受形式概念分析中因子分解的启发,借鉴属性约简的思想,从概念角度上思考,提出保持二元关系不变的概念约简.首先给出保持二元关系不变的概念约简的定义及概念协调集的判定定理.然后根据形式概念在保持二元关系不变的概念约简过程中所起的作用,将形式概念分为核心概念、相对必要概念、不必要概念.最后分别研究3类概念的特征,从二元关系和算子角度考虑,得到三类概念的相关结论.上述结果有助于进一步的算法研究与应用及更深入的理论分析工作.%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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