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。
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 .
出处
《重庆大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
2007年第7期138-143,共6页
Journal of Chongqing University
关键词
拟阵
模糊拟阵
模糊闭集
模糊超平面
matroids
fuzzy matroids
fuzzy closed sets
fuzzy hyperplanes
