  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.
