Attribute reduction is an important application of rough set theory. With the dynamic changes of data becoming more and more common, traditional attribute reduction, also called static attribute reduction, is no longer efficient. How to update attribute reducts efficiently gets more and more attention. In the light of the variation about the number of objects, we focus on incremental attribute reduction approaches based on knowledge granularity which can be used to measure the uncertainty in incomplete decision systems. We first introduce incremental mechanisms to calculate knowledge granularity for incomplete decision systems when multiple objects vary dynamically. Then, incremental attribute reduction algorithms for incomplete decision systems when adding multiple objects and when deleting multiple objects are proposed respectively. Finally, comparative experiments on different real-life data sets are conducted to demonstrate the effectiveness and efficiency of the proposed incremental algorithms for updating attribute reducts with the variation of multiple objects in incomplete decision systems.

中文翻译：

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不完全决策系统基于知识粒度的增量属性约简

属性约简是粗糙集理论的重要应用。随着数据的动态变化变得越来越普遍，传统的属性约简（也称为静态属性约简）不再有效。如何有效地更新属性约简得到越来越多的关注。鉴于对象数量的变化，我们将重点放在基于知识粒度的增量属性约简方法上，该方法可用于度量不完整决策系统中的不确定性。当多个对象动态变化时，我们首先引入增量机制来计算不完整决策系统的知识粒度。然后，分别提出了针对不完整决策系统在添加多个对象和删除多个对象时的增量属性约简算法。最后，