Soft rough sets based on covering and their applications

Soft rough based on covering $\mathcal {S}RC$ theory has become a useful and well-known area of research in theories of uncertainty. The present work follows up on this flourishing research topic. We introduce a new model of $\mathcal {S}RC$ in a fusion of soft set theory $\mathcal {S}ST$ and rough set depending on covering $\mathcal {C}RS$ . We put forth a definition of soft rough covering approximation space $\mathcal {S}CAS$ via neighborhood concept. Some axiomatic systems of our model of $\mathcal {S}RC$ are discussed. We study the relationship between our model of $\mathcal {S}RC$ and three other $\mathcal {S}RC$ -models. An algorithm for reduction of the attributes of the information systems using $\mathcal {S}CAS$ is established. Based on the theoretical discussion, we set forth some applications of our model which will be helpful in decision making process via $\mathcal {S}RC$ theory.