中文摘要：

多粒化粗糙集是Pawlak粗糙集非常重要的一种推广,主要给出当X是C（C＇）中任意有限个元素的并集时,乐观多粒化粗糙集（悲观多粒化粗糙集）上下近似对于交并运算的封闭性;得到若X是C＇中任意有限个元素的并集,乐观多粒化粗糙集和悲观多粒化粗糙集下近似相等;若～X是C＇中任意有限个元素的并集,乐观多粒化粗糙集和悲观多粒化粗糙集上近似相等.

英文摘要：

Multi-granulation Rough Set is an important extension of Pawlak rough set, and we mainly give properties on union and intersection of upper and lower approximation of optimistic（ pessimistic） multigranulation rough sets when X is the union of finite elements of C（ C＇）. Finally,we show that when X is the union of finite elements of C＇,the lower approximation of optimistic multi-granulation rough sets and pessimistic multi-granulation rough are equivalent; Same result to the upper approximation of optimistic multi-granulation rough sets and pessimistic multi-granulation rough when ～X is the union of finite elements of C＇.