The aim of this paper is to extend closure systems from being crisp sets with certain
fuzzy properties to proper fuzzy sets. The presentation of the paper shows a thorough
discussion on the different alternatives that could be taken to define the desired fuzzy
closure systems. These plausible alternatives are discarded if they are proven impossible
to be in a bijective correspondence with closure operators. Finally, a definition of fuzzy
closure system is established and a one-to-one relation with closure operators is proved.
