南京大学学报(自然科学版) ›› 2022, Vol. 58 ›› Issue (1): 19–28.doi: 10.13232/j.cnki.jnju.2022.01.003

• • 上一篇    下一篇

三元概念的增量式构造方法

王霞1,2(), 全园1, 李俊余1,2, 吴伟志1,2   

  1. 1.浙江海洋大学信息工程学院, 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:2021-06-16 出版日期:2022-01-30 发布日期:2022-02-22
  • 通讯作者: 王霞 E-mail:bblylm@126.com
  • 作者简介:E⁃mail： bblylm@126.com
  • 基金资助:
    国家自然科学基金(61573321);浙江省自然科学基金(LY18F030017)

Incremental construction method of triadic concepts

Xia Wang1,2(), Yuan Quan1, Junyu Li1,2, Weizhi Wu1,2   

  1. 1.School of Information Engineering, 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:2021-06-16 Online:2022-01-30 Published:2022-02-22
  • Contact: Xia Wang E-mail:bblylm@126.com

RichHTML

3

PDF (PC)

516

摘要：

三元概念的构造方法是三元概念分析的核心问题之一，当条件逐个增加时，研究三元概念的增量式构造方法.首先，详细分析增加一个新的条件后原三元背景中三元概念的变化以及新增加的条件对新背景的三元概念的影响.分别针对下述四种情况给出充分必要条件：（1）新添加的条件对原背景的三元概念不影响，它仍旧是新三元背景的三元概念；（2）原背景的三元概念被替换掉，它不再是新三元背景的三元概念，替换后的三元概念的外延和内涵与原来一致，但是方式增加了新的条件；（3）原背景的三元概念与新的条件共同生成一个新的三元概念；（4）新增加的条件不借助任何原背景的三元概念生成新的三元概念.在此基础上给出基于条件的三元概念的增量式构造算法.最后，通过实例阐明增量式方法生成三元概念的详细过程.

关键词: 三元概念分析, 三元背景, 三元概念, 增量式构造方法

Abstract:

The construction method of triadic concepts is one of the key problems in triadic concept analysis. When conditions increase one by one，the incremental construction method of triadic concepts is studied. First of all，it analyzes the changes of the original triadic concepts and the influence of the newly added condition on the new triadic concepts. Sufficient and necessary conditions are given for the following four cases. (1) The newly added condition has no effect on the original triadic concept. That is，it is still a triadic concept of the new triadic context. (2) The original triadic concept has been updated，which is no longer the triadic concept of the new triadic context. The extent and intent of the updated triadic concept are consistent with the original，but the newly added condition has been added to the modus of the updated triadic concept. (3) The original triadic concept and the newly added condition together generate a new triadic concept of the new triadic context. (4) The newly added condition generates a new triadic concept without the help of any original triadic concepts. Then the incremental construction algorithm of triadic concept based on conditions is given. Finally，an example is given to illustrate the detailed process of generating triadic concepts by incremental method.

Key words: triadic concept analysis, triadic context, triadic concept, incremental construction method

中图分类号: 

  • TP301

表1

三元背景K1,K2,K3,Y"

