An approximation space plays a vital role in the accuracy of approximations of a subset of the universal set. The main goal of this paper is to develop new kinds of soft rough sets models by using the concept of near open sets, where the accuracy of approximations is enhanced significantly. Firstly, the concepts of near soft rough approximations, denoted by
“JSR-approximations” for each J ∈ {P, S, γ, α, β} are proposed as a generalization some previously introduced notions.
Then, their properties and relationships are disclosed. Comparisons among the proposed methods and the previous one are obtained. An algorithm has been given for decision-making problems. The proposed algorithm is tested on hypothetical data for the purpose of comparison with already existing methods.