Attribute reduction in formal decision contexts based on OE-consistency

Attribute reduction, as a very important branch of formal concept analysis, is equally important in the three-way concept analysis. Based on object-induced concept lattices, attribute reduction theory which preserve OE-consistency of formal decision contexts is proposed, which enriches the reduction theory of three-way concept analysis. Firstly, OE-consistent set and OE-reduct of formal decision contexts are defined, and the attributes are classified into three categories according to their characteristics. Then, it is pointed out the essence of OE-reduct is minimal OE-consistent set, and several judgement theorems of OE-consistent set are given. By studying the necessary and sufficient conditions of OE-consistent set, judgement theorem of OE-reduct is obtained. Finally, the definition of OE-discernibility matrix and OE-discernibility function are given, and the method of calculating OE-reduct by using OE-discernibility matrix and OE-discernibility function is given.