Properties of the Fourth Type of Covering-Based Rough Sets
Properties of the Fourth Type of Covering-Based Rough Sets
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DOI：
10.1016/j.ins.2012.01.026
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发表时间：
2006-12
期刊：
影响因子：
--
通讯作者：
William Zhu;Fei-Yue Wang
中科院分区：
文献类型：
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作者：
William Zhu;Fei-Yue Wang
粗糙集作为一种粒计算技术，用于处理信息系统中的模糊性和粒度。基于覆盖的粗糙集被提出用来推广这一理论以便于更广泛的应用。针对不同的情况，研究了三种基于覆盖的粗糙集。为了使理论更加完备，本文提出了第四类基于覆盖的粗糙集。与已有的方法相比，新方法在上、下近似之间的相互依赖关系上显示出其独特的特点。我们对这一新理论进行了系统的研究。首先，我们讨论了正规性、压缩和单调等基本性质。然后，我们研究了这类基于覆盖的粗糙集满足Pawlak粗糙集性质的条件，并研究了上下近似运算之间的相互依赖关系。此外，还建立了上、下近似运算的公理系统。最后，我们讨论了这种基于覆盖的粗糙集与现有的三种覆盖粗糙集之间的关系。
As a technique for granular computing, rough sets deal with the vagueness and granularity in information systems. Covering-based rough sets have been proposed to generalize this theory for wider application. Three types of covering-based rough sets have been studied for different situations. To make the theory more complete, this paper proposes a fourth type of covering-based rough sets. Compared with the existing ones, the new type shows its special characteristic in the interdependency between its lower and upper approximations. We carry out a systematical study of this new theory. First, we discuss basic properties such as normality, contraction, and monotone. Then we investigate the conditions for this type of covering-based rough sets to satisfy the properties of Pawlak’s rough sets and study the interdependency between the lower and upper approximation operations. In addition, axiomatic systems for the lower and upper approximation operations are established. Lastly, we address the relationships between this type of covering-based rough sets and the three existing ones.