n-Strong-Direct-Product Formal Context

This paper constructs a new formal context called n-Strong-Direct-Product formal context (n-SDPFC, for short) by the strong direct product of n formal contexts, and then discusses the connection between the n-SDPFC and the n original contexts from four aspects: concept lattice, implications between attributes, irreducible elements and attribute characteristics. It is proved that the projection of every formal concept of a n-SDPFC on the i-th original formal context is also a concept of the corresponding original formal context, and under some given conditions, the product of n formal concepts of the n corresponding original formal contexts is a concept of the n-SDPFC. An implications between attributes of an n-SDPFC can be obtained if we know all of the implications between attributes in the original formal contexts, since it can be formed component-wise, and vice verse. A judgement theorem for irreducible elements in the concept lattice of an n-SDPFC is obtained, which is based on the irreducible elements in the n original concept lattices. Then we propose a method for the determination of the attribute characteristics in an n-SPDFC, which is based on the attribute characteristics of the original formal contexts. And this method makes it more easier to find out all of the attribute characteristics in an n-SDPFC.