Inspired by the ideas of factorization and attribute reduction, the concept reduction preserving binary relations is proposed. Firstly, the definition of concept reduction preserving binary relations is given and the judgment theorems of corresponding consistent sets and reduct are proposed. Secondly, according to the roles of formal concepts in the process of concept reduction preserving binary relations, formal concepts are classified into three types: core concepts, relative necessary concepts and unnecessary concepts. Finally, the characteristics of three types of concepts are discussed, and the related conclusions about three types of concepts are given from the perspective of binary relations and operators. The results in this paper provide a research basis for the further study in algorithm,application and deeper theoretical analysis.
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