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中文摘要：
属性约简是粗糙集理论研究的一个核心问题，很多情况下多个最小属性约简被期望能帮助用户做出更好的决策．文中提出一种基于蚁群优化的获取多个属性约简的方法．首先，结合蚁群优化方法将属性约简问题转化为受限制满足问题，并提出新的模型R—Graph，进而最小属性约简问题转化为在R—Graph中寻找最低成本路径问题．然后，定义吸收算子删除可辨识矩阵中冗余数据的方法以达到简化搜索空间的目的，并提出一个求解多个属性约简的算法（R—ACO）．最后，对比实验说明该方法在大多数情况下能得到更多的最小属性约简结果，并且算法效率较高．
英文摘要：
Attribute reduction is an important process in rough set theory. Minimal attribute reductions are expected to help clients make better decisions in some cases. In this paper, a heuristic approach for solving the minimal attribute reduction problem （MARP） is proposed based on the ant colony optimization （ACO） metaheuristic. Firstly, the MARP is transformed into an assignment which minimizes the cost in a constraint satisfaction model. Then, a preprocessing step is introduced that removes the redundant data in a discernibility matrix through the absorption operator to favor a smaller exploration of the search space at a lower cost. Next, an algorithm, R-ACO, is developed to solve the MARP. Finally, the simulation results show that the proposed approach finds more minimal attribute reductions efficiently in most cases.
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