An improved representation theorem of L-fuzzy sets

In this paper we present an extension of the famous representation theorem of Negoita and Ralescu. In this theorem the authors proved that the structure of lattice-valued fuzzy sets is dual isomorphic to the structure of lattice-valued flou sets for a special kind of lattices satisfying an additional condition that resembles the characterization of a supremum in chains. In this paper we show that this condition can be dropped and replaced by adding an antitone involution to both structures.