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.
Highlights
Most of traditional methods for formal modeling, reasoning, and computing are crisp, deterministic, and precise in character
The purpose of this paper is to investigate soft rough approximation operators and relationships among soft sets, soft rough sets, and topologies
Soft rough sets, which could provide a better approximation than rough sets do, can be seen as a generalized rough set model, and defining soft rough sets and some related concepts needs using soft rough approximation operators based on soft sets
Summary
Most of traditional methods for formal modeling, reasoning, and computing are crisp, deterministic, and precise in character. There are several theories: probability theory, fuzzy set theory, theory of interval mathematics, and rough set theory [1], which we can consider as mathematical tools for dealing with uncertainties. All these theories have their own difficulties (see [2]). Theory of probabilities can deal only with stochastically stable phenomena To overcome these kinds of difficulties, Molodtsov [2] proposed a completely new approach, which is called soft set theory, for modeling uncertainty. The purpose of this paper is to investigate soft rough approximation operators and relationships among soft sets, soft rough sets, and topologies.
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