| 群中模糊集的上近似集合与下近似集合 |
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| 引用本文： | 王莉,毕全起.群中模糊集的上近似集合与下近似集合[J].河北师范大学学报(自然科学版),2001,25(4):450-452. |
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| 作者姓名： | 王莉 毕全起 |
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| 作者单位： | 1. 锦州师范学院数学系,
2. 河北师范大学数学与信息科学学院, |
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| 基金项目： | 辽宁省教育厅攀登计划资助项目 ( 2 0 16 10 49) |
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| 摘 要： | 粗糙集概念是由Pawlak于1982年提出的，现已从许多方面作了推广，粗糙集与模糊集的结合近年来越来越受到国际学术界的关注，现在研究群中模糊集的上，下近似，并且讨论了近似算子的乘积结构，定义了粗糙模糊子群的概念，证明了模糊子群一定是粗糙模糊子群，在同态映射下，子群的像的上下近似也一定是它的上，下近似的同态像。
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| 关 键 词： | 粗糙模糊子群 上近似集合 下近似集合 粗糙集 模糊集 同态像 群 |
| 文章编号： | 1000-5854(2001)04-0450-03 |
| 修稿时间： | 2001年6月20日 |
The Upper and Lower Approximations of Fuzzy Sets in a Group |
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| WANG Li ,BI Quan qi.The Upper and Lower Approximations of Fuzzy Sets in a Group[J].Journal of Hebei Normal University,2001,25(4):450-452. |
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| Authors: | WANG Li BI Quan qi |
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| Institution: | WANG Li 1,BI Quan qi 2 |
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| Abstract: | The theory of rough set is proposed by Z.Pawlak in 1982.It is extended from various points of sides.The combination of rough set and fuzzy set is studied by many authors.The concepts of upper and lower approximations of fuzzy sets in a group are given,and the product structure of approximation operators is studied.The concept of rough fuzzy subgroup is also definde.It is proved that a fuzzy subgroup of a group is a rough fuzzy subgroup.Under a homostasis mapping,the upper and lower approximations of the images of a subgroup are just the images of their apper and lower approximations. |
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| Keywords: | fuzzy subgroup rough fuzzy subgroup upper approximation lower approximation |
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