Affiliations: Department of Applied Mathematics and Physics,
Institute of Science, PLA University of Science and Technology, Nanjing 211101
Jiangsu, P. R. China. bblylm@126.com | Institute for Information and System Sciences, Faculty
of Science, Xi'an Jiaotong University, Xi'an 710049
Shaan'xi, P. R. China
Note: [] Address for correspondence: Department of Applied Mathematics
and Physics, Institute of Science, PLA University of Science and Technology,
Nanjing 211101 Jiangsu, P. R. China
Abstract: As an effective tool for data analysis and knowledge processing, the
theory of concept lattices has been studied extensively and applied to various
fields. In order to discover useful knowledge, one often ignores some
attributes according to a particular purpose and merely considers the
subcontexts of a rather complex context. In this paper, we make a deep
investigation on the theory of concept lattices of subcontexts. An approach to
construct the concept lattice of a context is first presented by means of the
concept lattices of its subcontexts. Then the concept lattices induced by all
subcontexts of the context are considered as a set, and an order relation is
introduced into the set. It is proved that the set together with the order
relation is a complete lattice. Finally, the top element and the bottom element
of the complete lattice are also obtained.
Keywords: concept lattice, subcontext, congruence, closure operator, order relation
