关于H-模糊拟阵的注记  

Notes on the H-fuzzy Matroids

作　　者：李小南[1] 刘三阳[1] 

机构地区：[1]西安电子科技大学数学科学系,西安710071

出　　处：《工程数学学报》2011年第5期707-710,共4页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11071151);中央高校基本科研业务费专项基金(K50510700006)~~

摘　　要：本文讨论了Hsueh于1993年提出的H-模糊拟阵不是分明拟阵好的推广.首先给出闭完全模糊独立集系统的等价刻画,然后加强了Hsueh关于H-模糊拟阵水平结构的结论,接着举例说明H-模糊拟阵未必是闭或完全的模糊独立集系统,最后,证明了非平凡的H-模糊拟阵具有无限多个模糊基.关于H-模糊拟阵水平结构和模糊基的结论从两个方面说明H-模糊拟阵不是分明拟阵好的推广.This paper points out that the H-fuzzy matroids introduced by Hsueh in 1993 are not good extension of the crisp matroids.Firstly,we characterize the closed perfect fuzzy independent set system,and reinforce the result on r-levels of the H-fuzzy matroids given by Hsueh.Then we construct an example to verify that the H-fuzzy matroids need not to be closed or perfect fuzzy independent systems.Finally,we prove that the nontrival H-fuzzy matroids have infinitely many fuzzy bases.The results on r-levels and fuzzy bases of H-fuzzy matroids show that Hsueh fuzzy matroids are not the good extension of the crisp matroids.

关 键 词：GV-模糊拟阵 H-模糊拟阵 模糊基 

分 类 号：O157[理学—数学] O159[理学—基础数学]