Formal concept analysis based on hierarchical class analysis

The study of concept formation and learning is a central topic in cognitive informatics. Formal concept analysis can be viewed as an approach on this topic based on a formal context. In this paper, we study some basic data units for formal concept analysis based on hierarchical class analysis. In a formal context, objects and attributes can be grouped into equivalence classes based on equivalence relations. The order relations define the hierarchical structures of the equivalence classes. There exist some basic sets of objects and attributes that are used to not only reflect the equivalence relation and order relation, but also constitute all formal concepts derived from the formal context. The properties of these basic sets are studied and analyzed.