Abstract:

According to the inspiration of research on multi-granularity marker information system in rough set, for the formal background of multi-granularity marker, concept lattices made by different granularity markers have connections. This is the hotspot research in the formal concept analysis. In order to study connections between concept lattices in different granularity markers, this paper discusses the relation of extrema made by different  granularity markers firstly. Then using the relation of extrema, this paper researches connections between object-oriented concept lattice in different granularity markers. Using the complementary relationship between the attribute-oriented concept lattice and the object-oriented concept lattice, this paper studies the relationship between the attribute-oriented concept lattices formed under different granularity markers, and realizes the formal background under the narrower granularity and the formal background under the wider granularity. The knowledge under coarse-grained markers is inferred from the knowledge under fine-grained markers. Finally, a corresponding concept lattice generation method is proposed.

Key words: multi-granulation, formal context, attribute oriented, object oriented

摘要：

受粗糙集中多粒度标记信息系统研究的启发，对于多粒度标记的形式背景，不同粒度标记下形成的概念格之间存在着一些联系，这在形式概念分析理论中属于热点研究问题。为了研究不同粒度标记下形成的概念格之间的关系，首先讨论了不同粒度标记下的生成的极值算子之间的关系；其次通过极值算子之间的关系，对不同粒度标记下形成的面向对象的概念格之间的关系进行了研究；再利用面向属性的概念格和面向对象的概念格之间的互补关系，对不同粒度标记下形成的面向属性的概念格之间的关系进行了研究，实现了在已知细粒度标记下的形式背景、粗粒度标记下的形式背景，通过细粒度标记下的知识推断出粗粒度标记下的知识；最后在此基础上提出了相应的概念格生成的方法。

关键词: 多粒度, 形式背景, 面向属性, 面向对象