A comprehensive review on updating concept lattices and its application in updating association rules

Formal concept analysis (FCA) visualizes formal concepts in terms of a concept lattice. Usually, it is an NP‐problem and consumes plenty of time and storage space to update the changes of the lattice. Thus, introducing an efficient way to update and maintain such lattices is a significant area of interest within the field of FCA and its applications. One of those vital FCA applications is the association rule mining (ARM), which aims at generating a loss‐less nonredundant compact Association Rule‐basis (AR‐basis). Currently, the real‐world data rapidly overgrow that asks the need for updating the existing concept lattice and AR‐basis upon data change continually. Intuitively, updating and maintaining an existing concept‐lattice or AR‐basis is much more efficient and consistent than reconstructing them from scratch, particularly in the case of massive data. So far, the area of updating both concept lattice and AR‐basis has not received much attention. Besides, few noncomprehensive studies have focused only on updating the concept lattice. From this point, this article comprehensively introduces basic knowledge regarding updating both concept lattices and AR‐basis with new illustrations, formalization, and examples. Also, the article reviews and compares recent remarkable works and explores the emerging future research trends.