Soft sets and soft rough sets
Soft sets and soft rough sets
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DOI：
10.1016/j.ins.2010.11.004
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发表时间：
2011-03-15
影响因子：
8.1
通讯作者：
Jun, Young Bae
中科院分区：
文献类型：
--
作者：
Feng, Feng;Liu, Xiaoyan;Jun, Young Bae
在这项研究中，我们建立了一个有趣的联系之间的两个数学方法的精确性：粗糙集和软集。首次利用软集理论对Pawlak的粗糙集模型进行了推广。基于软近似空间这一新的粒度结构，引入了软粗糙近似和软粗糙集。软粗糙近似的基本性质，并支持一些说明性的例子。我们还定义了新的软集类型，如完全软集，交完全软集和划分软集。提出了软粗相等关系的概念，并研究了其相关性质。我们还表明，Pawlak的粗糙集模型可以被看作是软粗糙集的一个特殊情况下，这两个概念将重合的软近似空间中的底层软集是一个分区软集。最后给出了一个实例，并对粗糙集和软粗糙集进行了比较分析. (C)2010年爱思唯尔公司All rights reserved.
In this study, we establish an interesting connection between two mathematical approaches to vagueness: rough sets and soft sets. Soft set theory is utilized, for the first time, to generalize Pawlak's rough set model. Based on the novel granulation structures called soft approximation spaces, soft rough approximations and soft rough sets are introduced. Basic properties of soft rough approximations are presented and supported by some illustrative examples. We also define new types of soft sets such as full soft sets, intersection complete soft sets and partition soft sets. The notion of soft rough equal relations is proposed and related properties are examined. We also show that Pawlak's rough set model can be viewed as a special case of the soft rough sets, and these two notions will coincide provided that the underlying soft set in the soft approximation space is a partition soft set. Moreover, an example containing a comparative analysis between rough sets and soft rough sets is given. (C) 2010 Elsevier Inc. All rights reserved.