Notes on the H-fuzzy Matroids
Sanyang Liu · Gongcheng shuxue xuebao · 2011
This paper points out that the H-fuzzy matroids introduced by Hsueh in 1993 are not good extension of the crisp matroids.Firstly,we characterize the closed perfect fuzzy independent set system,and reinforce the result on r-levels of the H-fuzzy matroids given by Hsueh.Then we construct an example to verify that the H-fuzzy matroids need not to be closed or perfect fuzzy independent systems.Finally,we prove that the nontrival H-fuzzy matroids have infinitely many fuzzy bases.The results on r-levels and fuzzy bases of H-fuzzy matroids show that Hsueh fuzzy matroids are not the good extension of the crisp matroids.