中文摘要：

针对基于模糊等价关系建立的粗糙集模型，指出了现有相对约简算法的不合理，重新定义了相对约简，并提出利用改进的二进制粒子群优化（PSO）算法来求混合决策系统的相对约简。改进的二进制PSO算法引入遗传算法的交叉算子，同时对于种群中适应度最低的粒子，用新产生的粒子代替。根据“相对约简中属性的数量越少，相对熵之差绝对值越小，适应度函数的值越大”的原则设计适应度函数。实验证明算法对混合决策系统能进行有效的约简。

英文摘要：

The irrationality of the relative reduction algorithm of rough set model based on fuzzy equation relation was pointed out and the notion of relative reduction was redefined and an improved binary version of particle swarm optimization （PSO） algorithm was used to compute the relative reduction of the hybrid decision systems. The improved binary version of PSi9 referenced the crossing operator of genetic algorithm and the worst particle was taken the place of by a new one, The fitness function was constructed by the rule of ＂the smaller the number of the attributes in the reduct attribute set the larger the value of the fitness function and the smaller of absolute value of the difference of the relative entropy the larger the value of fitness function＇, Experiments show that the algorithm is effective for the reduction of hybrid decision systems.