Comparison of reduction in formal decision contexts

In formal concept analysis, many reduction methods have recently been proposed for formal decision contexts, and each of them was to reduce formal decision contexts with a particular purpose. However, little attention has been paid to the comparison of their differences from various aspects. In fact, this problem is very important because it can provide evidence to select an appropriate reduction method for a given specific case. To address this problem, our study mainly focuses on clarifying the relationship among the existing reduction methods in formal decision contexts. Firstly, we give a rule-based review of the existing reduction methods, revealing the type of rules that each of them can preserve. Secondly, we analyze the relationship among the consistencies introduced by the existing reduction methods. More specifically, Wei's first consistency (see [39]) is stronger than others, while her second one is weaker than the remainder except Wu's consistency (see [43]). Finally, we make a comparison of the existing reductions, concluding that Li's reduction (see [14]) maintaining the non-redundant decision rules of a formal decision context is coarser than others. The results obtained in this paper are beneficial for users to select an appropriate reduction method for meeting their requirements.