It is a big challenge to promise the quality of multidimensional association mining. The essential issue is how to represent meaningful multidimensional association rules efficiently. Currently we have not found satisfactory approaches for solving this challenge because of the complicated correlation between attributes. Multi-tier granule mining is an initiative for solving this challenging issue. It divides attributes into some tiers and then compresses the large multidimensional database into granules at each tier. It also builds association mappings to illustrate the correlation between tiers. In this way, the meaningful association rules can be justified according to these association mappings.