基于三元因子分析的三元概念约简

doi:10.13232/j.cnki.jnju.2020.04.006

南京大学学报(自然科学版) ›› 2020, Vol. 56 ›› Issue (4): 480–493.doi: 10.13232/j.cnki.jnju.2020.04.006

基于三元因子分析的三元概念约简

李俊余^1,²,李星璇¹,王霞^1,²(),吴伟志^1,²

^1.浙江海洋大学数理与信息学院，舟山，316022
^2.浙江省海洋大数据挖掘与应用重点实验室，浙江海洋大学，舟山，316022

收稿日期:2020-06-20 出版日期:2020-07-30 发布日期:2020-08-06
通讯作者: 王霞 E-mail:bblylm@126.com
基金资助:
国家自然科学基金(41631179);浙江省自然科学基金(LY18F030017)

Reduction of triadic concepts based on triadic factor analysis

Junyu Li^1,²,Xingxuan Li¹,Xia Wang^1,²(),Weizhi Wu^1,²

^1.School of Mathematics，Physics and Information Science，Zhejiang Ocean University，Zhoushan，316022，China
^2.Key Laboratory of Oceanographic Big Data Mining and Application of Zhejiang Province，Zhejiang Ocean University，Zhoushan，316022，China

Received:2020-06-20 Online:2020-07-30 Published:2020-08-06
Contact: Xia Wang E-mail:bblylm@126.com

摘要/Abstract

摘要：

三元概念的约简是三元概念分析的重要问题，因为它既能简化三元图的表示，又有助于更好地理解三元概念的语意并从中提取有价值的信息.基于三元因子分析,研究保持三元背景中所有三元关系不变的三元概念约简.首先，基于三元因子分析提出三元概念约简的定义.该方法是在保持三元背景不变的条件下寻找尽可能少的三元概念，即这些三元概念能够完整地反映原始三元背景所包含的所有三元关系.其次，讨论三元因子分解与三元概念协调集的关系，并给出三元概念协调集和约简的判定方法.最后，利用三元概念约简将三元概念分为三类：核心（绝对必要）概念、相对必要概念和不必要概念，并得到每类三元概念的充要条件.此外，通过实例给出由三元因子分解和概念约简定义两种方法寻找三元概念约简的详细过程.

关键词: 形式概念分析, 三元背景, 三元概念, 三元概念约简

Abstract:

The reduction of triadic concepts is an important problem in triadic concept analysis，because it can not only simplify the representation of triadic graphs，but also help to better understand the meaning of triadic concepts and extract valuable information from them. Based on the triadic factor analysis，reduction of triadic concepts is studied to keep all the triadic relationships in the triadic context. Firstly，a reduction of triadic concept is defined based on triadic factor analysis. The method is to find as few triadic concepts as possible under the condition of preserving the original triadic context. That is these selected triadic concepts can completely reflect all the triadic relations contained in the original triadic context. Secondly，the relationship between the triadic factorizations and the triadic concept consistent sets is discussed，and the necessary and sufficient conditions for consistent sets and reducts are given. Finally，the triadic concepts are classified into three categories by using triadic concept reduction: core （absolute necessary） concept，relative necessary concept and unnecessary concept. Moreover，the necessary and sufficient conditions for each class of triadic concepts are obtained. In addition，the detailed process of finding triadic concept reduct using triadic factorization and the definition of reduction is given by an example.

Key words: formal concept analysis, triadic context, triadic concept, triadic concept reduction

中图分类号:

TP301

李俊余, 李星璇, 王霞, 吴伟志. 基于三元因子分析的三元概念约简[J]. 南京大学学报(自然科学版), 2020, 56(4): 480–493.

Junyu Li, Xingxuan Li, Xia Wang, Weizhi Wu. Reduction of triadic concepts based on triadic factor analysis[J]. Journal of Nanjing University(Natural Sciences), 2020, 56(4): 480–493.

图/表 4

表1

图1

图2

表2

约简前后三元概念对比"

约简前三元概念	约简后三元概念
约简前三元概念	约简 $F 1$	约简 $F 2$	约简 $F 3$	约简 $F 4$	约简 $F 5$	约简 $F 6$	约简 $F 7$	约简 $F 8$
C1,C2,…,C18	C1,C2,C4,C5,C10,C13,C14,C16	C1,C2,C4,C8,C10,C13,C14,C16	C1,C4,C5,C7,C10,C13,C14,C16	C1,C4,C7,C8,C10,C13,C14,C16	C1,C2,C3,C5,C10,C13,C14,C16，C17	C1,C3,C5,C7,C10,C13,C14,C16，C17	C1,C2,C3,C8,C10,C13,C14,C16，C17	C1,C3,C7,C8,C10,C13,C14,C16，C17

表2

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[1]	王霞, 谭斯文, 李俊余, 吴伟志. 基于条件属性蕴含的概念格构造及简化[J]. 南京大学学报(自然科学版), 2019, 55(4): 553-563.
[2]	李俊余1，2，朱荣杰1，王　霞1，2*，吴伟志1，2. 三元概念与形式概念的关系[J]. 南京大学学报(自然科学版), 2018, 54(4): 786-.
[3]	郭铭铭，窦建华，杨彬 . 基于形式化概念分析和概念相似性度量的程序重组方法 [J]. 南京大学学报(自然科学版), 2011, 47(5): 594-604.

基于三元因子分析的三元概念约简

Reduction of triadic concepts based on triadic factor analysis

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