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.
Formal Concept Analysis （FCA） is an order-theoretic method for the mathematical analysis of scientific data, pioneered by R. Wille in mid 80＇s. Over the past twenty years, FCA has been widely studied and become a powerful tool for machine learning, software engineering and information retrieval. In addition to being a technique for classifying and defining concepts from data, FCA may be exploited to discover implications among the objects and the attributes. On the other hand, inclusion degree theory proposed by Prof. Zhang W. X. is a measure theory for order theory. In fact the synthesis between FCA and inclusion degree theory will be greatly advanta- geous to the further development of such domains as intelligent control, pattern recognition, knowledge processing etc. This paper serves to introduce partially ordered set （poset） and inclusion degree theory to FCA. For this, the authors establish three posets, namely, G poset, M poset as well as GM poset and based on the three posets, they define three inclusion degrees on them. Then they show the relationship between the posets and concept lattice, and prove that the basic concepts such as intents, extents and implications can be reconstructed either by the partial orders or by the inclusion degrees of the posets. These results will be very helpful for people to understand the essence of concepts and the structure of concept lattice in FCA, and can be regarded as the main foundation of quantitative measures which are defined for FCA.
出处
《计算机学报》
EI
CSCD
北大核心
2006年第2期219-226,共8页
Chinese Journal of Computers
基金
国家自然科学基金(70471003
60275019)
高等学校博士学科点专项科研基金(20050108004)
山西省自然科学基金(20031036
20041040
20041014)资助
关键词
形式概念分析
概念格
偏序集
包含度
概念
formal concept analysis
concept lattice
poset
inclusion degree
concept
