粗糙群定义的缺陷与修正

Defect and Revision of Definition of Rough Group

自Pawlak Z提出粗糙集理论以来,众多学者进行了广泛深入的研究,并将该理论拓展至粗糙代数领域.Biswas R和Nanda S首次提出了粗糙群(B-N粗糙群)的概念并给出了若干性质,但这一概念本身存在着一定缺陷.已有一些研究者指出了B-N粗糙群的定义和结论存在的一些问题,并给出了B-N粗糙群的修正定义,但B-N粗糙群定义仍有一个缺陷未能被发现.本文详尽分析了B-N粗糙群及其修正版的缺陷,提出了一种新的粗糙群修正定义,并用示例进行了说明.

Rough set theory,proposed by Pawlak Z,has evoked a lot of researches.Theoretic study has included algebra aspect of rough sets.The concept of rough group was introduced firstly by Biswas R and Nanda S,but with some deficiencies remaining.The concept of rough group was improved by other researchers,but there is another shortcoming in the concept of rough group introduced by Biswas R and Nanda S.In this paper,we examine the defects of the definition of rough group initiated by Biswas R and Nanda S and its improvements,and present a new revision of rough group.