Support vector machines have been widely applied in binary classification, which are constructed based on crisp data. However, the data obtained in practice are sometimes imprecise, in which classical support vector machines fail in these situations. In order to handle such cases, this paper employs uncertain variables to describe imprecise observations and further proposes a hard margin uncertain support vector machine for the problem with imprecise observations. Specifically, we first define the distance from an uncertain vector to a hyperplane and give the concept of a linearly α-separable data set. Then, based on maximum margin criterion, we propose an uncertain support vector machine for the linearly α-separable data set, and derive the corresponding crisp equivalent forms. New observations can be classified through the optimal hyperplane derived from the model. Finally, a numerical example is given to illustrate the uncertain support vector machine.

支持向量机已广泛应用于基于清晰数据构建的二元分类。然而，在实践中获得的数据有时是不精确的，经典的支持向量机在这些情况下会失败。为了处理这种情况，本文采用不确定变量来描述不精确观测，并进一步针对不精确观测问题提出了硬边际不确定支持向量机。具体来说，我们首先定义一个不确定向量到一个超平面的距离，并给出线性α-可分数据集的概念。然后，基于最大边际准则，我们提出了一个线性α的不确定支持向量机- 可分离的数据集，并导出相应的清晰等价形式。可以通过从模型导出的最佳超平面对新观察结果进行分类。最后给出了一个数值例子来说明不确定支持向量机。