Tri-granularity attribute reduction of three-way concept lattices

Abstract

A real-world dataset often generates a huge concept lattice that may be difficult to understand and impractical to use. The principle of granular computing is that we can understand and use a complex whole at multiple levels of granularity. In light of this, we propose a unified tri-granularity model of various types of concept lattices, which allows us to examine a huge concept lattice at three levels of granularity (i.e., the elementary granularity, local granularity and global granularity). Attribute reduction plays a fundamental role in three-way concept analysis, it simplifies the expression of three-way concepts and thus contributes to a better perception of the knowledge in three-way concept lattices. The tri-granularity model suggests an opportunity to investigate the tri-granularity attribute reduction of three-way concept lattices. The existing research on attribute reduction works at the global granularity but pays little attention to the local granularity, or, even less, to the elementary granularity. Driven by these issues, we supply definitions and methods of local granularity and elementary granularity attribute reduction of three-way concept lattices. These newly proposed two levels of attribute reduction with the existing global granularity attribute reduction together provide a framework for the tri-granularity attribute reduction of three-way concept lattices. We further analyze the relationships among the three levels of attribute reduction. Moreover, the efficacy of our suggested approach is illustrated by an example via the trisections induced by three-way concepts. Finally, we design two tri-granularity attribute reduction algorithms whose effectiveness is further examined by numerical experiments.