The aim of this work is to present an approach of interval fuzzy logic based on complete lattices. In particular, we study the extensions of the notions of t-conorms, fuzzy negations and S-implication, from the unit interval to arbitrary complete lattices. Some general properties of S-implications on complete lattices are analyzed. We show that the interval extensions of t-conorms, fuzzy negations and S-implications on complete lattices preserve the optimality property, being the best interval representations of these fuzzy connectives.
