An algorithm for mining lower closed itemsets

The generalized association rule base(GARB) presented by Li(2003) can efficiently solve the problem of quantity of rule in the process of acquiring rule by traditional association rule mining algorithms. Therefore, how to deduce all rules contained in the rule of GARB becomes an urgent issue in order to support more effective decision-making. In this paper, the notation of lower closed itemset of an itemset was proposed and some properties of it are proved. Then, it is concluded that the above problem can be solved if all the lower closed itemsets of frequent closed itemset(FCI) are obtained. Finally, an algorithm for mining all lower closed itemsets of an itemset was given and its validity is proved.