Four Research Constructor Concept Lattice

Formal concept analysis is a visual hierarchy theory, which was proposed by German mathematician Wille R. in1982, and was applied to build concept lattice. From then on, many experts and scholars made lots of efforts in this field, including lattice construction and compression and rules acquisition.Facing of huge data, studying how to get concept lattice, concept lattice of complement formal context, object-oriented concept lattice and property-oriented concept lattice quickly is meaningful and valuable.In this paper, on the basis of predecessor’s research, we make some research and get following results:1.Firstly, some concepts of complement context can be obtained by the operator+, and it can be proved that these concepts includes all the irreducible elements of complement context; then, the approach to find all the irreducible elements is given; finally, all the concepts of complement context can be obtained.2.A kind of operator based on a formal context is defined using the theory of inclusion degree, and it can be demonstrated that this new operator can induce concept lattice, concept lattice of complement formal context, object-oriented concept lattice and property-oriented concept lattice when inclusion degree takes particular values. This shows that the theory of inclusion degree can express and unify the form of the different lattices based on a formal context.