[0,1]-Fuzzy $beta$-rank functions

Abstract

In this paper, 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.