Posets,Inclusion Degree Theory and FCA
Qu Kai · Chinese Journal of Computers · 2006
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 advantageous 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.