中文摘要：

主要研究广义近似空间上粗糙近似算子的扩展模型。首先，将Cattaneo提出的抽象近似空间理论具体运用于广义近似空间中的粗糙集模型研究，利用空间中双论域间的二元关系，导出指定论域上的一个Brouwer－正交补算子，据此算子构造性地定义了指定论域上的两对粗糙近似算子。然后，研究了新算子的基本性质和代数表示，将它们与已有近似算子进行对比，指出它们的异同，给出它们之间的大小顺序关系。最后，研究了新近似算子和已有近似算子的等价性，给出它们与邻近算子之间等价的条件，讨论了等价条件之间的关系。

英文摘要：

The objective of this paper is to establish new rough set models on generalized approximation spaces .One basic notion in a generalized approximation space is the relation between the two universes of discourse .In the original rough set models of generalized approximation spaces ,the approximating sets and the approximated sets are located on different universes .Some extended models are thus proposed for many applications ,in which the approximating sets and the approximated sets are located on the same universe .According to the theory of abstract approximation spaces presented by Cattaneo ,a preclusivity relation on one of the two universes of a generalized ap‐proximation space is firstly induced from a relation between two universes ,and a Brouwer‐orthocomplentation operator on the universe is constructed .Consequently ,two pairs of lower and upper rough approximation operators are formulized by the Brouwer‐orthocomplentation operation ,which guarantees that the approximating sets and the approximated sets are located on the same universe .Secondly ,the representations and properties of the operators＆amp;nbsp;defined newly are explored .As a result ,it is discovered that one of the two pairs of new operators is equal to existing one ,and by the way ,an ordered relation among the new operators and the existing operators are given .At last ,the equivalence among them and the nearest operators in an ordered chain are investigated .Consequently ,some necessary and sufficient conditions are obtained and relations among them are illustrated .