对称形式背景及其概念约简
Symmetric formal context and its concept reduct
- 西北大学学报（自然科学版） 2023年53卷第5期 页码：794-802
- 作者机构：
1.西北大学 数学学院，陕西 西安 710127
2.咸阳师范学院 数学与统计学院，陕西 咸阳 712000
3.新疆政法学院 信息网络安全学院，新疆 图木舒克 844000
4.西安电子科技大学 计算机科学与技术学院，陕西 西安 710071
- 作者简介：
魏玲，女，教授，博士生导师，从事形式概念分析、粒计算、三支决策理论等研究，wl@nwu.edu.cn。
赵思雨，女，博士研究生，讲师，从事形式概念分析等研究，zzssyu@163.com。
- 基金信息：国家自然科学基金(12171392;61976244);陕西省自然科学基础研究计划(2021JM-141);西北大学研究生创新项目(CX2023065)
DOI：10.16152/j.cnki.xdxbzr.2023-05-011
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魏玲, 赵思雨, 祁建军. 对称形式背景及其概念约简[J]. 西北大学学报（自然科学版）, 2023,53(5):794-802.
WEI Ling, ZHAO Siyu, QI Jianjun. Symmetric formal context and its concept reduct[J]. Journal of Northwest University (Natural Science Edition), 2023,53(5):794-802.
魏玲, 赵思雨, 祁建军. 对称形式背景及其概念约简[J]. 西北大学学报（自然科学版）, 2023,53(5):794-802. DOI： 10.16152/j.cnki.xdxbzr.2023-05-011.
WEI Ling, ZHAO Siyu, QI Jianjun. Symmetric formal context and its concept reduct[J]. Journal of Northwest University (Natural Science Edition), 2023,53(5):794-802. DOI： 10.16152/j.cnki.xdxbzr.2023-05-011.
摘要
形式背景是形式概念分析的数据基础与研究起点。为刻画形式背景中满足自反性和对称性的二元关系，首先定义对称形式背景，并研究对称形式背景的概念格以及对象概念、属性概念、并不可约概念与交不可约概念的特征；其次，定义对称概念，并证明对称概念集是对称形式背景的一个概念约简；最后，从冲突分析与社交网络两个角度给出对称形式背景、对称概念以及对称概念集的实际语义与应用。
Abstract
A formal context is the data base and starting point for research in formal concept analysis. In order to describe the binary relations satisfying reflexivity and symmetry in a formal context, this paper firstly defines the symmetric formal context, and studies the characteristics of the concept lattice, the object concept, the attribute concept, the join irreducible concept and the meet irreducible concept of the symmetric formal context. Then, we propose the symmetric concept and prove that the symmetric concept set is a concept reduct of symmetric formal context. Finally, from the perspective of conflict analysis and social network, we show the practical semantics and application of the symmetric formal context, the symmetric concept and the symmetric concept set, respectively.
关键词
形式概念分析对称形式背景概念约简冲突分析社交网络
Keywords
formal concept analysissymmetric formal contextconcept reductconflict analysissocial network
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