基于集值映射的形式概念分析

数学季刊 ›› 2008, Vol. 23 ›› Issue (3): 390-396.

基于集值映射的形式概念分析

1. School of Mathematics Computer Engineering,Xihua University 2. Zheng zhou Industry Safety Vocational College 3. Department of Applied Mathemat-ics,Southwest Jiaotong University

收稿日期:2007-10-20 出版日期:2008-09-30 发布日期:2023-09-21
作者简介: CHEN Li-ya(1972- ), female, native of Xindu, Sichun, M.S.D., a lecturer of Xihua University, engages in uncertainty reasoning; HUANG Tao(1962- ), male, native of Zhoukou, Henan, M.S.D., a advanced lecturer of Zhengzhou Industry Safety Vocational College, engages in uncertainty reasoning; SONG Zhen-ming(1960- ), male, native of Zhengzhou, Henan, a professor of Southwest Jiaotong University, Ph.D.,engages in uncertainty reasoning; PEI Zheng(1968- ), male, native of Yulin, Shannxi, a professor f Xihua University, Ph.D., engages in uncertainty reasoning.
基金资助:
Supported by the Young Foundation of Sichuan Province(06ZQ026-037); Supported by
the Education Department Foundation of Sichuan Province(2005A121; 2006A084)

Formal Concept Analysis Based on Set-valued Mapping

1. School of Mathematics Computer Engineering,Xihua University 2. Zheng zhou Industry Safety Vocational College 3. Department of Applied Mathemat-ics,Southwest Jiaotong University

Received:2007-10-20 Online:2008-09-30 Published:2023-09-21
About author: CHEN Li-ya(1972- ), female, native of Xindu, Sichun, M.S.D., a lecturer of Xihua University, engages in uncertainty reasoning; HUANG Tao(1962- ), male, native of Zhoukou, Henan, M.S.D., a advanced lecturer of Zhengzhou Industry Safety Vocational College, engages in uncertainty reasoning; SONG Zhen-ming(1960- ), male, native of Zhengzhou, Henan, a professor of Southwest Jiaotong University, Ph.D.,engages in uncertainty reasoning; PEI Zheng(1968- ), male, native of Yulin, Shannxi, a professor f Xihua University, Ph.D., engages in uncertainty reasoning.
Supported by:
Supported by the Young Foundation of Sichuan Province(06ZQ026-037); Supported by
the Education Department Foundation of Sichuan Province(2005A121; 2006A084)

摘要/Abstract

摘要： Formal concept analysis (FCA) is a discipline that studied the hierarchical struc-tures induced by a binary relation between a pair of sets, and applies in data analysis, infor-mation retrieval, knowledge discovery, etc. In this paper, it is shown that a formal context T is equivalent to a set-valued mapping S : G → P(M), and formal concepts could be defined in the set-valued mapping S. It is known that the topology and set-valued mapping are linked. Hence, the advantage of this paper is that the conclusion make us to construct formal concept lattice based on the topology.

关键词: FCA, set-valued mapping, isomorphism

Abstract: Formal concept analysis (FCA) is a discipline that studied the hierarchical struc-tures induced by a binary relation between a pair of sets, and applies in data analysis, infor-mation retrieval, knowledge discovery, etc. In this paper, it is shown that a formal context T is equivalent to a set-valued mapping S : G → P(M), and formal concepts could be defined in the set-valued mapping S. It is known that the topology and set-valued mapping are linked. Hence, the advantage of this paper is that the conclusion make us to construct formal concept lattice based on the topology.

Key words: FCA, set-valued mapping, isomorphism

中图分类号:

O144

陈利娅, 黄涛, 宋振明等. 基于集值映射的形式概念分析[J]. 数学季刊, 2008, 23(3): 390-396.

CHEN Li-ya , HUANG Tao, SONG Zhen-ming , PEI Zheng. Formal Concept Analysis Based on Set-valued Mapping[J]. Chinese Quarterly Journal of Mathematics, 2008, 23(3): 390-396.

[1]	余德民, 李爱华. 一类特殊的无限维李代数的单性与同构[J]. 数学季刊, 2013, 28(4): 612-617.
[2]	李祖泉, 王久晶. 集值映射空间上的自然映射[J]. 数学季刊, 2011, 26(1): 21-25.
[3]	吴健荣, 柳海燕. Φ型压缩集值映射列的公共不动点定理[J]. 数学季刊, 2009, 24(4): 504-510.
[4]	陈倩华, 范兴奎. 弱P-反演半群上的P-核正规系[J]. 数学季刊, 2008, 23(2): 171-177.
[5]	钟育彬 . 幂群的同态与同构[J]. 数学季刊, 1997, 12(3): 7-14.