中文摘要：

为了对现实中既含有离散数据又有连续数据，甚至还有模糊数据的决策系统进行属性约简，基于模糊等价关系建立粗糙集模型，用熵来度量粗糙集中的不可分辨能量并定义约简．提出用遗传算法来求解含混合数据的决策系统的约简，论述了适应度函数的选择，给出了算法的具体实现．对经典数据集和UCI机器学习数据库中5个数据库约简的结果证明了算法的有效性和可行性．

英文摘要：

In order to reduce the real decision systems coming with discrete data as well as continuous data, even fuzzy data, a new rough set theory model based on fuzzy equation relation was established. Entropy was presented to measure the indiscernibility power and define the reduction. The genetic algorithm was proposed to reduce decision systems made up of hybrid data, the fitness function and reduction algorithm were presented as well. The validity and feasibility of the algorithm were demonstrated by the results of experiments on a classical data set and five UCI machine learning databases.