A Formal Fuzzy Concept-Based Approach for Association Rule Discovery with Optimized Time and Storage - Gamal F. Elhady; Haitham Elwahsh; Maazen Alsabaan; Mohamed I. Ibrahem; Ebtesam Shemis (Mathematics)
Association Rule Mining (ARM) relies on concept lattices as an effective knowledge representation structure. However, classical ARM methods face significant limitations, including the generation of misleading rules during data-to-formal-context mapping and poor handling of heterogeneous data types such as linguistic, continuous, and imprecise data. This study aims to address these limitations by introducing a novel fuzzy data structure called the “fuzzy iceberg lattice” and its corresponding construction algorithm. The primary objectives of this study are to enhance the efficiency of extracting and visualizing frequent fuzzy closed item sets and to optimize both execution time and storage requirements. The necessity of this research stems from the high computational cost and redundancy associated with traditional fuzzy approaches, which, while capable of managing quantitative and imprecise data, are often impractical for large-scale applications in real scenarios. The proposed approach incorporates a ‘fuzzy min-max basis algorithm’ to derive exact and approximate rule bases from the extracted fuzzy closed item sets, eliminating redundancy while preserving valuable insights. Experimental results on benchmark datasets demonstrate that the proposed fuzzy iceberg lattice outperforms traditional fuzzy concept lattices, achieving an average reduction of 74.75% in execution time and 70.53% in memory usage. This efficiency gain, coupled with the lattice’s ability to handle crisp, quantitative, fuzzy, and heterogeneous data types, underscores its potential to advance ARM by yielding a manageable number of high-quality fuzzy concepts and rules.