Fuzzy kernels are a special kind of kernels which are usually employed to calculate the upper and lower approximations, as well as the positive region in kernelized fuzzy rough sets, and the positive region characterizes the degree of consistency between conditional attributes and decision attributes. When the classification hyperplane exists between two classes of samples, the positive region is transformed into the sum of the distances from the samples to classification hyperplane. The larger the positive region, the higher the degree of consistency. In this paper, we construct a novel model to solve the classification hyperplane from the geometric meaning of the positive region in kernelized fuzzy rough sets. Then, a classification model is developed through maximizing the sum of the distances from the samples to classification hyperplane, and this optimization problem that addresses this objective function is transformed to its dual problem. Experimental results show that the proposed classification algorithm is effective.

模糊核是一种特殊的核，通常用于计算核近似的模糊粗糙集中的上下近似以及正区域，正区域表示条件属性与决策属性之间的一致性程度。当分类超平面存在于两类样本之间时，正区域将转换为样本到分类超平面的距离之和。正区域越大，一致性程度越高。在本文中，我们构造了一个新的模型，用于从核化模糊粗糙集中正区域的几何意义上求解分类超平面。然后，通过最大化样本到分类超平面的距离之和来开发分类模型，解决这个目标函数的优化问题转化为对偶问题。实验结果表明，该分类算法是有效的。