Fuzzy bases of fuzzy independent set systems

Compactness, closeness and SC are conditions to ensure the existence of fuzzy bases for polymatroids, G-V fuzzy matroids and H fuzzy matroids respectively. In this work, relations of these three conditions with different fuzzy independent systems are studied. Furthermore, the equivalence of compactness, closeness and SC for G-V fuzzy matroids is proved and the existence of fuzzy bases of H fuzzy matroids is verified. Finally, it has been pointed out that H fuzzy matroids and E fuzzy matroids induced from polymatroids are the same and the question whether an H fuzzy matroid is a fuzzy pre-matroid is solved.