南京大学学报(自然科学版) ›› 2019, Vol. 55 ›› Issue (4): 553–563.doi: 10.13232/j.cnki.jnju.2019.04.005

• • 上一篇    下一篇

基于条件属性蕴含的概念格构造及简化

王霞1,2(),谭斯文1,李俊余1,2,吴伟志1,2   

  1. 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:2019-05-28 出版日期:2019-07-30 发布日期:2019-07-23
  • 通讯作者: 王霞 E-mail:bblylm@126.com
  • 基金资助:
    浙江省自然科学基金(LY18F030017)

Constructions and simplifications of concept lattices based onconditional attribute implications

Xia Wang1,2(),Siwen Tan1,Junyu Li1,2,Weizhi Wu1,2   

  1. 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:2019-05-28 Online:2019-07-30 Published:2019-07-23
  • Contact: Xia Wang E-mail:bblylm@126.com

RichHTML

31

PDF (PC)

988

摘要：

基于三元背景研究三类概念格的构造和简化.首先，基于三元背景构造一个条件属性蕴含形式背景，该背景以三元背景属性集上的属性蕴含为对象，以三元背景的条件为属性.并针对条件属性蕴含形式背景给出形式概念的定义，构造相应的概念格.其次，由于条件属性蕴含形式背景中对象的个数随着三元背景中属性个数的增加呈指数级增长，这使得条件属性蕴含形式背景往往是一个比较大的数据表，因此，对条件属性蕴含形式背景进行对象约简，将原来的对象集替换为单个条件下形式背景的极小属性蕴含构成的集合.该对象约简方法不仅在很大程度上简化了条件属性蕴含形式背景，而且简化后的形式背景对应的概念格与原来的概念格同构.最后，在条件属性蕴含形式背景上引入了可能性算子和必然性算子，在此基础上定义了对象定向概念格和属性定向概念格.

关键词: 概念格, 三元背景, 条件属性蕴含, 对象定向概念格, 属性定向概念格

Abstract:

Constructions and simplifications of three types of concept lattice are studied based on a triadic context. Firstly，a new formal context is constructed based on conditional attribute implications，which takes the implications between attributes of the triadic context as the objects and the conditions of the triadic context as the attributes. Then definitions of formal concept and concept lattice are given in the conditional attribute implication context. Secondly,since the number of objects in the conditional attribute implication context increases exponentially with the increase of the number of attributes in the triadic context，which makes the conditional attribute implication context usually becomes a large data table. The object reduction of the conditional attribute implication context is carried out，and the original object set is replaced with the set of minimal attribute implications of the formal context under each single condition. It is shown that the object reduction method can simplify the conditional attribute implication context to a great extent，and the concept lattice corresponding to the simplified context is isomorphic to the original concept lattice. Finally，the possibility operator and necessary operator are introduced in the conditional attribute implication context to define the object oriented concept lattice and property oriented concept lattice of the new context.

Key words: concept lattice, triadic context, conditional attribute implication, object oriented concept lattice, property oriented concept lattice

中图分类号: 

  • TP301

表1

三元背景"

c1c2c3
m1m2m3m1m2m3m1m2m3
g1101011101
g2010110110

表2

在条件c1下的形式背景Kc1"

m1m2m3
g1101
g2010

表3

条件属性蕴含形式背景Cimp(K)"

c1c2c3
?→m1001
?→m2010
?→m3000
m1→m2010
m1→m3100
m2→m1001
m2→m3000
m3→m1101
m3→m2010
{m1,m2}?→m3100
{m1,m3}?→m2010
{m2,m3}?→m1101

图1

概念格L(Cimp(K))"

表4

简化背景SCimp(K)"

c1c2c3
?→m1001
?→m2010
m1→m3100
m3→m1101

图2

概念格L(SCimp(K))"

图3

对象定向概念格LO(Cimp(K))"

图4

对象定向概念格LO(SCimp(K))"

图5

属性定向概念格LP(Cimp(K))"

