Generalized association rule mining is an extension of traditional association rule mining to discover more informative rules,given a taxonomy.In this paper, we describe a formal framework for the problem of mining generalized association rules.In the framework, The subset-superset and the parent-child relationships among generalized itemsets are introduced to present the different views of generalized itemsets, i.e. the lattice of generalized itemsets and the taxonomies of k-generalized itemsets ,respectively. We present an optimization technique to reduce the time consuming by applying two constraints each of hich corresponds to each view of generalized itemsets.In the mining process, a new set enumeration algorithm, named SET, that utilizes these constraints to fasten mining all generalized frequent itemsets is proposed. By experiments on synthetic data, the results show that SET outperforms the current most efficient algorithm, Prutax, by an order of magnitude or more.