Soft Rough Approximation Operators and Related Results

Abstract

Soft set theory is a newly emerging tool to deal with uncertain problems. Based on soft sets, soft rough approximation operators are introduced, and soft rough sets are defined by using soft rough approximation operators. Soft rough sets, which could provide a better approximation than rough sets do, can be seen as a generalized rough set model. This paper is devoted to investigating soft rough approximation operations and relationships among soft sets, soft rough sets, and topologies. We consider four pairs of soft rough approximation operators and give their properties. Four sorts of soft rough sets are investigated, and their related properties are given. We show that Pawlak's rough set model can be viewed as a special case of soft rough sets, obtain the structure of soft rough sets, give the structure of topologies induced by a soft set, and reveal that every topological space on the initial universe is a soft approximating space.

Soft -Rough Set and Its Applications in Decision Making of Coronavirus

“…Definition 2.4 [15] Let Ŝ = (F, A) be a soft set over Ŵ . Then the pair A Ŝ = Ŵ , Ŝ is called a soft approximation space, we define the soft A Ŝ-lower and soft A Ŝ-upper approximations of any subset M ⊆ Ŵ respectively by the following two operations:…”

“…etc. Researchers have implementing various kinds of soft, rough and fuzzy sets (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]).…”

“…Using soft set approach and accordingly they expand this approach to fuzzy soft set theory in [13]. Soft rough model was defined by [15].…”

“…The main objective of our belief is to have a certain influence on the continuous approximation of such basic mathematical principles and to provide a modern method for computational mathematics of real-life problems. In fact, it considers latest generalized soft, rough approximations, called soft ζ -rough approximations, are defined as a generalization to Zhaowen et al [15] approximations and their properties are studied. We will prove that our approaches are more accurate and general from Zhaowen et al approaches.…”

Bipolar soft rough relations

“…To …nd approximation of a set, Shabir et al [43] proposed modi…ed soft rough sets. Li et al [26] investigated soft rough approximation operators and showed that Pawlak's rough set model are a special case of soft rough sets and every topological space on initial universe is a soft approximation spaces. Sun and Ma [44] proposed a new concept of soft fuzzy rough set by combining the fuzzy soft set with the traditional fuzzy rough set.…”