1 LehmannF，WilleR. A triadic approach to formal concept analysis∥Ellis G，Levinson R，Rich W,et al. Conceptual Structures：applications，Implemen?tation and Theory. Springer Berlin Heidelberg，1995：32-43.
2 WilleR. The basic theorem of triadic concept analysis. Order，1995，12(2)：149-158.
3 WilleR. Restructuring lattice theory：an approach based on hierarchies of concepts∥Rival I. NATO Advanced Study Institute (Ordered Sets). Springer Berlin Heidelberg，1982：445-470.
4 GanterB，WilleR. Formal concept analysis：mathematical foundations. Springer Berlin Heidelberg，1999,17-61.
5 WeiL，QianT，WanQ，et al. A research summary about triadic concept analysis. International Journal of Machine Learning and Cybernetics，2018，9(4)：699-712.
6 魏玲,万青,钱婷等.三元概念分析综述.西北大学学报(自然科学版),2014,44(5)：689-699.
Wei L，Wan Q，Qian T，et al.An overview of triadic concept analysis. Journal of Northwest University (Natural Science Edition)，2014，44(5)：689-699.
7 StummeG. Attribute exploration with background implications and exceptions∥Bock H H，Polasek W. Data Analysis and Information Systems. Springer Berlin Heidelberg，1996：457-469.
8 BělohlávekR，VychodilV. Attribute implications in a fuzzy setting∥Missaoui R，Schmid J. Formal Concept Analysis. Springer Berlin Heidelberg，2006：45-60.
9 VychodilV. On the importance of fuzzy attribute implications∥2008 IEEE International Conference on Fuzzy Systems. Hong Kong，China：IEEE，2008：281-286.
10 VychodilV. On minimal sets of graded attribute implications. Information Sciences，2015，294：478-488.
11 ZhaiY H，LiD Y，QuK S. Decision implication canonical basis：a logical perspective. Journal of Computer and System Sciences，2015，81(1)：208-218.
12 Rodríguez?LorenzoE，AdarichevaK，CorderoP，et al. From an implicational system to its corresponding D?basis∥Sadok B Y，Jan K. The 12th International Conference on Concept Lattices and Their Applications. Clermont?Ferrand，France：Blaise Pascal University，2015：217-228.
13 安秋生，孔祥玉. 函数依赖与属性蕴含的关系研究. 小型微型计算机系统，2017，38(9)：2000-2005.
An Q S，Kong X Y.Relationship study of functional dependency and attribute implication. Journal of Chinese Computer Systems，2017，38(9)：2000-2005.
14 TriskaJ，VychodilV. Logic of temporal attribute implications. Annals of Mathematics and Artificial Intelligence，2017，79(4)：307-335.
15 VityaevE E，DeminA V，PonomaryovD K. Probabilistic generalization of formal concepts. Programming and Computer Software，2012，
38(5)：219-230.
16 BiedermannK. A foudation of the theory of trilatttices. Ph. D.Dissertation. Aachen:TU Darmstadt，1998.
17 GanterB，ObiedkovS A. Implications in triadic formal contexts∥Wolff K E，Pfeiffer H D，Delugach H S. Conceptual Structures. Springer Berlin Heidelberg，2004：186-195.
18 GlodeanuC V. Fuzzy?valued triadic implications∥Napoli A，Vychodil V. The 8th International Conference on Concept Lattices and Their Applications. Springer Berlin Heidelberg，2011：159-173.
19 Rodríguez?LorenzoE，CorderoP，EncisoM，et al. CAISL：simplification logic for conditional attribute implications∥Huchard M，Kuznetsov S O. The 13th International Conference on Concept Lattices and Their Applications. Moscow，Russia：National Research University，2016：337-348.
20 Rodríguez?LorenzoE，CorderoP，EncisoM，et al. An axiomatic system for conditional attribute implications in triadic concept analysis. International Journal of Intelligent Systems，2017，32(8)：760-777.
