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中文摘要：
粒计算是知识表示与数据挖掘的一种方法．在粒计算看来，一个粒是由多个比较小的颗粒组成更大的一个单元．在许多场合下，由于不同标记尺度对数据有不同的分割，会得到不同层次的信息粒度．首先介绍了多标记信息系统的概念，考虑到不完备信息系统的情况，重新定义了粒信息变换函数，并给出了不完备多标记信息系统的概念．在不完备多标记信息系统中，利用粒信息变换函数，可以获得知识粒度的一个层次结构．在每一个层次中，利用相似关系定义相似类，进而定义多粒度粗糙集的下近似、上近似、边界、近似精度和粗糙度等概念．在不同层次之间，分别讨论了下近似、上近似、边界、近似精度和粗糙度的变化性质，在不同的标记粒度下探索的知识粒度的变化规律．
英文摘要：
Granular computing is an approach for knowledge representation and data mining. The key to granular computing is to make use of granules in problem solving. With the view point of granular computing,the notion of a granule may be interpreted as one of the numerous small particles forming a larger unit. In many situations, there are different granules at different levels of scale in data sets having hierarchical scale structures. Therefore, the concept of multi-labeled information system is first introduced. Take into consideration the existence of incomplete information systems, a new function of granular information transformation is defined, and the concept of the incomplete multi-labeled information system is also proposed. With the function of granular information transformation,a hierarchical structure of granules can be obtained in incomplete multi-labeled information system. For each level, the similarity class can be defined by using similarity relation. Then the lower approximation and upper approximation of multi-granulation rough sets are defined by using similarity classes. Analogously, accuracy of approximations and roughness are also defined as usual at every level. Furthermore, the properties of lower approximations, upper approximations,accuracy of approximations and roughness between different levels are discussed re spectively. Those properties may be useful to find laws of knowledge variation in multi-labeled incomplete information system while the granular size changing.
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