The construction of attribute (object)-oriented multi-granularity concept lattices

How to reduce the complexity of lattice construction is an important research topic in formal concept analysis. Based on granularity tree, the relationship between the extent and the intent of the attribute (object)-oriented concept before and after granularity transformation are investigated. Then, zoom algorithms for attribute (object)-oriented concept lattices are proposed. Specifically, zoom-in algorithm is applied to change the attribute granularity from coarse-granularity to fine-granularity, and zoom-out algorithm achieves changing the attribute granularity from fine-granularity to coarse-granularity. Zoom algorithms deal with the problems of fast construction of the attribute (object)-oriented multi-granularity concept lattices. By using zoom algorithms, the attribute (object)-oriented concept lattice based on different attribute granularity can be directly generated through the existing attribute (object)-oriented concept lattice. The proposed algorithms not only reduce the computational complexity of concept lattice construction, but also facilitate further data mining and knowledge discovery in formal contexts. Furthermore, the transformation algorithms among three kinds of concept lattice are proposed.