Axioms for bases of closed regular fuzzy matroids

This paper represents an attempt to define a set of bases which can determine a closed regular fuzzy matroid, and to study some properties of section fuzzy matroids, elementary section fuzzy matroids and elementary fuzzy matroids. Axioms for bases of both elementary fuzzy matroids and closed regular fuzzy matroids are presented, respectively. It is proved that the set of bases of all closed regular fuzzy matroids on a set equipped with a suitable order is order-isomorphic to the set of systems of independent sets of all closed regular fuzzy matroids on this set, equipped with the inclusion order.