The "representation problem" in abstract algebraic logic is that of finding necessary and sufficient conditions for a structure, on a well defined abstract framework, to have the following property: that for every structural closure operator on it, ...

Isotone and anti-isotone mappings from a poset into a complete lattice are investigated as lattice-valued up-sets and down-sets, respectively. Cuts of these are shown to be analogue crisp sub-posets of the domain: up-set or semi-filters and down-sets or ...

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 ...