关于模糊拟阵的独立子集套和独立集函数

本文的研究方法主要是将模糊拟阵问题转化为普通拟阵问题来研究的方法。本文首先建立独立子集套概念,并使用这个概念和独立集函数概念构建了闭模糊拟阵的充要条件和模糊独立集的充要条件;然后,本文仔细分析了模糊基的性质,找到了一个使用独立子集套和独立集函数来描述的模糊基的充要条件;最后,利用模糊基的这个充要条件提出并证明了闭正规模糊拟阵的充要条件。

The Research of Independent-subset Sets and Independent-set Functions on Fuzzy Matroids

The research method of this paper is mainly the method which the research of fuzzy matroids have been exchanged the research of matroids. First, the article has established the concept of independent-subset sets, and found the necessary condition and sufficient condition of closed fuzzy matroids and independent fuzzy sets. Second, from analyzing properties of fuzzy bases carefully, the article has gained the necessary condition and sufficient condition for fuzzy bases. These conditions have been described by independent-ubset sets and independent set functions.Last, with help of these conditions, the paper has put forward and proved the necessary condition and sufficient condition for closed regular fuzzy matroids.