關聯規則在許多研究中被廣泛的應用與討論，其目的在於從大量數據中挖掘出有價值的數據項之間的相關關係。關聯規則可應用在醫學診斷、生物科技、市場分析、商業決策等。最常被應用於企業的交易資料庫中，用以分析商品之間的關聯性。傳統的關聯規則僅能表達項目之間的相關性，但無法表達購買的時間間隔與購買行為之間的相關性。現今網路購物已成為現代人普遍的購物方式之一，購物的下單時間及購買品項都會被記錄於交易資料庫，若利用傳統的關聯規則分析，無法得知顧客間隔多久消費一次以及下次購買品項為何，便無法適時給予廣告或是促銷活動，刺激消費者購買力以增加利潤。
本文提出加入顧客交易時間間隔以探討消費間隔時間及顧客消費行為之相關性，在此呈現的關聯規則，可以得知商品被購買的順序以及消費的時間間隔長度，其中亦考慮到顧客交易時間間隔太長，將導致規則不被感興趣，因此在生成規則的過程中，加入交易時間間隔長度的限制。加入時間間隔的關聯規則帶來的資訊可以更加了解顧客的消費習慣，如:間隔多久消費一次？下次購買的物品為何？依照發現的關聯規則，在對的時間發送廣告給不同的消費者，刺激顧客的購買力，進而增進顧客的忠誠度，客源將逐漸擴大以提高利潤。此研究將挖掘出交易時間間隔影響交易品項所產生具時間意義的關聯規則。

Association rules mining are widely used in many studies and applications and the aim is to find out the valuable relationships among two itemsets in large database. Association rules can apply in medical diagnostics, biotechnology, market analysis, business decision-making. It commonly be used in business transactions database to analysis the correlations between the items. Traditional association rules can only show the relationships between items but cannot present the correlation among the transaction time-interval and purchase behavior. Nowadays, online shopping has become one of modern popular way to shop that the shopping order time and items purchased will be recorded in the transaction database. Using traditional association rules mining that we cannot know how long the customer will come back to buy and what items they will buy, so we cannot give advertising or promotion in the right time to stimulate consumer purchasing power to increase profits.
In this study, we consider the transaction time-interval in ARM to discuss the correlation between transaction time-interval and customer behavior. Here, the new rules can know the order of items were purchased and the transaction time-interval length which also take into account the interval is too long to lead the rules become not interested. Therefore, in the process of generating the rules will give a restriction to limit the time-interval length. ARM with time-interval can bring more information to understand the purchasing behavior of customer. For example, how often to go shopping? What will be purchased next time? According to the rules with that we can send different advertisement to different customer at right time to stimulate consumer purchasing power and increase the customer loyalty. We will find out the significance rules with time-interval.

References
1. Ahn, K.-I. (2012). Effective product assignment based on association rule mining in retail. Expert Systems with Applications, 39(16), 12551-12556.
2. Ale, J. M. & Rossi, G.H. (2000). An Approach to Discovering Temporal Association Rules. ACM.
3. Agrawal, R. & Srikant, R. (1995). Mining Generalized Association Rules. Department of Computer Science, University of Wisconsin.
4. Agrawal, R., Imielinski, T. & Swami, A. (1993). Mining association rules between sets of items in large databases. ACM.
5. Chang, J. H. (2011). Mining weighted sequential patterns in a sequence database with a time-interval weight. Knowledge-Based Systems, 24(1), 1-9.
6. Chen, Y. (2003). Discovering time-interval sequential patterns in sequence databases. Expert Systems with Applications, 25(3), 343-354.
7. Hu, Y.-H., Huang, T. C.-K., Yang, H.-R., & Chen, Y.-L. (2009). On mining multi-time-interval sequential patterns. Data & Knowledge Engineering, 68(10), 1112-1127.
8. Lan, G.-C., Hong, T.-P., Tseng, V. S., & Wang, S.-L. (2014). Applying the maximum utility measure in high utility sequential pattern mining. Expert Systems with Applications, 41(11), 5071-5081.
9. Lee, D., Park, S.-H., & Moon, S. (2013). Utility-based association rule mining: A marketing solution for cross-selling. Expert Systems with Applications, 40(7), 2715-2725.
10. Lin, C.-W., & Hong, T.-P. (2011). Temporal data mining with up-to-date pattern trees. Expert Systems with Applications, 38(12), 15143-15150.
11. Lan, G.-C., Hong, T.-P., & Tseng, V. S. (2011). Discovery of high utility itemsets from on-shelf time periods of products. Expert Systems with Applications, 38(5), 5851-5857.
12. Lee, Y. J., Lee, J. W., Chai, D. J., Hwang, B. H., & Ryu, K. H. (2009). Mining temporal interval relational rules from temporal data. Journal of Systems and Software, 82(1), 155-167.
13. Li, D. & Deogun, J., S. (2005). Discovering Partial Periodic Sequential Association Rules with Time Lag in Multiple Sequences for Prediction. Department of Computer Science and Engineering, University of Nebraska-Lincoln, 332-341.
14. Li, Y., Ning, P., Wang, X. S. & Jajodia, S. (2003). Discovering Calendar-based Temporal Association Rules. Center for Secure Information Systems, George Mason University.
15. Lee, Y. J., Lee, J. W., Chai, D. J., Hwang, B. H., & Ryu, K. H. (2002). Discovering Temporal Relation Rules Mining from Interval Data. Springer-Verlag Berlin Heidelberg, 57-66.
16. Railean, I., Lenca, P., Moga, S., & Borda, M. (2013). Closeness Preference – A new interestingness measure for sequential rules mining. Knowledge-Based Systems, 44, 48-56.
17. Tsai, P. S. M., & Chen, C.-M. (2004). Mining interesting association rules from customer databases and transaction databases. Information Systems, 29(8), 685-696.
18. Tansel, A. U. & Imberman, S.P. (1998), Discovery of Association Rules in Temporal Databases. Department of Computer Engineering and Information Science, Bilkent University.
19. Winarko, E., & Roddick, J. F. (2007). ARMADA – An algorithm for discovering richer relative temporal association rules from interval-based data. Data & Knowledge Engineering, 63(1), 76-90.
20. Xiao, Y., Tian, Y., & Zhao, Q. (2014). Optimizing frequent time-window selection for association rules mining in a temporal database using a variable neighbourhood search. Computers & Operations Research, 52, 241-250.
21. Yiyong, R. Zhang and I. Kaku (2011), A new framework of mining association rules with time-windows on real-time transaction database. International Journal of Innovative Computing, Information and Control, 7, 3239–3253.