21 TangY Q，FanM，LiJ H. An information fusion technology for triadic decision contexts. International Journal of Machine Learning and Cybernetics，2016，7(1)：13-24.
22 祁建军，魏玲. 三元背景及概念三元格的简化. 计算机科学，2017，44(9)：53-57.
Qi J J，Wei L.Simplification of triadic contexts and concept trilattices. Computer Science，2017，44(9)：53-57.
23 王霞，张茜，李俊余等. 基于粗糙集的三元概念分析. 山东大学学报(理学版)，2017，52(7)：37-43.
Wang X，Zhang Q，Li J Y,et al.Triadic concept analysis based on rough set theory. Journal of Shandong University (Natural Science)，2017，52(7)：37-43.
24 李俊余，朱荣杰，王霞等. 三元概念与形式概念的关系. 南京大学学报(自然科学)，2018，54(4)：786-793.
Li J Y，Zhu R J，Wang X,et al.The relationship between triadic concepts and formal concepts. Journal of Nanjing University (Natural Science)，2018，54(4)：786-793.
25 王霞，江山，李俊余等. 三元概念的一种构造方法. 计算机研究与发展，2019，56(4)：544-853.
Wang X，Jiang S，Li J Y,et al. A construction method of triadic concepts. Journal of Computer Research and Development，2019，56(4)：544-853.
26 HwangS H. A triadic approach of hierarchical classes analysis on folksonomy mining. International Journal of Computer Science & Network Security，2007，7(8)：193-198.
27 HwangS H，KimE H. An approach for mining folksonomies based on the triadic class hierarchies. Advanced Science Letters，2012，9(1)：844-849.
28 刘晓今. 概念三元格构造算法及应用研究. 博士学位论文. 西安：西安电子科技大学，2013.
Liu X J.Study on the construction algorithem of concept trilattices and its applicationPh. DDissertation. Xi’an：Xidian University，2013.
29 王寿彪，李新明，刘东等. 基于大数据的装备体系三元概念认知系统模型构造框架. 系统工程与电子技术，2016，38(11)：2537-2545.
Wang S B，Li X M，Liu D,et al.Constructing framework of triadic concepts cognitive system model of equipment system of systems based on big data. Systems Engineering and Electronics，2016，38(11)：2537-2545.
30 李贞，张卓，王黎明. 基于三元概念分析的文本分类算法研究. 计算机科学，2017，44(8)：207-215.
Li Z，Zhang Z，Wang L M.Research on text classification algorithm based on triadic concept analysis. Computer Science，2017，44(8)：207-215.
31 王红敏，张卓，王黎明. 三元概念分析的联盟应用研究. 小型微型计算机系统，2018，39(12)：2571-2576.
Wang H M，Zhang Z，Wang L M.Application research on coalition of triadic concept analysis. Journal of Chinese Computer Systems，2018，39(12)：2571-2576.
32 HaoF，ParkD S，MinG Y，et al. K?Cliques mining in dynamic social networks based on triadic formal concept analysis. Neurocomputing，2016，209：57-66.
33 KumarC A，MouliswaranS C，LiJ H，et al. Role based access control design using triadic concept analysis. Journal of Central South University，2016，23(12)：3183-3191.
[1] 高云樵,马建敏. 变精度区间集概念格[J]. 南京大学学报(自然科学版), 2020, 56(4): 437-444.
[2] 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.
[3] 姚　丽1，曹仪铭2，崔　慧2，邹　丽1*. 一种基于直觉模糊语言概念格的规则提取方法[J]. 南京大学学报(自然科学版), 2018, 54(4): 758-.
[4] 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-.
[5] 李俊余1，2，王　霞1，2*，刘庆凤3. 属性定向概念格的协调近似表示空间[J]. 南京大学学报(自然科学版), 2017, 53(2): 333-.
[6] 李俊余1，2，王　霞1，2*. 对象定向概念格的不协调决策约简[J]. 南京大学学报(自然科学版), 2016, 52(5): 853-.
[7] 石慧 魏玲*. 面向对象(属性)概念格的布尔表达[J]. 南京大学学报(自然科学版), 2015, 51(2): 415-420.
[8] 李同军** ,王 霞,徐优红. 形式概念的布尔计算方法[J]. 南京大学学报(自然科学版), 2013, 49(5): 553-560.
[9]  马丽1,2**李仲玲1，米据生1
.  基于相似度的Galois格*[J]. 南京大学学报(自然科学版), 2012, 48(4): 445-451.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
[1] 狄　岚, 何锐波, 梁久祯. 基于可能性聚类和卷积神经网络的道路交通标识识别算法[J]. 南京大学学报(自然科学版), 2019, 55(2): 238 -250 .
[2] 梅志伟,王维东. 基于FPGA的卷积神经网络加速模块设计[J]. 南京大学学报(自然科学版), 2020, 56(4): 581 -590 .

版权所有 © 2021 《南京大学学报(自然科学)》

地址：江苏省南京市鼓楼区汉口路22号，南京大学学报编辑部，210093

电话：025-83592704 , 传真：025-83592704        技术支持：北京玛格泰克科技发展有限公司