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《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (3): 70-80.doi: 10.6040/j.issn.1671-9352.4.2019.068

• • 上一篇    

三支区间集概念格

刘营营1,米据生1*,梁美社1,2,李磊军1   

  1. 1.河北师范大学数学与信息科学学院, 河北 石家庄 050024;2.石家庄职业技术学院, 河北 石家庄 050081
  • 发布日期:2020-03-27
  • 作者简介:刘营营(1994— ), 女, 硕士研究生, 研究方向为人工智能数学基础. E-mail:15732155710@163.com*通信作者简介:米据生(1966— ), 男, 博士, 教授, 博导,研究方向为人工智能数学基础. E-mail:mijsh@263.net
  • 基金资助:
    国家自然科学基金资助项目(61573127,61502144);河北省自然科学基金资助项目(F2018205196);河北省高等学校科学技术研究项目(BJ2019014,QN2017095);河北省博士后择优资助科研项目(B2016003013);河北省“三三三人才工程”培养经费资助项目(A2017002112);河北师范大学博士基金项目(L2017B19);河北师范大学硕士研究生创新项目(CXZZSS2019062)

Three-way interval-set concept lattice

LIU Ying-ying1, MI Ju-sheng1*, LIANG Mei-she1,2, LI Lei-jun1   

  1. 1. College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050024, Hebei, China;
    2. Shijiazhuang University of Applied Technology, Shijiazhuang 050081, Hebei, China
  • Published:2020-03-27

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摘要： 分别在完备和不完备形式背景下提出了三支区间集概念格模型,然后讨论对象诱导的三支区间集概念格与区间集概念格之间的关系,证明由区间集概念得到对象诱导的三支区间集概念的充要条件,并设计相应的算法。最后讨论对象诱导的三支区间集概念与经典概念之间的联系,证明由经典概念得到对象诱导的三支区间集概念的充要条件,并设计相应的算法。

关键词: 概念格, 区间集, 形式概念分析, 三支概念

Abstract: This paper respectively proposes a three-way interval-set concept lattice model in complete and incomplete formal context, and systematically analyses the connections between the object-induced three-way interval-set concept lattice and the interval-set concept lattice. In addition, the necessary and sufficient conditions for constructing the object-induced three-way interval-set concept on the basis of the interval-set concept are proved, and the corresponding algorithm is formulated. Finally, the relationships between the object-induced three-way interval-set concept and the interval-set concept are studied. The necessary and sufficient conditions for constructing the object-induced three-way interval-set concept on the basis of the classical concept are proved.

Key words: concept lattice, interval set, formal concept analysis, three-way concept

中图分类号: 

  • O236
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