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-re-duct 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.
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