On structures of rough topological spaces based on neighborhood systems

Keeping in view the generalized approximation space, the goal of this paper is to suggest and investigate four different styles for approximating rough sets. The proposed approximations are based on various general topologies. In fact, we first generalize the notion of the initial-neighborhood and thus we construct four different topologies generated from these neighborhoods. The relationships between the new neighborhoods (respectively, topologies) and the previous are studied. Comparisons of the degrees of different accuracy of the presented approximations are investigated. The essential characteristics of these operators are obtained.