Exploring invariance of concept stability for attribute reduction in three-way concept lattice

By incorporating three-way decision model into formal concept analysis (FCA) methodology, an emerging novel data analysis methodology, termed three-way concept analysis (3WCA), has been widely used in both computer science and social science areas. However, the construction of three-way concept lattice is quite time-consuming and proved as an NP-complete problem. Thus, it makes the knowledge discovery from three-way concept lattice difficult. To facilitate the knowledge acquisition in three-way concept lattice, both attribute reduction and three-way concept stability are utilized for pruning the size of three-way concept lattice and extracting informative three-way concepts. Aiming to extract hidden knowledge efficiently, this paper first attempts to figure out the relations of three-way concept stability in the original three-way concept lattice and reduced three-way concept lattice. We then propose a theorem on the invariance of three-way concept stability for attribute reduction of three-way concept lattice. To validate the correctness of our finding, we also conducted an empirical case study.