We develop techniques for discovering patterns with periodicity in this work. Patterns with periodicity are those that occur at regular time intervals, and therefore there are two aspects to the problem: finding the pattern, and determining the periodicity. The difficulty of the task lies in the problem of discovering these regular time intervals, i.e., the periodicity. Periodicities in the database are usually not very precise and have disturbances, and might occur at time intervals in multiple time granularities. To overcome these difficulties and to be able to discover the patterns with fuzzy periodicity, we propose the fuzzy periodic calendar which defines fuzzy periodicities. Furthermore, we develop algorithms for mining fuzzy periodicities and the fuzzy periodic association rules within them. Experimental results have shown that our method is effective in discovering fuzzy periodic association rules.