Cluster-Based Membership Function Acquisition Approaches for Mining Fuzzy Temporal Association Rules

In real-world applications, transactions are typically represented by quantitative data. Thus, fuzzy association rule mining algorithms have been proposed to handle these quantitative transactions. In addition, items generally have certain lifespans or temporal periods in which they exist in a database. Therefore, fuzzy temporal association rule mining algorithms have also been proposed in the literature. A key factor in the acquisition of fuzzy temporal association rules (FTARs) is the design of appropriate membership functions. Because current approaches have been designed to generate membership functions for mining fuzzy association rules (FARs) in market-basket analysis, in this paper, we propose a membership function tuning mechanism for a fuzzy temporal association rule mining algorithm. The proposed approach modifies an existing cluster-based method to generate unique membership functions that are specifically tailored to each item in a dataset. Two factors are utilized to decide the appropriate membership functions of each item: (1) the density similarity among intervals corresponding to the density similarity within intervals, and (2) the information closeness within an interval corresponding to the similarity in the number of data points between intervals. A parameter $\theta $ is used to indicate the relative importance of these two factors. As a result, the membership functions are generated based on the quantitative ranges of individual items, and the generated membership functions of items are different in terms of the values of each interval and the number of intervals. The generated membership functions are subsequently used in a fuzzy temporal association rule mining algorithm. Computational experiments were conducted on both a synthetic dataset and a real-world one to demonstrate the effectiveness of the proposed approach.