Study On The Construction Algorithm Of Concept Trilattices

Concept lattice, also called formal concept analysis, is a mathematical theory produced by Wille in 1982. The structure of concept lattice is a tool that can find the structure of concept from data set. It is foundation of information representation. It has successfully been applied to many fields, such as psychology, sociology, anthropology, medicine, biology, linguistics, computer sciences, mathematics and industrial engineering. Concept lattice has developed 30 years to now and has matured. Concept lattice can process dual data set directly. But as with triple data set, we must translate a tri-context to two dual contexts fist.Wille proposed concept trilattices in 1995 based on concept lattice to process triple data set. It is also called triadic concept analysis(TCA). TCA provides a theoretical basis for processing triple data set directly. It can mine triple concepts from triple data set directly for classification and can construct visualized concept trilattices, representing the relation of concepts and the relation of three dimentions. With Folksonomy emerging rapidly on the internet, Tri-concept lattice has become popular. It can build a more complicated structure from triple data set, and the process is hard. Like concept lattice, the key step of producing concept trilattices is algorithm. An efficient algorithm can produce Tri-concept quickly, which also is the key step of data analysis. Unfortunately, now the research of algorithm of computing Tri-concepts is just starting at home and abroad, and there are few algorithms of constructing Tri-concept lattice. Wille just proposed a primary algorithm in his paper.This thesis is aimed to design some algorithms of constructing concept trilattices in a less complex method. Fist, we review three algorithms constructing concept lattice, including Nextclosure that computes concepts in dictionary order, Cbo that uses canonical test and Fcbo that uses better canonical test. Second, we translate a tri-context of(U,T,R,Y) to a context of(U,T×R,Y?) and design three triple algorithms, including Tri-Nextclosure, TriCbo and Tri-Fcbo based on the three different dual algorithms. Last, we implement them and contrast their efficient from aspects of objects, attributes, conditions and context density. We also illustrate the application of concept trilattices in Folksonomy by mining data of Bibsonomy.