资源描述：
《偏序集_包含度与形式概念分析》由会员上传分享，免费在线阅读，更多相关内容在行业资料-天天文库。
1、第29卷第2期计算机学报Vol.29No.22006年2月CHINESEJOURNALOFCOMPUTERSFeb.2006偏序集、包含度与形式概念分析曲开社翟岩慧(山西大学计算机与信息技术学院太原030006)摘要在形式背景上建立了3个偏序集:G偏序集、M偏序集和GM偏序集,并将包含度的概念引入到3个偏序集上.讨论了偏序集上的偏序关系和包含度与概念格之间的联系,并且证实了形式概念分析中的内涵、外延和蕴涵规则均可归结为偏序集上的序表示及包含度表示,这将有助于人们深刻理解形式概念分析中概念的含义及概念格的结构,为从定量分析角度研究形式概念分析提供了依据.关键词形式概念分析;
2、概念格;偏序集;包含度;概念中图法分类号TP301Posets,InclusionDegreeTheoryandFCAQUKai2SheZHAIYan2Hui(SchoolofComputerandInformationTechnology,ShanxiUniversity,Taiyuan030006)AbstractFormalConceptAnalysis(FCA)isanorder2theoreticmethodforthemathematicalanalysisofscientificdata,pioneeredbyR.Willeinmid80′s.Overthe
3、pasttwentyyears,FCAhasbeenwidelystudiedandbecomeapowerfultoolformachinelearning,softwareengineeringandinformationretrieval.Inadditiontobeingatechniqueforclassifyinganddefiningconceptsfromdata,FCAmaybeexploitedtodiscoverimplicationsamongtheobjectsandtheattributes.Ontheotherhand,inclusionde
4、greetheoryproposedbyProf.ZhangW.X.isameasuretheoryforordertheory.InfactthesynthesisbetweenFCAandinclusiondegreetheorywillbegreatlyadvanta2geoustothefurtherdevelopmentofsuchdomainsasintelligentcontrol,patternrecognition,knowledgeprocessingetc.Thispaperservestointroducepartiallyorderedset(p
5、oset)andinclu2siondegreetheorytoFCA.Forthis,theauthorsestablishthreeposets,namely,Gposet,Mpo2setaswellasGMposetandbasedonthethreeposets,theydefinethreeinclusiondegreesonthem.Thentheyshowtherelationshipbetweentheposetsandconceptlattice,andprovethatthebasicconceptssuchasintents,extentsandim
6、plicationscanbereconstructedeitherbythepartialordersorbytheinclusiondegreesoftheposets.TheseresultswillbeveryhelpfulforpeopletounderstandtheessenceofconceptsandthestructureofconceptlatticeinFCA,andcanberegar2dedasthemainfoundationofquantitativemeasureswhicharedefinedforFCA.Keywordsformalc
7、onceptanalysis;conceptlattice;poset;inclusiondegree;concept提出的一种从形式背景(formalcontext)建立概念1引言格来进行数据分析和规则提取的强有力工具,已被[2～5][6]广泛地研究,并应用到机器学习、软件工[1][7～10][11～13]形式概念分析(formalconceptanalysis)是Wille程和信息获取等领域.收稿日期:2005204224;修改稿收到日期:2005210211.本课题得到国家自然科学基金(70471003,60275019
