The strong direct product of formal contexts

Abstract

The theory of Formal Concept Analysis is used as a knowledge representation mechanism and as a conceptual clustering method. Formal context is a basic notion in this theory. This paper proposes a kind of formal context, called n-Strong-Direct-Product-Formal-Context (n-SDPFC, for short), by the strong direct product of n formal contexts. It is found that the new context is closely related to the n original formal contexts in many aspects, for example, the concept lattices, and the implications between attributes, and so on. With the help of Kronecker product of boolean matrices, the main features of an n-SDPFC is given, and the method how to represent a formal context with such features by the strong direct product of some small formal contexts is brought forward. With this method, the workload for knowledge acquisition in formal context will be eased enormously.