A heuristic knowledge-reduction method for decision formal contexts

Computing a minimal reduct of a decision formal context by Boolean reasoning is an NP-hard problem. Thus, it is essential to develop some heuristic methods to deal with the issue of knowledge reduction especially for large decision formal contexts. In this study, we first investigate the relationship between the concept lattice of a formal context and those of its subcontexts in preparation for deriving a heuristic knowledge-reduction method. Then, we construct a new framework of knowledge reduction in which the capacity of one concept lattice implying another is defined to measure the significance of the attributes in a consistent decision formal context. Based on this reduction framework, we formulate an algorithm of searching for a minimal reduct of a consistent decision formal context. It is proved that this algorithm is complete and its time complexity is polynomial. Some numerical experiments demonstrate that the algorithm can generally obtain a minimal reduct and is much more efficient than some Boolean reasoning-based methods.