| 模糊拟阵闭集的结构 |
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| 引用本文： | 吴德垠,刘志花,李永红. 模糊拟阵闭集的结构[J]. 重庆大学学报(自然科学版), 2007, 30(7): 138-143 |
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| 作者姓名： | 吴德垠 刘志花 李永红 |
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| 作者单位： | 重庆大学,数理学院,重庆,400030;重庆邮电大学,计算机科学与技术学院,重庆,400065 |
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| 摘 要： | 模糊闭集和模糊超平面是模糊拟阵的2个基本概念,在模糊拟阵理论中起着重要的作用.文中研究了模糊闭集和模糊超平面的性质和结构,得到了相关的几个结论:模糊拟阵的闭集和它的导出拟阵的闭集之间的关系;普通拟阵所有超平面的交集是最小闭集且秩为0;模糊拟阵所有超平面交集也是最小的闭集且秩为0;利用数学归纳法证明了闭模糊拟阵模糊闭集的结构特征;找到了判定闭模糊拟阵的模糊闭集的一个充要条件.这些结果有利于进一步研究模糊拟阵的其他性质.
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| 关 键 词： | 拟阵 模糊拟阵 模糊闭集 模糊超平面 |
| 文章编号： | 1000-582X（2007）07-0138-06 |
| 修稿时间： | 2007-02-19 |
Structure of Closed Sets in Fuzzy Matroid |
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| WU De-yin,LIU Zhi-hu,LI Yong-hong. Structure of Closed Sets in Fuzzy Matroid[J]. Journal of Chongqing University(Natural Science Edition), 2007, 30(7): 138-143 |
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| Authors: | WU De-yin LIU Zhi-hu LI Yong-hong |
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| Affiliation: | 1. College of Mathematics and Physics, Chongqing University, Chongqing 400030, China ; 2. College of Computer Science and Technology, Chongqing University of Posts and Telecommunications, Chongqing 400065, China |
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| Abstract: | The authors study the properties and structures of fuzzy closed sets and fuzzy hyperplanes.The relationship between the closed set and it's derived matroid's closed set;The intersection of all hyperplanes in matroids is the smallest closed set and its rank is zero;The intersection of all fuzzy hyperplanes in fuzzy matroids is the smallest closed set and its rank is zero;The characteristics of structures of fuzzy closed sets is showed in using mathematical induction;a necessary and sufficient condition has been found in judging whether a fuzzy set is closed or not. |
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| Keywords: | matroids fuzzy matroids fuzzy closed sets fuzzy hyperplanes |
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