GV状模糊拟阵的秩与圈-陕西师范大学学报期刊社网站

陕西师范大学学报（自然科学版）

数学与计算机科学

GV状模糊拟阵的秩与圈

赵航1，路玲霞2，李生刚1*，陶倩1，李亚平1

（1 陕西师范大学数学与信息科学学院，陕西西安 710119；2 石家庄经济学院数理学院，河北石家庄 050031)

李生刚,男,教授，博士生导师。E-mail:shengganglinew@126.com

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。

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

收稿日期：

2016-04-23

中图分类号：

O157.1

文献标识码：

文章编号：

1672-4291(2017)03-0006-03doi:10.15983/j.cnki.jsnu.2017.03.132

基金项目：

国家自然科学基金(11641002)；河北省自然科学青年基金(A2014403008)

Doi:

Ranks and circuits of the GV-like fuzzy matroids

ZHAO Hang1， LU Lingxia2， LI Shenggang1*, TAO Qian1, LI Yaping1

(1 School of Mathematics and Information Science, Shaanxi Normal University,Xi′an 710119, Shaanxi, China;2 School of Mathematics and Sciences, Shijiazhuang University of Economics,Shijiazhuang 050031, Hebei, China)

Abstract:

Ranks and circuits of GV-like fuzzy matroids are studied by using the idea of specialization.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 matroid independent sets on a set S can be determindeed by a tower of families of normal matroid bases 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.

KeyWords:

rank of a GV-like fuzzy matroid;normal GV-like fuzzy matroid;tower of families of normal matroid bases; tower of families of normal matroid independent sets;circuit of a GV-like fuzzy matroid