Covering soft rough sets and its topological properties with application

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