# A One-Phase Tree-Structure Method to Mine High Temporal Fuzzy Utility Itemsets
## 6 Conclusions  
In this paper, to solve the problem of mining _HTFUIs_ in determining temporal knowledge, the _ATTFUIM_ algorithm is proposed. The proposed method is used to handle linguistic terms in each transaction for a temporal database using the concepts of the FP-tree and the upper-bound model for downward closure property. Each node in the proposed tree has the upper-bound value and the array-list information, keeping the information in  
Figure 7: The comparisons of memory consumption for two methods in distinct thresholds.  
different transactions. Therefore, the upper-bound values are used to derive the potential candidates from the conditional pattern trees in the mining process. Along with each node in a conditional pattern tree, the _HTFUIs_ can be completely obtained using the array-list information in nodes.  
Compared with the non-temporal fuzzy utility mining, the proposed approach can provide a more flexible consideration to real applications. When the number of time periods is one, the temporal fuzzy utility mining degenerates to the fuzzy utility mining. Thus, the former can be thought of as a generalization of the latter. Besides, compared to the previous temporal fuzzy utility mining approach, the experimental results on the three real databases showed that the proposed ATTFUM algorithm is superior to the FHTFUP algorithm in temporal fuzzy utility mining problems in terms of the execution time. Furthermore, by adopting the array-list structure to store mining information in each node, the proposed _ATTFUM_ can efficiently mine _HTFUIs_, although it uses more memory usage than _FHTFUP_. The proposed _ATTFUM_ can reduce the execution time due to the avoidance of the database rescan in the second phase when compared with the previous _FHTFUP_ approach.  
For further research issues, different tree structures and other data structures could be designed to improve the performance of the _ATTFUM_ algorithm. Besides, the scenario of inserting new transactions into a database may be considered, and different maintenance problems of the TFUIM may be handled. How to process different exhibition time periods of items in fuzzy mining is also an interesting challenge. Some variants, such as mining with multiple minimum thresholds, can also be designed based on the proposed architecture.  
Conceptualization, T.-P.H. and C.-Y.L.; methodology, T.-P.H. and C.-Y.L.; software, C.-Y.L. and W.-M.H.; validation, T.-P.H. and S.-L.W.; formal analysis, T.-P.H. and J.C.-W.L.; data curation, W.-M.H. and S.-L.W.; writing--original draft preparation, T.-P.H., C.-Y.L. and W.-M.H.; writing--review and editing, S.-M.L. and J.C.-W.L.; supervision, S.-M.L.; funding acquisition, T.-P.H. All authors have read and agreed to the published version of the manuscript.  
This research was supported by the Ministry of Science and Technology of the Republic of China under Grant MOST 109-2221-E-390-013-MY2.  
Not applicable.  
Data Availability StatementData is available at [[http://fimi.cs.helsinki.fi/data/](http://fimi.cs.helsinki.fi/data/)]([http://fimi.cs.helsinki.fi/data/](http://fimi.cs.helsinki.fi/data/)) (accessed on 28 February 2022).  
This is a modified and expanded version of the paper \"One-phase temporal fuzzy utility mining [37],\" presented at the 2020 IEEE International Conference Fuzzy Systems (FUZZ-IEEE), 2020, Glasgow, UK. We also claim that this present study has not been published or accepted for publication in other journals.