准模糊图拟阵基的性质

The Properties of Bases of Quasi-Fuzzy Graph Matriods

本文主要研究准模糊图拟阵模糊基的一些重要性质。通过模糊拟阵的初等模糊集方法、导出拟阵序列法和基交换法等方法,得到了若导出拟阵所含基的个数都相同,则这个准模糊图拟阵是闭正规模糊拟阵;得出了用初等模糊集描述的准模糊图拟阵模糊基的结构定理,即存在数组{λ1,λ2,…,λl},使得μ∈Θ,μ=∨eijk∈suppμω({eijk},λjk);找到了准模糊图拟阵模糊基与导出拟阵序列的基的一一对应关系;最后在参考文献[3]的基础上,得到了结果更强的准模糊图拟阵模糊基交换定理——准模糊图拟阵模糊基对称交换定理,即若Θ是准模糊图拟阵的模糊基集,u1,u2∈Θ,则对任意的e∈supp u1,都有e′∈supp u2,使得(u1\e)‖u2e′∈Θ,(u2\)e′‖u1e∈Θ。

In the paper, we mainly study the some important properties of fuzzy bases of quasi-fuzzy graph matriod. With the help of methods of element fuzzy sets, induced matroid sequences, and bases-exchang, we found that if there is the same number of bases among indeced matroids, quasi-fuzzy graph matroids is closed regular matroids, we have also obtained the structure-theorm of bases of quasi-fuzzy graph matroids, there is a set {λ1, λ2, ……,λ1}, for μ∈,μ=eijk∨∈supp μω（{eijk},λjk）,that is, for arbitrary base of quasi-fuzzy graph matroids, we can use elementary fuzzy sets to describe it. and the one to one correspondence be- tween bases of quasi-fuzzy graph matroids and bases of indeced matroids sequences; Bases on the paper E3; of References, we have gained the symmetrical exchange-theorem of bases of quasi-fuzzy graph matroid. If O is fuzzy bases set of quasi-fuzzy graph matroids, u1, u2∈, then for arbitraryeEsuppul, there ise＇∈supp u2, so that （u1/e）｜｜u2e＇∈ ,（u2／e＇）｜｜u1e∈ . This conclusion is better than the exchange-theorem of bases of quasi-fuzzy graph matroid in the Third Referrence.