I'm asking for the following problem:
Let $E$ be a finite set and $\mathcal{I}$ a given independence system (i.e. a non-empty collection of subsets of $E$ closed under taking subsets).
Is there a way to construct a matroid starting from $\mathcal{I}$? If yes, is this matroid unique (up to isomorphisms)? Can you report me some paper on such an issue?