模糊拟阵研究  

On Fuzzy Matroids

作　　者：李小南[1] 李海洋[2] 李生刚[3] 

机构地区：[1]西安电子科技大学数学科学系,西安710071 [2]西安工程大学理学院,西安710048 [3]陕西师范大学数学与信息科学学院,西安710062

出　　处：《工程数学学报》2009年第3期431-436,共6页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(10271069);西安工程大学校管科研资助项目(2006XG40)

摘　　要：李传东等人研究了模糊子拟阵,然而,这些工作是在作者误认为模糊拟阵和次模糊拟阵等价的前提下做出的。本文首先给出两个例子说明模糊拟阵和次模糊拟阵是两个不同的概念。其次,把分明拟阵中的限制,截短等运算推广到模糊拟阵中,并且定义了模糊拟阵的垂直截短、水平截短、水平限制等运算。最后证明了模糊拟阵的基本列包含其水平限制的基本列。Fuzzy submatroids was studied by Li Chuan-dong et al. However, a mistake was made by them, their research was based on the idea that fuzzy matroids and fuzzy hypomotroids were equivalent. In this paper, two examples are firstly given to show that the concept of fuzzy matroids is different from fuzzy hypomotroids. Then, the operations of crisp matroids such as restriction and truncation are extended to the situation of fuzzy matroids. And vertical truncation, horizontal truncation and horizontal restriction of fuzzy matroids axe defined. In the end, the conclusion that the fundamental sequence of fuzzy matroids contains the fundamental sequence of fuzzy matroids is proved.

关 键 词：垂直截短 水平截短 水平限制 

分 类 号：O157[理学—数学] O159[理学—基础数学]