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Association rule mining is one of the most important research areas in data mining. Yet there exist two big problems in process of acquiring rule by traditional mining algorithms, i.e., the quantity and the quality of rule. Presently there are many methods focus on resolving these two problems. Although these methods can reduce the amount of rules derived to some extent, but the total number is too big as ever. We first propose the notations of upper closed itemset and generalized association rule base, and obtain a generalized association rule base of a database, which not only contains the whole information of all association rules, but also has conform structure that is convenient for practical applications. Also, we propose a mining algorithm of generalized association rule base. From our propositions and example, the algorithm is shown valid and can efficiently solve the problem of quantity of rule.