多粒化的粗糙集代数

Rough Set Algebra of Multi-granulation

众所周知,一个粗糙集代数是由一个集合代数加上一对近似算子构成的。一方面,在公理化的方法下对经典的多粒化粗糙集代数系统进行了讨论,可知经典的粗糙集代数没有很好的性质;另一方面,给出了单调等价关系的定义,并给出了基于单调等价关系的多粒化近似算子的概念,在此基础上讨论了粗糙集代数的性质,并得到了诸多结果。

It is well known that a rough set algebra is a set algebra with added dual pair of rough approximation operators.On the one hand,we discussed the classical rough set algebra of multi-granulation by axiomatic approach.It is shown that the classical rough set algebra does not possess good properties.On the other hand,we defined the concept of monotone equivalence relations.Moreover,multi-granulation approximation operators based on monotone equivalence relations were defined.We discussed the properties of the rough set algebra based on monotone equivalence relations and got many excellent results.