摘要
本文首先推广模糊横贯拟阵概念,定义了更为广泛的模糊横贯拟阵;然后,通过模糊拟阵导出集合函数概念,证明了所有模糊横贯拟阵都是闭模糊拟阵;利用这个闭性,研究了模糊横贯拟阵的基本序列和导出拟阵序列特性;通过这两个特性和“截短模糊集族”概念,得到了模糊横贯拟阵的独立模糊集和模糊基的等价刻画;借助建立“子集族串”概念,找到了模糊集族的全部模糊部分横贯能够组成模糊横贯拟阵的一个等价刻画。
The paper has extended the conception of fuzzy transversal matroids to define more general fuzzy transversal matroids;With the help of the induced set function of fuzzy matroids,this paper has proven that all of fuzzy transversal matroids are closed;Then,fundamental sequences and induced matroid sequence of these fuzzy matroids have been studied by the closed property;By the aid of these research and truncated fuzzy set family,the paper has got a equivalent characterization of independent fuzzy sets and fuzzy bases;Lastly,this paper has found out a equivalent characterization which all fuzzy partial transversal of a fuzzy set family can compose a fuzzy transversal matroid.
作者
吴德垠
WU De-yin(College of Mathematics and Statistics,Chongqing University,Chongqing 401331,China)
出处
《模糊系统与数学》
北大核心
2019年第3期1-18,共18页
Fuzzy Systems and Mathematics
