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The goal of this paper is to use an efficient data structure to improve our earlier research. In the earlier research, we attempted to find the generalized association rules between the items at different levels in the taxonomy tree under the assumption that the original frequent itemsets and association rules were generated in advance. In the paper, we proposed an efficient data structure called a frequent closed enumeration table (FCET) to store the relevant information using a well-known algorithm. It stores only maximal itemsets, and can be used to derive the information of the subset itemsets in a maximal itemset through a hash function. From experimental results, we found that the combinations of FCET and the hash function not only save spaces, but also speed up producing the generalized association rules.