Multi-scaled concept lattices based on neighborhood systems

Formal concept analysis (FCA) has been applied to many fields as an effective tool for data analysis and knowledge discovery. In fact, the problem of obtaining a concept lattice of appropriate complexity and size is one of the most important problems of FCA. In this paper, based on a kind of Galois connection via a concept of inclusion degree using a special neighborhood system, we propose a multi-scaled concept lattice. The presented method can effectively reduce the number of concepts, while conserving the main formal structure. A formal context can be converted into an induced context through a kind of inclusion degree which is used to cope with a special covering of the objects set. Moreover, we show that the concept lattice produced by the original context is equal to the concept lattice produced by the induced context. Finally, the multi-scaled concept lattice determined by an inclusion degree is constructed from the induced context.