On irredundant incomplete decision table

In rough set (RS) theory, the issues raised by attribute reduction are significant [14]. Currently, these issues garner interest and extensive research from numerous scientists worldwide. To investigate the problem of incomplete decision tables (IDTs), M. Kryszkiewicz developed the notion of relative relation (also known as tolerance relation) [13]. In this study, researchers address algorithmic issues related to attribute reduction in IDTs using a relational database approach. In [12], the authors proved that the result of the Sperner system (SS) is equivalent to the reduct set within the incomplete decision table. Specifically, for a given Spener system K, there exists an inverted version of the IDT, referred to as the redundancy set of K. In this study, based on the objects in the IDT, we propose the concept of an IDT without redundancy, meaning its rows are not redundant in the IDT. According to the columns and rows of the decision table, we have developed an effective algorithm whose complexity is the most polynomial. We can locate an irredundant incomplete decision table because the algorithm supports IDT.