On modified soft rough sets on a complete atomic Boolean lattice

Abstract

Uncertainty has been used in different areas in our life such as medical diagnosis, social studies, pharmacology and others. The soft set theory and rough set theory are treated as mathematical approaches to deal with uncertainty. In 2011, Feng et al. introduced the notion of soft rough sets. In 2013, we introduced the notion of soft rough sets on a complete atomic Boolean lattice as a generalization of soft rough sets. In this paper, we strengthen the concept of soft rough set on a complete atomic Boolean lattice by defining the concept of modified soft rough set (MRS-set) on a complete atomic Boolean lattice. In this model, some properties which were not satisfied in soft rough sets on a complete atomic Boolean lattice can be proved. Finally, we will use this concept to introduce the concept of modified soft rough topology and we apply this concept in diabetes mellitus.