Fuzzy Matroid's Expression And Sum And The Study On Bases Of Quasi-Fuzzy Graph Matriods

In this paper I study on the three aspects of the structure of fuzzy matroid on the basis of the existing theories,stated as follows:(l)Fuzzy matroid' s expression and sum:I discover a series of characters of fuzzy matroid with the help of the properties of fuzzy matroid studied at first in the paper,and give four expression theorems and four sum properties theorems and two sum theorems of fuzzy matroid . The former demonstrates existent sufficiency and necessary condition of fuzzy matroid. The follower demonstrates sum sufficiency condition and sum order and basic properties .(2) Basic Graph of Quasi-Fuzzy Graph Matriod:Basic graph is extending tree graph,and it is an important tool by which matroid is studied. Basic Graph is a graph for which basis set of matroid is consisting of vertex set. Two vertexs are adjoining if and only if there are exactly p(M)-l commonality elements in their bases. Thus it plays an important role in the further studying . I bring forward the "basis graph" of quasi-fuzzy graph matroid with the help of the quasi-fuzzy graph matroid by my tutor ffu Deyin in the paper. Then we discuss eight properties of basis graph of quasi-fuzzy graph matroid. They demonstrate connection properties,vertex distance,determining the label numbers of the vertices and path existing properties.(3) Basis Exchange Theorem of quasi-fuzzy graph matroid:Basic exchange is also an important tool in studying matroid. It is in fact that the basis is still a basis by two elements exchanging order. Basis exchange theorem of quasi-fuzzy graph matroid plays an important role in studying fuzzy matroid too. It cannot be shorten for matroid theorems. I demonstrate three propertic theorems and four deductions of basis exchange of quasi-fuzzy graph matroid with the help of the quasi-fuzzy graph matroid by my tutor Wu Deyin. Existing properties and determination of fuzzy basis exchange are studied in the paper. Order basis definition is given in the paper. Order basis definition is that two bases are also bases by exchange order each other .There are bijections mapping .Three propertic theoremsare proved.All of three aspects of fuzzy matroid are important contents of fuzzy matroid,and they were not studied by antecedences . The researchs are the basis for the further studying.