Soft sets and soft topology on nearness approximation spaces

Near Soft Connected Spaces

“…Every family of neighborhoods may be considered a as soft set (Tasbozan et al, 2017). Let is an initial universe set in soft set and ℱ is a collection of all possible parameters with respect to and , ⊆ ℱ.…”

“…The relative complement of a near soft set denoted by , is defined where ( ) = − ( ) for all ∈ (Tasbozan et al, 2017).…”

“…Definition 2.14 Let ( , , ) be a nsts over , then the members of are said to be near soft open sets (Tasbozan et al, 2017 1) The set ∩ { ⊇ : is a near soft closed set of } is called the near soft closure of in , denoted by ( ).…”

Comparison of near sets by means of a chain of features

“…The algebraic properties of near sets are described in [9]. Recent work has considered near soft sets [20], soft nearness approximation spaces [4], near groups [3], isometries in proximity spaces [18], and applications of near sets [17,19]. The fundamental idea of near set theory is object description and classification according to perceptual knowledge.…”

Near Approximations in Vector Spaces

“…The space where we obtain the near sets is the nearness approximation space. Tasbozan [25] introduce the soft sets based on a near approximation space. The group and ring structure of algebraic structures on near sets are defined.…”