概念格共有与独有属性(对象)的关系研究
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摘要
Wille概念格可用于共有属性(对象)的数据分析,而面向对象概念格和面向属性概念格可用于独有属性(对象)的数据分析,这两种数据分析方法在形式概念分析理论中均属于热点研究问题。为了区分这两种数据分析方法,首先引入了共有属性(对象)与独有属性(对象)的概念,对它们的算子性质进行了研究。其次围绕命题"共有属性(对象)是独有属性(对象)"展开讨论。具体地,证明了该命题的充分条件和必要条件均不成立,并提出了该命题成立的充要条件;在此基础上,表明了一个对象属性序对既是共有概念又是独有概念时,在概念序关系意义下它是唯一的,即不存在比该序对更大的概念,也不存在比该序对更小的概念。最后从共有与独有属性(对象)的角度给出了Wille概念格、面向对象概念格和面向属性概念格的异同。
Willes concept lattice can be used for common attributes(objects) data analysis, while object-oriented and property-oriented concept lattices can be used for unique attributes(objects) data analysis. In fact, these two kinds of data analysis methods have become hot research topics in the theory of formal concept analysis. In order to distinguish them from each other, the notions of common attributes(objects) and unique attributes(objects) are first defined, and some properties on their operators are also studied. Then this paper discusses whether a common attribute(object) is a unique attribute(object) or not. Specifically, this paper proves that neither the sufficient condition nor the necessary condition is true. Furthermore, the necessary and sufficient conditions are established to demonstrate that an ordered pair of object and attribute sets will become unique with respect to the concept partial order when it is not only a common attribute concept but also a unique attribute concept. In other words, there exists neither a greater concept nor a less concept than the ordered pair. Finally, the similarities and differences among Willes, object-oriented and property-oriented concept lattices are shown from the perspectives of common attributes(objects) and unique attributes(objects).
Willes concept lattice can be used for common attributes(objects) data analysis, while object-oriented and property-oriented concept lattices can be used for unique attributes(objects) data analysis. In fact, these two kinds of data analysis methods have become hot research topics in the theory of formal concept analysis. In order to distinguish them from each other, the notions of common attributes(objects) and unique attributes(objects) are first defined, and some properties on their operators are also studied. Then this paper discusses whether a common attribute(object) is a unique attribute(object) or not. Specifically, this paper proves that neither the sufficient condition nor the necessary condition is true. Furthermore, the necessary and sufficient conditions are established to demonstrate that an ordered pair of object and attribute sets will become unique with respect to the concept partial order when it is not only a common attribute concept but also a unique attribute concept. In other words, there exists neither a greater concept nor a less concept than the ordered pair. Finally, the similarities and differences among Willes, object-oriented and property-oriented concept lattices are shown from the perspectives of common attributes(objects) and unique attributes(objects).
引文
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[18]Li J H,Wu W Z.Granular computing approach for formal concept analysis and its research outlooks[J].Journal of Shandong University(Natural Science),2017,52(7):1-12.
[2]罗忠诚,张志强,王忠浩,等.语义背景下基于形式概念分析的产品族组件规划与类型识别研究[J].中国机械工程,2007,18(22):2729-2733.
[5]蒋平,任胜兵,林鹃.形式概念分析在软件工程中的应用[J].计算机技术与发展,2008,18(4):127-129.
[8]刘旭龙,洪文学,张涛,等.基于形式概念分析的中医辨证可视化方法[J].燕山大学学报,2010,34(2):162-164.
[10]张文修,魏玲,祁建军.概念格的属性约简理论与方法[J].中国科学:信息科学,2005,35(6):628-639.
[11]洪文学,李少雄,张涛,等.大数据偏序结构生成原理[J].燕山大学学报,2014,38(5):388-393.
[12]张涛,任宏雷,洪文学,等.基于属性拓扑的可视化形式概念计算[J].电子学报,2014,42(5):925-932.
[17]徐伟华,李金海,魏玲,等.形式概念分析理论与应用[M].北京:科学出版社,2016.
[18]李金海,吴伟志.形式概念分析的粒计算方法及其研究展望[J].山东大学学报(理学版),2017,52(7):1-12.
