ON FUZZIFICATION OF MATROIDS

Abstract

In this paper, we propose one possible fuzzification of matroids which entends the independence axioms of matroids from set systems to fuzzy set systems and preserves most basic properties of matroids. By representing a fuzzy subset of a finite set E as a subset of E x (0, 1], we obtain fuzzy matroids by fuzzifying independence spaces on E x (0, 1]. Alternatively, by representing fuzzy subsets of E as functions from E into [0, 1], we can obtain fuzzy matroids from polymatroids associated with 'real' rank functions. We also investigate the duality for fuzzy matroids.