On $\delta \mathbb{P}$-approximation Spaces

In order to deal with imprecision, ambiguity, and uncertainty in data analysis, Pawlak introduced rough set theory in 1982. This paper aims to expand the scope of basic set theory developed by presenting the notions of $\delta \mathbb{P}$-upper and $\delta \mathbb{P}$-lower approximations, that are based on the notion of $\delta \mathbb{P}$-open sets, we additionally examine a few of their fundamental characteristics.