Summary: The concepts of \([0,1]\)-fuzzy \(\beta\)-rank function and \([0, 1]\)-fuzzy \(\alpha\)-rank function are presented. The set of all closed and perfect \([0,1]\)-matroids (i.e. closed Goetschel-Voxman fuzzy matroids) on \(E\) and that of all \([0,1]\)-fuzzy \(\beta\)-rank functions on \(E\) are in one-to-one correspondence. A \([0,1]\)-fuzzy \(\alpha\)-rank function on \(E\) is equivalent to a \([0,1]\)-fuzzy \(\beta\)-rank function on \(E\).