Covering soft rough sets and its topological properties with application

Abstract

AbstractIn this article, we introduce the notion of the complementary soft neighborhood and present three kinds of covering soft rough set ($$\mathcal {CSR}$$ CSR ) models. The basic properties of these models are investigated. The relationships among these models are also discussed. Moreover, we establish the topological approach to $$\mathcal {CSR}$$ CSR say, $$\varDelta $$ Δ -topological spaces (i.e., $$\varDelta $$ Δ -TS). Hence, the topological properties for $$\varDelta $$ Δ -TS models such as $$\varDelta $$ Δ -open sets, $$\varDelta $$ Δ -closed sets, $$\varDelta $$ Δ -interior, $$\varDelta $$ Δ -closure, $$\varDelta $$ Δ -boundary, $$\varDelta $$ Δ -neighborhood and $$\varDelta $$ Δ -limit point are studied and the relationships between them are given. Finally, we make use of an algorithm for these proposed models to deal with uncertainties for solving the MGDM problems using the constructed topologies.