The construction of multi-granularity generalized one-sided concept lattices

Formal concept analysis (FCA) is an important analytical tool for cognitive science. The generalized one-sided concept lattice extends the classical concept lattice, which considers the order between the attributes values. The structure of generalized one-sided concept lattice is more complicated than the classical concept lattice. The complexity of constructing generalized one-sided concept lattice is added when the original formal context extends to a multi-granularity formal context. To address this problem, this paper proposes Zoom algorithms based on the granularity trees and the existing generalized one-sided concept lattices. Firstly, the Zoom-in algorithm is designed to construct the generalized one-sided concept lattice when changing the granularity of the attribute value from coarse-granularity to fine-granularity. Then, Zoom-out algorithm is explored to produce the generalized one-sided concept lattice when changing the granularity of the attribute value from fine-granularity to coarse-granularity. Finally, experimental results explain the effectiveness of our algorithms.