准模糊图拟阵模糊基的研究.pdf

准模糊图拟阵模糊基的研究







重庆大学硕士学位论文
(学术学位)


学生姓名:夏军
指导教师:吴德垠教授
专业:运筹学与控制论
学科门类:理学



重庆大学数学与统计学院
二 O 一三年四月
The Study on Bases of Quasi-Fuzzy
Graph Matriods



The Thesis Submitted to Chongqing University
in Partial Fulfillment of the Requirement for the
Master’s Degree of Science
By
Xia Jun

Supervised by Prof. Wu Deyin
Specialty: Operational Research and ics


College of Mathematics and Statistics of
Chongqing University, Chongqing, China
April, 2013
重庆大学硕士学位论文中文摘要

摘要

在现有拟阵和模糊拟阵理论的基础上,本文主要研究了模糊拟阵模糊基,特
别是准模糊图拟阵模糊基的性质。
1) 研究了模糊拟阵的闭、正规与其模糊基的存在性之间的关系,给出了闭模
糊拟阵的一类模糊基的构造方法;
2) 分析了准模糊图拟阵与闭正规模糊拟阵之间的关系,找到了准模糊图拟阵
是闭正规模糊拟阵的一个充分条件;
3) 研究了准模糊图拟阵模糊基的性质,得到了准模糊图拟阵的模糊基结构定
理。还证明了准模糊图拟阵的模糊基与其导出拟阵 M 的基有一一对应关系。最后
r1
还得到了准模糊图拟阵模糊基的对称交换定理;
4) 研究了准模糊图拟阵的模糊基有序问题,得到了准模糊图拟阵是模糊基有
序的一个充要条件。
本文比较深入的研究了准模糊图拟阵的模糊基及其与导出拟阵 M 的基之间
r1
的关系等。这些研究对丰富准模糊图拟阵的理论有重要意义。

关键词:模糊拟阵,准模糊图拟阵,正规模糊拟阵,基,模糊基















I
重庆大学硕士学位论文英文摘要

ABSTRACT

On the base of the original theory of crisp matroids and fuzzy matroids,the paper
studies mainly about the properties of bases of fuzzy matroids, especially, and studies
the properties of bases of quasi-fuzzy graph matroids.
1) The paper studies the relationship between the closed or regular properties of
fuzzy matroids and the existence of fuzzy bases of fuzzy have obtained a
method to structure a fuzzy base in the closed fuzzy matroid;
2) The relationship between quasi-fuzzy graph matroids and closed regular fuzzy
matroids had been analyzed,we have got one of sufficient conditions which quasi-fuzzy
graph matroids is closed regular fuzzy matroids;
3) The properties of bases of quasi-fuzzy graph matroids were studied,and we
have also obtained the structure-theorm of bases of quasi-fuzzy graph have
proved the existence of the bijection between bases of quasi-fuzzy g