c1c2c3
g1g2g3g4g5g6g1g2g3g4g5g6g1g2g3g4g5g6
x1110011110010011001
x2100101000101101010
x3011100111110110101
1 Lehmann F，Wille R. A triadic approach to formal concept analysis∥Conceptual Structures：Applications，Implementation and Theory. Springer Berlin Heidelberg，1995：32-43.
2 Wille R. Restructuring lattice theory：An approach based on hierarchies of concepts∥Rival I. Ordered sets. Springer Berlin Heidelberg，1982：445-470.
3 Ganter B，Wille R. Formal concept analysis：Mathematical foundations. Berlin：Springer，1999，17-61.
4 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.
5 Wei L，Qian T，Wan Q，et al. A research summary about triadic concept analysis. International Journal of Machine Learning and Cybernetics，2018，9(4)：699-712.
6 Wille R. The basic theorem of triadic concept analysis. Order，1995，12(2)：149-158.
7 Biedermann K. Triadic Galois connections∥Denecke K，Lüders O. General algebra and applications in discrete mathematics. Aachen：Shaker Verlag，1997：23-33.
8 Biedermann K. An equational theory for trilattices. Algebra Universalis，1999，42(4)：253-268.
9 Groh B，Wille R. Lattices of triadic concept graphs∥8th International Conference on Conceptual Structures. Springer Berlin Heidelberg，2000：332-341.
10 孙斌斌. 概念三元格构造算法研究. 硕士学位论文. 西安：西安电子科技大学，2015.
Sun B B. Study on the construction algorithm of concept trilattices. Master Dissertation. Xi'an：Xidian University，2015.
11 Biedermann K. How triadic diagrams represent conceptual structures∥5th Conceptual Structures：Fulfilling Peirce's Dream. Springer Berlin Heidelberg，1997：304-317.
12 Ganter B，Obiedkov S A. Implications in triadic formal contexts∥12th International Conference on Conceptual Structures. Springer Berlin Heidelberg，2004：186-195.
13 Missaoui R，Kwuida L. Mining triadic association rules from ternary relations∥9th International Conference on Formal Concept Analysis. Springer Berlin Heidelberg，2011：204-218.
14 Dau F，Wille R. On the modal understanding of triadic context∥Decker R，Gaul W. Classification and information processing at the turn of the millennium. Springer Berlin Heidelberg，2000：83-94.
15 Jaschke R，Hotho A，Schmitz C，et al. TRIAS：An algorithm for mining iceberg tri?lattices∥6th Inter?national Conference on Data Mining.Hong Kong，China：IEEE，2006：907-911.
16 Kavtoue M，Kuznetsov S，Macko J，et al. Mining biclusters of similar values with triadic concept analysis. 2011,arXiv:.
17 Kaytoue M，Kuznetsov S O，Macko J，et al. Biclustering meets triadic concept analysis. Annals of Mathematics and Artificial Intelligence，2014，70(1/2)：55-79.
18 Belohlavek R，Vychodil V. Optimal factorization of three?way binary data∥2010 IEEE International Conference on Granular Computing. San Jose，CA，USA：IEEE，2010：61-66.
19 Glodeanu C. Factorization methods of binary，triadic，real and fuzzy data. Informatica，2011，56(2)：81-86.
20 Belohlavek R，Glodeanu C，Vychodil V. Optimal factorization of three?way binary data using triadic concepts. Order，2013，30(2)：437-454.
21 Glodeanu C V. Tri?ordinal factor analysis∥International Conference on Formal Concept Analysis. Springer Berlin Heidelberg，2013：125-140.
22 Belohlavek R，Osicka P. Triadic concept analysis of data with fuzzy attributes∥2010 IEEE International Conference on Granular Computing. San Jose，CA，USA：IEEE，2010：661-665.
23 Belohlavek R，Osicka P. Triadic concept lattices of data with graded attributes. International Journal of General Systems，2012，41(2)：93-108.
24 Konecny J，Osicka P. Triadic concept lattices in the framework of aggregation structures. Information Sciences，2014，279：512-527.
25 Glodeanu C V. Fuzzy?Valued triadic implications∥Proceedings of the 8th International Conference on Concept Lattices and Their Applications. Nancy，France：CEUR?WS.org，2011：159-173.
26 Belohlavek R，Osicka P. Triadic fuzzy Galois connections as ordinary connections. Fuzzy Sets and Systems，2014(249)：83-99.
27 汤亚强，范敏，李金海. 三元形式概念分析下的认知系统模型及信息粒转化方法. 山东大学学报(理学版)，2014，49(8)：102-106.
Tang Y Q，Fan M，Li J H. Cognitive system model and approach to transformation of information granules under triadic formal concept analysis. Journal of Shandong University (Natural Science)，2014，49(8)：102-106.
28 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.
29 魏玲，曹丽，祁建军. 三元背景基于二元关系不变的约简. 西北大学学报(自然科学版)，2017，47(3)：313-320.
Wei L，Cao L，Qi J J. Reduction based on the binary relations for triadic contexts. Journal of Northwest University (Natural Science Edition)，2017，47(3)：313-320.
30 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.
31 Zhuk R，Ignatov D I，Konstantinova N. Concept learning from triadic data. Procedia Computer Science，2014(31)：928-938.
32 Kumar C A，Mouliswaran S C，Li J H，et al. Role based access control design using triadic concept analysis. Journal of Central South University，2016，23(12)：3183-3191.
33 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.
34 薛金蓉，安秋生，郑军. 概念格的内涵缩减与数据库推理依赖. 计算机研究与发展，2014，51(1)：96-103.
Xue J R，An Q S，Zheng J. Intent reduction of concept lattice and database inference dependence. Journal of Computer Research and Development，2014，51(1)：96-103.
35 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)：844-853.
Wang X，Jiang S，Li J Y，et al. A construction method of triadic concepts. Journal of Computer Research and Development，2019，56(4)：844-853.
[1] 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.
[2] 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.
[3] 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-.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!

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