粗糙集约简的闭算子方法

Rough Set Reduction Using Method of Closed Operator

从属性集角度分析信息系统约简问题。在信息系统的属性集及其幂集上分别定义了等价关系r和R,研究了两者生成的闭算子C(r)和C(R),以及闭集族Cr和CR的诸多性质和关系,证明了Cr与CR相等的充分必要条件,并由此获得信息系统属性集的约简方法,进一步,证明了该方法与文[7]方法等价。

Attribute reduction is one of the most important problems in knowledge discovery in information system. The general method to study attribute reduction in information system is rough set theory, whose theoretical basis is the equivalence relations on attribute set and its power set. Our method is as follows. For an information system, three equivalence relations r, R and Г（＇） are defined on attribute set and its power set Separately. Then, two closed operators C（R）, C（r）, and two correspondig closed set families ——Cr,CR are created by r and R. Further, the necessary and sufficient condition about Cr =CR is gotten, under which, a method of closed operator to attribute reduction is also gotten. Finally, it is proved that this method is equivalent to another one in reference[7] when Cr=CR.