Most existing results about attribute reduction are reported by considering one and only one granularity, especially for the strategies of searching reducts. Nevertheless, how to derive reduct from multi-granularity has rarely been taken into account. One of the most important advantages of multi-granularity based attribute reduction is that it is useful in investigating the variation of the performances of reducts with respect to different granularities. From this point of view, the concept of Sequential Granularity Attribute Reduction (SGAR) is systemically studied in this paper. Different from previous attribute reductions, the aim of SGAR is to find multiple reducts which are derived from a family of ordered granularities. Assuming that a reduct related to the previous granularity may offer the guidance for computing a reduct related to the current granularity, the idea of the three-way is introduced into the searching of sequential granularity reduct. The three different ways in such process are: (1) the reduct related to the previous granularity is precisely the reduct related to the current granularity; (2) the reduct related to the previous granularity is not the reduct related to the current granularity; (3) the reduct related to the previous granularity is possible to be the reduct related to the current granularity. Therefore, a three-way based forward greedy searching is designed to calculate the sequential granularity reduct. The main advantage of our strategy is that the number of times to evaluate the candidate attributes can be reduced. Experimental results over 12 UCI data sets demonstrate the following: (1) three-way based searching is superior to some state-of-the-art acceleration algorithms in time consumption of deriving reducts; (2) the sequential granularity reducts obtained by proposed three-way based searching will provide well-matched classification performances. This study suggests new trends concerning the problem of attribute selection.

关于属性约简的大多数现有结果是通过考虑一种和仅一种粒度来报告的，特别是对于搜索归约策略。然而，很少考虑如何从多粒度获得还原。基于多粒度的属性约简的最重要优点之一是，它可用于研究还原操作相对于不同粒度的变化。从这个角度出发，本文系统地研究了顺序粒度属性约简（SGAR）的概念。与以前的属性约简不同，SGAR的目的是找到多个归类于一组有序粒度的约简。假定与先前粒度有关的归约可以为计算与当前粒度有关的归约提供指导，则将三向的思想引入到顺序粒度归约的搜索中。在此过程中，三种不同的方式是：（1）与先前粒度有关的还原恰好是与当前粒度有关的还原；（2）与先前粒度有关的还原不是与当前粒度有关的还原；（3）与先前粒度有关的归约可能是与当前粒度有关的归约。因此，设计了一种基于三向前向贪婪搜索的方法来计算顺序粒度的减少。我们策略的主要优点是可以减少评估候选属性的次数。在12个UCI数据集上的实验结果表明：（1）基于三向的搜索在推导还原的时间消耗方面优于某些最新的加速算法；（2）通过提出的基于三向搜索的顺序粒度减少将提供良好匹配的分类性能。这项研究提出了有关属性选择问题的新趋势。