Combination and Decomposition Theories of Formal Contexts Based on Same Attribute Set

The theory of concept lattices is an efficient tool for knowledge discovery. To make the knowledge discovery of a larger formal context easier, this paper discusses the combination and decomposition of formal contexts when the attribute set is the same, and obtains the corresponding concept lattices. First, the methods how to obtain the whole concept lattice from sub-contexts of a larger formal context is proposed. Then, the converse situation is also studied, and the method how to obtain a sub-lattice from the original formal context is given. At the same time, the relationship between intension set of original context and that of its sub-context is analyzed. Finally, the combination and decomposition theories are generalized when there are multiple sub-contexts.

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