| 粗糙群和基于子群的群的粗糙 |
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| 引用本文： | 张贤勇,莫智文.粗糙群和基于子群的群的粗糙[J].四川师范大学学报(自然科学版),2006,29(3):253-256. |
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| 作者姓名： | 张贤勇 莫智文 |
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| 作者单位： | 四川师范大学,基础部,四川,成都,610110;四川师范大学,数学与软件科学学院,四川,成都,610066 |
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| 基金项目： | 中国科学院资助项目;四川省青年科学基金 |
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| 摘 要： | 运用粗糙集理论的思想，在群中基于子群定义了群的近似空间，并定义了集合的运算，用集合的近似进行了研究．用近似群重新定义了粗糙群理论中的粗糙群、粗糙子群、粗糙不变子群、粗糙商群、粗糙同态、粗糙同构等一系列概念，并在传统的和新定义的两种粗糙群理论体系中，研究了基于子群的群的粗糙的性质．
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| 关 键 词： | 粗糙集 群 粗糙群 近似群 粗糙同态 |
| 文章编号： | 1001-8395（2006）03-0253-04 |
| 收稿时间： | 2003-09-28 |
| 修稿时间： | 2003年9月28日 |
Rough Group and the Roughness of Group Based on Subgroup |
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| ZHANG Xian-yong,MO Zhi-wen.Rough Group and the Roughness of Group Based on Subgroup[J].Journal of Sichuan Normal University(Natural Science),2006,29(3):253-256. |
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| Authors: | ZHANG Xian-yong MO Zhi-wen |
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| Institution: | 1. Section of Fundamental Studies, Sichuan Normal University, Chengdu 610110, Sichuan ; 2. College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, Sichuan |
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| Abstract: | In this Paper, in terms of the rough set theory the concept of approximate space of group is defined based on a subgroup. Operations of sets are defined and studied by set approximation. The notions in rough group theory are redefined by approximate groups, such as rough group, rough subgroup, rough invariant subgroup, rough quotient group, rough homomorphism, rough isomorphism, etc. In both systems of traditional rough group theory and redefined one, the properties of roughness of group based on subgroup are studied. |
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| Keywords: | Rough set Group Rough group Approximate group Rough homomorphism |
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