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粗糙集的公理化是该理论研究的重要课题之一. 文中在分析对称关系下粗糙近似算子的特征公理基础上,提出强对称二元关系. 对比等价关系的性质,讨论该二元关系的一些重要特征,给出对称关系成为强对称关系的充要条件,并研究其下广义粗糙集的性质,得到强对称关系下粗糙近似算子的公理化特征. 利用相应的特征公理与精确集之间的联系,探讨一般二元关系下论域中精确集的一些重要特征,对拓广粗糙集理论及其应用提供一定帮助.
The axiomatization of rough sets is one of the important topics in the theoretical research.In this paper, based on the analysis of the characteristic axioms of rough approximation operators, a strong symmetric binary relation is proposed. By comparing the properties of equivalence relations and discussing the binary relation The necessary and sufficient conditions for the symmetric relation to be a strong symmetric relation are given, and the properties of the generalized rough set under it are studied. The axiomatic characteristics of the rough approximation operator under the strongly symmetric relation are obtained. Using the corresponding axioms and exact sets , Discusses some important features of the exact set in universe of discourse in the general binary relation, and provides some help to the extension of rough set theory and its application.