计算机科学

计算机科学 ›› 2025, Vol. 52 ›› Issue (6): 151-158.doi: 10.11896/jsjkx.240600055

• 数据库&大数据&数据科学 • 上一篇    下一篇

三元概念约简与概念约简的关系

李萱1,3, 张琴1,3, 魏玲1,2,3   

  1. 1 西北大学数学学院 西安 710127
    2 闽南师范大学数学与统计学院 福建 漳州 363000
    3 西北大学概念、认知与智能研究中心 西安 710127
  • 收稿日期:2024-06-06 修回日期:2024-08-26 出版日期:2025-06-15 发布日期:2025-06-11
  • 通讯作者: 魏玲(wl@nwu.edu.cn)
  • 作者简介:(L201721278723@163.com)
  • 基金资助:
    国家自然科学基金(12171392);陕西数理基础科学研究项目(23JSZ008);西北大学研究生科研创新项目(CX2024128)

Relationship Between Triadic Concept Reducts and Concept Reducts

LI Xuan1,3, ZHANG Qin1,3, WEI Ling1,2,3   

  1. 1 School of Mathematics,Northwest University,Xi'an 710127,China
    2 School of Mathematics and Statistics,Minnan Normal University,Zhangzhou,Fujian 363000,China
    3 Institute of Concepts,Cognition and Intelligence,Northwest University,Xi'an 710127,China
  • Received:2024-06-06 Revised:2024-08-26 Online:2025-06-15 Published:2025-06-11
  • About author:LI Xuan,born in 1999,master.Her main research interests include formal concept analysis,three-way decision and granular computing.
    WEI Ling,born in 1972.Ph.D,professor,Ph.Dsupervisor.Her main research interests include formal concept analysis,rough set,three-way decision and granular computing.
  • Supported by:
    National Natural Science Foundation of China(12171392),Shaanxi Fundamental Science Research Project for Mathematics and Physics(23JSZ008) and Graduate Innovation Fund of Northwest University(CX2024128).

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摘要： 三元概念分析是形式概念分析理论的扩展,三元背景所反映的三元关系与基于条件下的二元关系相对应,因此保持二元关系不变的概念约简与保持三元关系不变的三元概念约简之间有着紧密联系。基于此,研究概念约简和三元概念约简之间的关系。首先,将三元背景中每一个条件下的数据看作是一个形式背景,根据形式概念与三元概念的关系,证明了所有条件确定的形式背景的概念约简构成的集合可以生成三元概念协调集。其次,利用三元概念按照相同条件构成的集合可以得到对应条件下的概念集,进一步证明了三元概念约简可以生成每个条件确定的形式背景的概念协调集,并给出概念约简与三元概念约简相互生成的等价命题。最后,探讨并给出概念约简与三元概念约简中不同类型的3种概念之间的关系。

关键词: 三元背景, 三元概念, 形式概念, 概念约简, 三元概念约简

Abstract: Triadic concept analysis is an extension of formal concept analysis,and the ternary relation reflected in the triadic context corresponds to the binary relation based on the condition,so there is a close connection between the concept reduction that keeps the binary relation unchanged and the triadic concept reduction that keeps the ternary relation unchanged.Based on this,the relationship between concept reducts and triadic concept reducts is investigated.Firstly,the data under each condition in the tri-adic context is regarded as a formal context,and according to the relationship between formal concepts and triadic concepts,it is proved that the sets formed by the concept reducts of all conditionally determined formal contexts can generate triadic concept consistent sets.Secondly,using the set formed by triadic concepts according to the same conditions can get the set of concepts under the corresponding conditions.It is further proved that the concept consistent sets of formal contexts determined by all conditions can be generated from triadic concept reducts,and the equivalent proposition that triadic concept reducts and concept reducts are generated by each other is given.Finally,the relationship between the three types of formal concepts and the three types of triadic concepts is discussed with respect to the three types of concepts that play different roles in concept reducts and triadic concept reducts.

Key words: Triadic context, Triadic concept, Formal concept, Concept reduction, Triadic concept reduction

中图分类号: 

  • O29
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