# A One-Phase Tree-Structure Method to Mine High Temporal Fuzzy Utility Itemsets
## 1 Introduction  
Frequent itemset mining (FIM) is one of the most popular data-mining problems. It uses a pre-defined threshold to determine the important itemsets in a dataset [1, 2, 3]. With the mining procedure, useful and implicit information in a dataset is discovered to help managers make good decisions efficiently. It can also be further utilized to find other kinds of knowledge, such as association rules [4, 5] and sequential patterns [6]. In business, frequent itemsets derived by FIM usually have low profits because cheap items are usually sold the most. However, the favorable itemsets may be the ones with high profits, but they often have small counts. For example, in a supermarket, television has a much higher gain than a piece of bread, even when the frequency of the former is much less than that of the latter. Therefore, the combinations of items that can obtain good total profits are more important than those of only high frequencies. Thus, in 2004, the utility itemset mining (UIM) problem was proposed to concern both the amounts of items sold and the unit profits of items while determining desired itemsets [7]. The problem uses a measure for itemsets, and those satisfying the utility threshold constraint are regarded as high utility itemsets. It, however, does not hold the downward-closure property and thus needs more processing time than association-rule mining. In 2005, [PERSON] et al. proposed a method with two phases to solve the UIM problem [8; 9]. They presented an upper-bound measure to keep the anti-monotonic property in the searching process, thus reducing the search space and execution time. In the first phase, a database needs to be processed, and the upper-bound value of each itemset is calculated to decide whether it is a candidate. Thus, unpromising itemsets can be trimmed early. In the second phase, the candidate itemsets kept in phase 1 are checked for whether they are really high utility itemsets by the second scan of the database. In addition to item amounts and profits, the transaction time is another critical factor to business strategy. Goods in a supermarket are registered with their exhibition time periods. In other words, different goods sold may be on the shelf at different time periods. If all items in a supermarket are considered to be of the same length as that in the whole database, the mined result may cause some biases. The temporal relationships among items sold are complicated and not strictly explained in UIM. Some studies claimed mining approaches to determine the orderly association among items with the temporal relationship. For example, the PPM (progressive partition miner) method suggested by [PERSON] et al. is to find temporal patterns with the exhibition time of items [10]. The SPF (segmented progressive filter) method suggested by [PERSON] et al. is to mine corresponding temporal rules. They considered that items had certain lifespans in which they were available for being purchased [11]. The SLMCM approach suggested by [PERSON] viewed different products with their marked times [12]. He used the marked times for all items and presented a measuring method to mine relevant patterns for avoiding generating useless itemsets. For helping humans to understand the knowledge easily, the fuzzy set theory [13] was applied to FUIM to interpret quantitative values as linguistic terms. [PERSON] et al. suggested a method to derive fuzzy association rules with the temporal property [14]. They used the membership-function tuning mechanism to transform item quantities into fuzzy sets. [PERSON] et al. introduced the LEFT2 algorithm to find fuzzy frequent itemsets [15]. In recent years, some FUIM approaches [16; 17] were proposed to combine transformed fuzzy terms with UIM. They considered the fuzzy-set theory, quantitative information, and utility factor to find the itemsets with high fuzzy utility values. For example, [PERSON] et al. introduced the TP-TFU method to solve it [16]. They also suggested a two-phase approach.