基于序列和传递关系的粗糙集的拟阵结构
Matroidal structure of rough sets based on serial and transitive relations
摘要：
粗糙集理论关注的是对象通过论域上的二元关系的上下近似。它已被应用于机器学习、知识发现和数据采掘等领域。拟阵理论是向量空间中线性无关性的推广。它已被用于组合优化和算法设计中。为了充分利用粗糙集和拟阵的优点，本文提出了一种基于论域上序列传递关系的粗糙集拟阵结构。定义了论域上关系的所有极小邻域族，并证明了当关系是串行传递的时，它满足拟阵的圈公理。为了进一步研究这种拟阵结构，我们研究了这种结构的逆：由拟阵诱导关系。研究了基于关系的粗糙集上近似算子与拟阵闭包算子在这两种构造中的关系。此外，我们还探讨了这两种结构之间的联系。
英文摘要：
The theory of rough sets is concerned with the lower and upper approximations of objects through a binary relation on a universe. It has been applied to machine learning, knowledge discovery and data mining. The theory of matroids is a generalization of linear independence in vector spaces. It has been used in combinatorial optimization and algorithm design. In order to take advantages of both rough sets and matroids, in this paper we propose a matroidal structure of rough sets based on a serial and transitive relation on a universe. We define the family of all minimal neighborhoods of a relation on a universe, and prove it satisfy the circuit axioms of matroids when the relation is serial and transitive. In order to further study this matroidal structure, we investigate the inverse of this construction: inducing a relation by a matroid. The relationships between the upper approximation operators of rough sets based on relations and the closure operators of matroids in the above two constructions are studied. Moreover, we investigate the connections between the above two constructions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
