A study of fixed point sets based on Z-soft rough covering models

Z-soft rough covering models are important generalizations of classical rough set theory to deal with uncertain, inexact and more complex real world problems. So far, the existing study describes various forms of approximation operators and their properties by means of soft neighborhoods. In this paper, we propose the notion of $Z$-soft rough covering fixed point set (briefly, $\mathcal{Z}$- $\mathcal{S}\mathcal{R}\mathcal{C}\mathcal{F}\mathcal{P}$-set) induced by covering soft set. We study the conditions that the family of $\mathcal{Z}$- $\mathcal{S}\mathcal{R}\mathcal{C}\mathcal{F}\mathcal{P}$-sets become lattice structure. For any covering soft set, the $\mathcal{Z}$- $\mathcal{S}\mathcal{R}\mathcal{C}\mathcal{F}\mathcal{P}$-set is a complete and distributive lattice, and at the same time, it is also a double p-algebra. Furthermore, when soft neighborhood forms a partition of the universe, then $\mathcal{Z}$- $\mathcal{S}\mathcal{R}\mathcal{C}\mathcal{F}\mathcal{P}$-set is both a boolean lattice and a double stone algebra. Some main theoretical results are obtained and investigated with the help of examples.