Journal of Frontiers of Computer Science and Technology ›› 2019, Vol. 13 ›› Issue (4): 702-710.DOI: 10.3778/j.issn.1673-9418.1804040

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Research on Relationship Between Common and Unique Attributes (Objects) of Concept Lattice

YAN Mengyu1,2, LI Jinhai1,2+   

  1. 1. Data Science Research Center, Kunming University of Science and Technology, Kunming 650500, China
    2. Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China
  • Online:2019-04-01 Published:2019-04-10



  1. 1. 昆明理工大学 数据科学研究中心,昆明 650500
    2. 昆明理工大学 理学院,昆明 650500

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

摘要: Wille概念格可用于共有属性(对象)的数据分析,而面向对象概念格和面向属性概念格可用于独有属性(对象)的数据分析,这两种数据分析方法在形式概念分析理论中均属于热点研究问题。为了区分这两种数据分析方法,首先引入了共有属性(对象)与独有属性(对象)的概念,对它们的算子性质进行了研究。其次围绕命题“共有属性(对象)是独有属性(对象)”展开讨论。具体地,证明了该命题的充分条件和必要条件均不成立,并提出了该命题成立的充要条件;在此基础上,表明了一个对象属性序对既是共有概念又是独有概念时,在概念序关系意义下它是唯一的,即不存在比该序对更大的概念,也不存在比该序对更小的概念。最后从共有与独有属性(对象)的角度给出了Wille概念格、面向对象概念格和面向属性概念格的异同。

关键词: 概念格, 共有属性, 共有对象, 独有属性, 独有对象