[2]Luo Z C,Zhang Z Q,Wang Z H,et al.Research on component planning and category recognition of product family based on formal concept analysis in semantic context[J].China Mechanical Engineering,2007,18(22):2729-2733.
[3]Kaytoue M,Kuznetsov S O,Napoli A,et al.Mining gene expression data with pattern structures in formal concept analysis[J].Information Sciences,2011,181(10):1989-2001.
[4]Ferjani F,Elloumi S,Jaoua A,et al.Formal context coverage based on isolated labels:an efficient solution for text feature extraction[J].Information Sciences,2012,188(1):198-214.
[5]Jiang P,Ren S B,Lin J.Using formal concept analysis for software engineering[J].Computer Technology and Development,2008,18(4):127-129.
[6]Tonella P.Using a concept lattice of decomposition slices for program understanding and impact analysis[J].IEEETransactions on Software Engineering,2003,29(6):495-509.
[7]Huysegomsa T,Snoecka M,Dedenea G,et al.Visualizing variability management in requirements engineering through formal concept analysis[J].Procedia Technology,2013,9:189-199.
[8]Liu X L,Hong W X,Zhang T,et al.A visualization method for differential diagnosis in TCM based on formal concept analysis[J].Journal of Yanshan University,2010,34(2):162-164.
[9]Korobko A V,Penkova T G.On-line analytical processing based on formal concept analysis[C]//Proceedings of the International Conference on Computational Science,University of Amsterdam,May 31-Jun 2,2010.New York:Elsevier Science Inc,2010:2311-2317.
[10]Zhang W X,Wei L,Qi J J.Attribute reduction theory and approach of concept lattice[J].Science in China,Series F:Information Sciences,2005,35(6):628-639.
[11]Hong W X,Li S X,Zhang T,et al.Generation principle of partial ordered structure towards big data[J].Journal of Yanshan University,2014,38(5):388-393.
[12]Zhang T,Ren H L,Hong W X,et al.The visualizing calculation of formal concept that based on the attribute topologies[J].Acta Electronica Sinica,2014,42(5):925-932.
[13]Zhang T,Ren H L,Wang X M.A calculation of formal concept by attribute topology[J].ICIC Express Letters,Part B:Applications,2013,4(3):793-800.
[14]Yao Y Y.Concept lattices in rough set theory[C]//Proceedings of the IEEE Annual Meeting of the Fuzzy Information,Banff,Jun 27-30,2004.Piscataway:IEEE,2004:796-801.
[15]Düntsch I,Gediga G.Modal-style operators in qualitative data analysis[C]//Proceedings of the 2002 IEEE International Conference on Data Mining,Maebashi City,Dec 9-12,2002.Washington:IEEE Computer Society,2002:155-162.
[16]Wang X,Zhang W X.Relations of attribute reduction between object and property oriented concept lattices[J].KnowledgeBased Systems,2008,21(5):398-403.
[17]Xu W H,Li J H,Wei L,et al.Formal concept analysis:theory and application[M].Beijing:Science Press,2016.
[18]Li J H,Wu W Z.Granular computing approach for formal concept analysis and its research outlooks[J].Journal of Shandong University(Natural Science),2017,52(7):1-12.
[2]罗忠诚,张志强,王忠浩,等.语义背景下基于形式概念分析的产品族组件规划与类型识别研究[J].中国机械工程,2007,18(22):2729-2733.
[5]蒋平,任胜兵,林鹃.形式概念分析在软件工程中的应用[J].计算机技术与发展,2008,18(4):127-129.
[8]刘旭龙,洪文学,张涛,等.基于形式概念分析的中医辨证可视化方法[J].燕山大学学报,2010,34(2):162-164.
[10]张文修,魏玲,祁建军.概念格的属性约简理论与方法[J].中国科学:信息科学,2005,35(6):628-639.
[11]洪文学,李少雄,张涛,等.大数据偏序结构生成原理[J].燕山大学学报,2014,38(5):388-393.
[12]张涛,任宏雷,洪文学,等.基于属性拓扑的可视化形式概念计算[J].电子学报,2014,42(5):925-932.
[17]徐伟华,李金海,魏玲,等.形式概念分析理论与应用[M].北京:科学出版社,2016.
[18]李金海,吴伟志.形式概念分析的粒计算方法及其研究展望[J].山东大学学报(理学版),2017,52(7):1-12.