On Goetschel and Voxman fuzzy matroids

Abstract

The concepts of fuzzy pre-matroid and hereditary fuzzy pre-matroid are introduced and investigated. The property "to be perfect" for hereditary fuzzy pre-matroids is also considered. It is shown that Goetschel and Voxman fuzzy matroids coincide with perfect hereditary fuzzy pre-matroids. It is also shown that Goetschel and Voxman fuzzy matroids can be described via three fuzzy axioms, two of which are direct fuzzy counter-parts of the crisp matroid axioms in terms of elementary fuzzy sets and the third one is a decomposition axiom, also in terms of elementary fuzzy sets. © 2001 Elsevier Science B.V.