摘要
运用特殊化思想研究GV状模糊拟阵的秩与圈。定义了GV状模糊拟阵的秩和规范GV状模糊拟阵,并且给出了GV状模糊拟阵有秩的充要条件。引入了规范拟阵基系塔和规范拟阵独立集系塔的概念,证明了可以用规范拟阵基系塔或规范拟阵独立集系塔确定规范GV状模糊拟阵独立集系。定义了GV状模糊拟阵的圈并证明它类似于拟阵圈的一些性质。
Ranks and circuits of GV-like fuzzy matroids are studied by using the idea of specializa- tion. The notions rank of a GV-like fuzzy matroid and normal GV-like fuzzy matroid are defined and some necessary and sufficient conditions under which a GV-like fuzzy matroid has a rank is given. Based on this the notions of tower of familis of normal matroid bases and tower of familis of normal matroid independent sets are defined. It is proved that a system of GV-like fuzzy ma- troid independent sets on a set S can be determindeed by a tower of families of normal matroid ba- ses on S and by a tower of familis of normal matroid independent sets on S. The notion of circuit of a normal GV-like fuzzy matroid is defined and the some of their properties similar to those of matroid circuits are shown.
出处
《陕西师范大学学报（自然科学版）》
CAS
CSCD
北大核心
2017年第3期6-8,28,共4页
Journal of Shaanxi Normal University：Natural Science Edition
基金
国家自然科学基金(11641002)
河北省自然科学青年基金(A2014403008)
关键词
GV状模糊拟阵的秩
规范GV状模糊拟阵
规范拟阵基系塔
规范拟阵独立集系塔
GV状模糊拟阵的圈
rank of a GV-like fuzzy matroid
normal GV-like fuzzy matroid
tower of families ofnormal matroid bases
tower of families of normal matroid independent sets
circuit of a GV-likefuzzy matroid
