# A One-Phase Tree-Structure Method to Mine High Temporal Fuzzy Utility Itemsets
## 2 Related Works  
FIM from a database is fundamental but important in knowledge discovery. Many approaches are proposed for FIM, and among them, the Apriori algorithm is a classical level-by-level processing method [1; 2; 3]. In Apriori, multiple database scans are used to find frequent itemsets and association rules; therefore, it spends a large amount of execution time in mining frequent itemsets. In order to overcome the problem, [PERSON] et al. presented the FP-tree (frequent pattern tree) strategy to store mining information in each node [19]. This strategy finds frequent itemsets by recursively building conditional FP-trees and traversing them. It only needs two database scans to find desired itemsets, much less than that required in Apriori. Unlike FIM, the UIM problem [7] was proposed to avoid considering only frequencies in FIM. UIM is more complicated than FIM. It takes the following properties for each item: the amounts appearing in transactions and the unit profit. It defines the utility measure from the two property values and uses it to judge whether an item or itemset is useful based on a given utility threshold constraint. A high utility itemset thus means such a useful itemset. Several studies were developed to solve the UIM problem. For example, [PERSON] et al. applied a data structure to store mining information and then designed a tree-based method to reduce any candidates generated in mining [20]. [PERSON] et al. used the concept of genetic algorithms to determine most of the high utility itemsets by using crossover operations [21] within a limited time. Besides, [PERSON] et al. used transaction merging and dataset projection to find top-k utility itemsets [22]. However, UIM in the mining procedure does not have the anti-monotonic property. In other words, the utility value of an itemset is not certainly less than those of its subsets. Therefore, the search space in UIM is large, which results in expensive searching costs. In order to reduce the search space in UIM, the transaction weighted utilization (TWU) was proposed [9] as an upper-bound measure, and it was also adopted in some other methods [23; 24]. The itemsets using the measure of TWU possess the anti-monotonic property, so [PERSON] et al. designed a two-phase algorithm based on the measure [9]. In the first phase, this algorithm obtains the candidates with TWU values not less than the utility threshold. The algorithm then scans the database again in the second phase to find the actual utility values of the candidates and judge whether they satisfy the threshold constraint. However, this method consumes much execution time due to the level-wise processing. Some approaches combining the TWU and the FP-tree concepts were then proposed to improve the execution efficiency of UIM [25; 26]. Fuzzy sets [13] were used to handle linguistic and uncertain situations in many domains, such as technology, economy, and business. They are easily comprehended and consistent with human perception and sense. Fuzzy sets can be thought of as an extension of crisp sets. When using fuzzy sets for FIM, item quantities in a quantitative dataset are first transformed into linguistic terms with membership values, and then the linguistic terms are processed by modifying the traditional mining procedures. Some quantitative FIM approaches were proposed. For example, [PERSON] and [PERSON] introduced a method to derive quantitative association rules by dividing the quantitative values of items into some intervals [27]. [PERSON] et al. considered fuzzy multi-level association-rule mining [28] and used the cumulative probability distribution to generate the number of intervals and build membership functions of all the items. Besides, practical applications about transformed linguistic terms from quantitative information were proposed. For example, [PERSON] and [PERSON] improved and expanded the fuzzy mining approach to analyze and extract critical factors affecting breast cancer from the quantitative database for health information [29].