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中文摘要：
粗糙拟阵是同时推广了粗糙集和拟阵的数学工具,它既可以被理解为是借助拟阵研究粗糙集,也可以被当作是通过粗糙集来研究拟阵.粗糙拟阵能够利用粗糙集和拟阵各自的优势处理和分析数据.通过等价关系上可定义集的性质,研究了基于等价关系的上粗糙拟阵和下粗糙拟阵.事实上,基于等价关系的上粗糙拟阵同时也是基于这个等价关系的下粗糙拟阵.因此给出了基于等价关系的粗糙拟阵的概念.类比拟阵中基的概念,定义了基于等价关系的粗糙拟阵的基,并且研究了这些基的性质.根据基的性质得到一个论域上所有的粗糙拟阵.特别地,讨论了论域的任何一个子集与该论域上的粗糙拟阵之间的某种对应关系.
英文摘要：
Rough matroids are the generalization of rough sets and matroids.They not only reflect some important properties of rough sets,but also have the advantages of matroids.It is important and necessary to investigate the properties of rough matroids.This paper discusses the upper and lower rough matroid based on equivalence relation by the characters of definable sets on the equivalence relation.In fact,a lower rough matroid based on an equivalence relation is also an upper rough matroid based on this equivalence relation.Therefore,the concept of rough matroid with respect to a set based on the equivalence relation is presented by definable sets.Inspired by the definition of bases of the matroid,we present the base of the rough matroid with respect to a set based on an equivalence relation.In addition,properties of the base of this rough matroid are investigated.For instance,all rough matroids with respect to a set based on an equivalence relation are represented when the base is given.Finally,all rough matroids with respect to a set based on the equivalence relation are presented.Especially,we find that there exists a correspondence relation between a subset of the universe and a rough matroid.
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