关键词: 概念格, 共有属性, 共有对象, 独有属性, 独有对象

Abstract: Wille's concept lattice can be used for common attributes (objects) data analysis, while object-oriented and property-oriented concept lattices can be used for unique attributes (objects) data analysis. In fact, these two kinds of data analysis methods have become hot research topics in the theory of formal concept analysis. In order to distinguish them from each other, the notions of common attributes (objects) and unique attributes (objects) are first defined, and some properties on their operators are also studied. Then this paper discusses whether a common attribute (object) is a unique attribute (object) or not. Specifically, this paper proves that neither the sufficient condition nor the necessary condition is true. Furthermore, the necessary and sufficient conditions are established to demonstrate that an ordered pair of object and attribute sets will become unique with respect to the concept partial order when it is not only a common attribute concept but also a unique attribute concept. In other words, there exists neither a greater concept nor a less concept than the ordered pair. Finally, the similarities and differences among Wille's, object-oriented and property-oriented concept lattices are shown from the perspectives of common attributes (objects) and unique attributes (objects).

Key words: concept lattice, common attributes, common objects, unique attributes, unique objects