The Properties of Bases of Quasi-Fuzzy Graph Matriods

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 *,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 between bases of quasi-fuzzy graph matroids and bases of indeced matroids sequences; Bases on the paper [3] of References, we have gained the symmetrical exchange-theorem of bases of quasi-fuzzy graph matroid. If -Θ is fuzzy bases set of quasi-fuzzy graph matroids,-u1,u2∈Θ，then for arbitrary e∈supp u1，there is e′∈supp u2，so that u1＼e‖u2e′∈Θ,u2＼e′‖u1e∈Θ.This conclusion is better than the exchange-theorem of bases of quasi-fuzzy graph matroid in the Third Referrence.(* Indicates a formula, please see the full text)