Different rough approximation spaces could be induced for an information system by its different attribute subsets, thus the multigranularity rough approximations of a fuzzy concept could be developed. Research on the uncertainty in multi-granulation spaces becomes a basic issue of uncertainty measure. If the uncertainty measure is not accurate enough, two different rough approximation spaces of a fuzzy concept may have the same uncertainty, and the difference between them for describing a fuzzy concept cannot be reflected. In this case, attribute reduction, granularity selection, and multigranularity measure cannot be conducted effectively. Therefore, establishing an uncertainty measure model with strong distinguishing ability in multi-granulation spaces is a key issue in uncertainty knowledge processing. In this paper, this problem will be solved in the view of knowledge distance. First, a fuzzy knowledge distance measure (FKD) based on the Earth Mover's distance is introduced. Even if two rough approximation spaces possess the same uncertainty when describing a fuzzy concept, they can be discriminated by FKD. Then, by studying the change rules of the FKD in a hierarchical quotient space structure, it is found that the FKD between any two rough approximation spaces in an HQSS is equal to the difference between their granularity measure or information measure. Furthermore, in order to show the applicability of the FKD, the FKD is used in granularity selection, attribute reduct, and multigranularity measure. The experimental results show that the FKD-based attribute significance function has a more powerful ability to obtain shorter reduct and it is more robustness, which show the effectiveness of the FKD.

中文翻译：

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模糊概念多粒度粗近似的知识距离测度

信息系统的不同属性子集可以为信息系统引入不同的粗略近似空间，从而可以开发模糊概念的多粒度粗略近似。研究多粒度空间中的不确定性成为不确定性测度的基本问题。如果不确定性测度不够准确，一个模糊概念的两个不同的粗逼近空间可能具有相同的不确定性，而不能反映它们描述模糊概念的差异。在这种情况下，不能有效地进行属性约简、粒度选择和多粒度度量。因此，在多粒度空间中建立具有较强区分能力的不确定性测度模型是不确定性知识处理的关键问题。在本文中，这个问题将在知识距离的角度得到解决。首先，介绍了一种基于地球移动器距离的模糊知识距离度量（FKD）。即使两个粗近似空间在描述一个模糊概念时具有相同的不确定性，它们也可以被 FKD 区分。然后，通过研究层次商空间结构中FKD的变化规律，发现HQSS中任意两个粗近似空间之间的FKD等于它们的粒度测度或信息测度之差。此外，为了展示FKD的适用性，在粒度选择、属性约简和多粒度度量中使用了FKD。