The Concept Lattice Projection

In this thesis we first present the definition of projection in concept lattice.And then we give some results about the relation between the projection and the direct sum of the context. First, Let K:=(G,M,I) be a context, then for any sets X,Y(?)M, we have Kx+Ky=Kx+y.Obviously, the concept lattice of Kx+Ky and the concept lattice of Kx+y is identical. Secondly, Let K1:(G1,m,I1), K2:=(G2,M,I2) be two contexts, then for any set N(?)M, we have (K1+K2) N=K1N+K2N. Obviously, the concept lattice of ([K1+K2)N and of K1N+K2N is identical.At last, we present the relation between the projection and the attribute which includes many-valued attribute, attribute implication and dependency. We give two properties. First, Let Aâ†'>B be a attribute implication in context K:=(G,M,I), for (?)N(?)M, if AcN, N∩)B≠?, for VCcN∩B, we have Aâ†'C in KN. Secondly, Let K:=(G, M, W, I) be a many-valued attribute, X(?)M, Y(?)M, Y depend on X,(?)N(?)M, if X(?)N, Y∩N≠?, for (?)ZcY∩N, we have Z depend on X in KN.