Ahlswede–Zhang style identities of rough set approximations

Rough set theory is a recently developed mathematical framework that has been widely used in big-data analysis and knowledge discovery. In this paper, we establish a novel connection between rough set theory and combinatorial extremal theory by introducing some interesting identities of rough sets of Ahlswede–Zhang style. We prove these identities using combinatorial techniques, providing new insights into the relationship between these two areas. Our results have theoretical implications for rough set theory and its applications in various fields such as data analysis, machine learning, and decision making.