粗糙集理论中基于依赖空间的分布约简

约简是粗糙集理论中的一个核心问题，常用的约简方法有分辨矩阵和启发式算法两种。为了求得决策系统中的下、上近似和边界域分布约简，以构建在条件属性集合幂集上的等价关系为同余关系，利用同余关系依赖空间，提出了求得下、上近似和边界域分布约简的新方法，并给出了与这些约简对应的判定定理。通过实例分析验证了采用依赖空间方法可以求得保持所有决策类下、上和边界域都不发生变化的最小属性子集，为从决策系统中删除冗余属性提供了新的理论基础与技术手段。

Dependence space based distribution reduction in rough set theory

Reduction is one of the key problems in rough set theory. The widely used approaches to reductioninclude discernibility matrix and heuristic algorithm. To obtain the lower, upper approximate and boundary region distribution reduction in decision systems, congruence relations are defined on the power set of the conditional attributes and then the corresponding dependence spaces are constructed, from which the new approaches to the lower, upper approximate and boundary region distribution reductions are obtained. The judgment theorems for finding those reductions are also presented. An example is employed to demonstrate the conceptual argument. It provides a new theoretical basis and technique for deleting redundant attributes in decision systems.