Journal of Frontiers of Computer Science and Technology ›› 2018, Vol. 12 ›› Issue (9): 1506-1512.DOI: 10.3778/j.issn.1673-9418.1709104

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Property Oriented Interval-Set Concept Lattice

HE Xiaoli1,2, WEI Ling1+, QIAN Ting2   

  1. 1. School of Mathematics, Northwest University, Xi'an 710127, China
    2. College of Science, Xi'an Shiyou University, Xi'an 710065, China
  • Online:2018-09-01 Published:2018-09-10


贺晓丽1,2,魏  玲1+,钱  婷2   

  1. 1. 西北大学 数学学院,西安 710127
    2. 西安石油大学 理学院,西安 710065

Abstract: Property oriented concept lattice is an important data structure of formal concept analysis. To characterize the structure of property-oriented concepts in the context of incomplete information, this paper introduces interval set approach into the study of property-oriented concept lattices, and the notion of property-oriented interval set concept lattice is thus proposed, which realizes the combination of formal concept analysis, rough set and interval set. Based on the fundamental notion, some properties about operators in property oriented interval set concept lattice are discussed. It is proven that the collection of property-oriented interval set concepts forms a lattice. Moreover, the relationship between property oriented concept lattice and property oriented interval set concept lattice is established. Lastly, the construction method of property oriented interval set concept lattice and its corresponding algorithm are presented.

Key words: formal context, concept lattice, property oriented concept lattice, interval set

摘要: 面向属性概念格是形式概念分析中的一种重要数据结构。为刻画不完备信息环境下的属性概念认知结构,将描述不完备信息的区间集方法引入到面向属性概念格的研究之中,由此定义了面向属性的区间集概念格, 实现了形式概念分析与粗糙集、区间集3种方法的交叉融合。在给出基本定义之后,进一步细致研究了面向属性的区间集概念格算子的一些代数性质,证明了全体面向属性的区间集概念构成的集合在一定的偏序关系下是一个完备格,并建立起了面向属性概念格与面向属性的区间集概念格之间的密切联系,最后给出了面向属性的区间集概念格的构造方法及相应的建格算法。

关键词: 形式背景, 概念格, 面向属性概念格, 区间集