With the rapidly growing volumes of data from various sources, new tools and computational theories are required to extract useful information (knowledge) from large databases. Data mining techniques such as association rules have been proved to be effective in searching hidden knowledge in a large database. However, if we want to extract knowledge from data with temporal components, it becomes necessary to incorporate temporal semantics with the traditional data mining techniques. As mining techniques evolves, mathematical techniques become more involved to help improve the quality and diversity of mining. Fuzzy theory is one that has been adopted for this purpose. Up to now, many approaches have been proposed to discover temporal association rules or fuzzy association rules, respectively. However, no work is contributed on mining fuzzy temporal patterns. We propose in this thesis two data mining systems for discovering fuzzy temporal association rules and fuzzy periodic association rules, respectively. The mined patterns are expressed in fuzzy temporal and periodic association rules which satisfy the temporal requirements specified by the user. Temporal requirements specified by human beings tend to be ill-defined or uncertain. To deal with this kind of uncertainty, a fuzzy calendar algebra is developed to allow users to describe desired temporal requirements in fuzzy calendars easily and naturally. Moreover, the fuzzy calendar algebra helps the construction of desired time intervals in which interesting patterns are discovered and presented in terms of fuzzy temporal and periodic association rules. In our system of mining fuzzy temporal association rules, a border-based mining algorithm is proposed to find association rules incrementally. By keeping useful information of the database in a border, candidate itemsets can be computed in an efficient way. Updating of the discovered knowledge due to addition and deletion of transactions can also be done efficiently. The kept information can be used to help save the work of counting and unnecessary scans over the updated database can be avoided. Simulation results show the effectiveness of the proposed system for mining fuzzy temporal association rules. In our mining system for discovering fuzzy periodic association rules, we develop techniques for discovering patterns with periodicity. 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. Periodicites in the database are usually not very precise and have disturbances, and might occur at time intervals in multiple time granularities. To discover the patterns with fuzzy periodicity, we utilize the information of crisp periodic patterns to obtain a lower bound for generating candidate itemsets with fuzzy periodicities. Experimental results have shown that our system is effective in discovering fuzzy periodic association rules.