The Topology Structure In Lattice And Concept Lattice

Classical concept lattice was first proposed by professor Wile.R in1982. The establishment of the concept lattice is a clustering process of concept, it is mainly used to find sort and display of the concept. The theory is an important tool of the data analysis and knowledge processing.Firstly, in order to form the concept, a construction algorithm about the concept lattice is gived in this paper-the generating methods about the root concept. further more, the concept lattice about formal context’s direct sum is researched in this article. the result is that the concept lattice about formal context’s direct sum and the concept’s cartesian product about every formal context are isomorphic.Secondly, in this article the upper or lower case topology is explained with the ideal and the filter glue on the basis of previous studies. The relation of the upper case topology and the lower case topology is also studied. the result is that both of them are reverse lattice topology.Finally, the general topology about the lattice is derived based on the upper or the lower case topology. The general topology about the concept lattice is also gived in this paper. These results laid a solid theoretical basis for the continuity or homeomorphism study about different concept lattice.