的λ?最优规划,求解模糊系数规划得到模糊最优解(模糊集合)以及模糊最优分类函数集(取值为最优分类函数而隶属度为λ(0≤λ≤1)的模糊集合),从而构造线性模糊支持向量分类机。对于非线性模糊分类问题,引入核函数,类似于线性模糊分类问题得到非线性模糊支持向量分类机。最后构造显示模糊支持向量分类机特点的模糊支持向量集(取值为模糊训练点,隶属度为λ(0≤λ≤1)的模糊集合)。模糊支持向量分类机较好地解决了支持向量机中含有模糊信息的分类问题。

关键词: 支持向量机, 模糊数, 模糊系数规划, 模糊支持向量分类机

Abstract: This paper focuses on the construction of support vector machines when the output of training point is fuzzy number.For linear fuzzy classification problem,first the paper transforms it to fuzzy coefficient programming,then solves it based on λ ? programming to derive fuzzy optimal solutions(fuzzy set) and fuzzy optimal classification function set(a fuzzy set which value is fuzzy optimal classification function and member degree is λ(0≤ λ ≤ 1)),therefore the linear fuzzy support vector machine is constructed.For nonlinear fuzzy classification problem,the paper introduces kernel functions to get nonlinear fuzzy support vector machine like the case of linear problem.Finally,the definition of fuzzy support vector set is given,which can declare the characters of FSVC.FSVC can deal with the classification problem with fuzzy information in SVM better.

中图分类号: 

• TP18