In this paper we discuss some basic properties of rough SOFT SETS and hence we introduce the notion of rough SOFT group. Basic properties of rough SOFT group are presented and supported by some illustrative examples.

The key aim of this article is to familiarize some basic results in SOFT bi topological spaces. The idea of SOFT Limit Point in SOFT bi topological space is introduced and related results are also discussed with respect to ordinary and SOFT points. SOFT interior point in SOFT bi topological space and related results with respect to ordinary and SOFT points are also studied. The relation between SOFT space and SOFT-Closures is discussed in SOFT topological space with respect to SOFT-open set. Also the same relation is discussed with respect to SOFT-open and set P-open SETS. SOFT neighborhood in SOFT bi topological space is defined and related results are studied. SOFT sequences uniqueness of limit in SOFT-Hausdorff space and SOFT-Hausdorff space is studied. The product of SOFT Hausdorff spaces with respect to SOFT points in different SOFT weak open SETS are also discussed. The marriage between SOFT Hausdorff space and the diagonal is also planted here.

In this paper, two related quotient structures are investigated utilizing the concept of coset. At first, a new hypervector space F/V = (F/V,\circ,\circledcirc,K) is created, which is composed of all coSETS of a bipolar fuzzy SOFT set (F;A) over a hypervector space V . Then it will be shown that dim F/V = dim V/W, where the quotient hypervector space V/W includes all coSETS of an especial subhyperspace W of V. Also, three bipolar fuzzy SOFT SETS over the quotient hypervector space V/W are presented and in this way some new bipolar fuzzy SOFT hypervector spaces are defined.

The main purpose of this paper is to introduce and study new classes of SOFT closed SETS like SOFT regular generalized b-closed SETS in SOFT topological spaces (briefly SOFT-rgb-closed set) Moreover, SOFT rga-closed, SOFT gpr-closed, SOFT gb-closed, SOFT gsp-closed, SOFT ga-closed, SOFT gab-closed, and SOFT sgb-closed SETS in SOFT topological spaces are introduced in this paper and we investigate the relations between SOFT rgb-closed set and the associated SOFT SETS. Also, the concept of SOFT semi-regularization of SOFT topology is introduced and studied their some properties. We introduce these concepts which are defined over an initial universe with a fixed set of parameters.