Research The Theory Of Concept Lattices

Formal context is a triple from the set of objects, attribute sets and the relationship between objects and attributes posed. Concept lattice is based on the form of background objects and properties to establish a binary relation between a data structure, grid is a concept for each node. Concept lattice was found suitable as the basic rules of data structure used to discover the rules of knowledge.Firstly, the concept lattice partially ordered sets and order isomorphism relationship was studied. The background of existing literature in the form Z = (U, A, I) of the object set U, attribute sets A and U∪A partial order is defined, that a partial order set (U,≤) with the concept of a collection of objects (γ(U),≤), or between the partially ordered set (A,≤) and attribute the concept of set (μ(A),≤) relation between the order isomorphism is given a structuralγ(U) orμ(A ) all the connotation and extension of the concept of the method. We form the background by defining Z = (U, A, I) of the object set power set P (U) and the properties of a collection of power set P (A) the partial order, that the partially ordered set (P (U),≤) or (P (A),≤) with the concept lattice∪(Z) isomorphic relationship between the order and use the relationship between order isomorphism gives a structure∪(Z) in the connotation and extension of all the methods .Secondly, the paper also forms the background of decision formal context, the coordination of consistent decision formal context and attribute reduction set determination was studied. Existing, E = A-D and D (?) (D≠(?)). Aliterature for the formal context (U, A, I) and D verifying whether the element in the equation satisfy the conditions of theorem to determine whether D coordinate set. To further simplify the corresponding theorems in literature determine the conditions and to reduce the workload of the relevant calculation, this paper further introduces G = E-D **, proved that the new consistent sets of decision theorem and some simple theorems. As the expansion theorem, also proved that A coordinate set and A is the reduction.Finally, the concept lattice is finer than, the concept lattice is isomorphic concept lattice coordinate set and concept lattice reduction set of definitions, we prove that the properties of coordinated set of formal context is a form of coordination properties of the coordination properties of the background subset, form the background The attribute reduction set is consistent decision formal context of attribute reduction subset.