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《山东大学学报(理学版)》 ›› 2022, Vol. 57 ›› Issue (8): 60-67.doi: 10.6040/j.issn.1671-9352.0.2022.055

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FCA中的互补概念及其性质与生成

韩培磊1,2,魏玲1,2*,王振1,2,赵思雨1,2,3   

  1. 1.西北大学数学学院, 陕西 西安 710127;2.西北大学概念、认知与智能研究中心, 陕西 西安 710127;3.咸阳师范学院数学与统计学院, 陕西 咸阳 712000
  • 出版日期:2022-08-20 发布日期:2022-06-29
  • 作者简介:韩培磊(1996— ),女,硕士研究生,研究方向为形式概念分析、粗糙集、粒计算等. E-mail:1827619808@qq.com*通信作者简介:魏玲(1972— ),女,博士,教授,博士生导师,研究方向为形式概念分析、三支决策理论、粒计算等. E-mail:wl@nwu.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(12171392,62006190);陕西省自然科学基础研究计划资助项目(2021JM-141)

Complementary concepts and their properties and generation in FCA

HAN Pei-lei1,2, WEI Ling1,2*, WANG Zhen1,2, ZHAO Si-yu1,2,3   

  1. 1. School of Mathematics, Northwest University, Xian 710127, Shaanxi, China;
    2. Institute of Concepts, Cognition and Intelligence, Northwest University, Xian 710127, Shaanxi, China;
    3. School of Mathematics and Statistics, Xianyang Normal University, Xianyang 712000, Shaanxi, China
  • Online:2022-08-20 Published:2022-06-29

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摘要： 在形式概念分析中,概念格上的偏序关系刻画了概念间的泛化和特化关系,而概念格中不可比概念之间也存在着值得研究的特定语义信息。受此启发,提出互补概念这一定义并给出其形式化描述。首先,通过给定两个对象子集关于某个特定属性子集互补程度的描述,根据不同实际需求分别定义强、弱互补关系。在此基础上,研究互补概念及相关性质,并在不同语义背景下探究最优强互补概念和最优弱互补概念,给出相应生成算法。最后,通过实例说明所研究内容的合理性与可适用性。

关键词: 概念格, 形式概念分析, 强互补概念, 弱互补概念

Abstract: In formal concept analysis, partial order relation of concept lattice describes generalization and specialization between concepts. There also exists some specific semantic information that is worth studying between incomparable concepts. Inspired by this, complementary concepts are studied in this paper. Firstly, the complementary degree of two object subsets is described by considering a specific attribute subset in formal context, based on which the strong and weak complementary relations are defined according to different actual needs. Further, the complementary concepts and their related properties are studied, and the optimal strong complementary concept and optimal weak complementary concept are explored under different semantics, and the corresponding algorithms are also given. Finally, examples are presented given to illustrate the rationality and applicability of the content of this paper.

Key words: concept lattice, formal concept analysis, strong complementary concept, weak complementary concept

中图分类号: 

  • TP18
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