A fuzzifying closure system is introduced as a fuzzy set on the collection of subsets of a nonempty set. It is proved that
this structure is a particular fuzzy lattice ordered poset. Conversely, every lattice ordered poset is isomorphic to a fuzzifying
closure system. In particular, each complete fuzzy lattice is representable by a fuzzifying closure system.
Keywords fuzzifying closure system - fuzzy lattice - fuzzy complete lattice - lattice ordered fuzzy poset