Thining Base,Abandoning Base Operation On Matroids And Generalized Uniform Matroids

In order to deeply describe the properties of matroids,thining base operation and abandoning base of a matroids and generalized uniform matroids are defined.Thining base operation and abandoning base of a matroids,that is,start from the element of matroid bases,make the number of the bases or the families of matroid bases decreases gradually,so a new matroid bases and an independent sets of matroid that corresponding to it axe obtained.The results show that these two new matroid operations can be used to construct normal GV like fuzzy matroids.Generalized uniform matroids,combination the one to one correspondence relation between the families of independent sets of ordinary matroids and the families of bases of it and some properties of it,the conception of generalized uniform matroids and its some properties are investigated in this paper,we can investigate some equivalent description and their properties and the methods of how to calculate the parameter of the generalized uniform matroids.This paper is divided into four chapters and its concrete structure is as follows:In chapter 1,we recall some concepts and conclusions about lattice theory,matroid theory,fuzzy mathematics and fuzzy matroid which will be used in this paper.Thining base operation and abandoning base on matroids are defined and their properties are investigated in chapter 2.The obtained results can be used to characterize normal GV-like fuzzy matroids.The conception of generalized uniform matroids is given,and some equivalent description of the generalized uniform ma-troids are acquired in chapter 3.In chapter 4,Based on the families of independent sets of generalized uniform matroids.Analogous to ordinary matroids,there exists one to one corresponding relations between the families of independent sets and the families of bases,the families of closed set in generalized uniform matroids,thus,we can investigate some equivalent description and their properties and the methods of how to calculate the parameter of the generalized uniform matroids.