Since the completeness of concept lattice

the time complexity of building concept lattice is a factor restricting the application of formal concept analysis.Based on the horizontal and vertical combination in formal contexts

this paper defines the independent or consistent contexts and lattices in attribute field;and also defines the horizontal addition operation between contexts or concepts and the horizontal union operation between concept lattices.In addition

we prove that the concept lattice of subcontexts horizontally combined is isomorphic to the horizontal union of sublattices of these subcontexts.Using the inherent general-special relation between concepts in sublattice

the horizontal union algorithm of multiple concept lattices to construct the concept lattice is also presented.Experimental results show that the time complexity of this algorithm is much better than that of other construction algorithm of concept lattice from whole formal context.Evidently

our algorithm is very suitable for constructing concept lattice in parallel and distributed system.