An important problem of interactive data mining is "to find frequent item sets contained in a subset C of set of all items on a given database". Reducing the database on C or incorporating it into an algorithm for mining frequent item sets (such as Charm-L, Eclat) and resolving the problem are very time consuming, especially when C is often changed. In this paper, we propose an efficient approach for mining them as follows. Firstly, it is necessary to mine only one time from database the class LGA containing the closed item sets together their generators. After that, when C is changed, the class of all frequent closed item sets and their generators on C is determined quickly from LGA by our algorithm MINE_CG_CONS. We obtain the algorithm MINE_FS_CONS to mine and classify efficiently all frequent item sets with constraint from that class. Theoretical results and the experiments proved the efficiency of our approach.