Several rough set models in quotient space

[摘要] In order to deal with coarse-grained and multi-grained calculation problems, as well as granularity transformation problems in information system, quotient space theory is introduced in rough set theory. The main idea of this research is to try to maintain the important properties of the original space into the quotient space. Aimed to preserve the micro properties and the macro properties, two pairs of approximation operators on the quotient space are defined. When it comes to the composite of quotient spaces, the idea of these operators shows greater advantages. Examples are cited to illustrate possible applications of these operators, and their matrix representations are also given to make the calculations easy. Finally, all approximation operators on the quotient space involved so far are compared and their relationships are shown through a diagram.

[学科分类] 数学（综合）

[关键词] approximation theory;rough set theory;matrix algebra;mathematical operators