There are several operators related to fuzzy logic which in general are generalization of classical ones. For instance, triangular norms and conorms (t-norms and t-conorms for short) generalize the operators "and" and "or" from classical logic. A natural question arises: Without loss of generality if we consider a t-norm T defined on a sublattice M of bounded lattice L which satisfies a property P is it possible (1) to extend T to a function T' on L in such way that T' is also a t-norm and (2) T' also satisfy the property P. In this talk we present two different methods for extending t-norms, t-conorms, fuzzy negations and implications (namely, extension via retractions and extension via e-operators) from a sublattice to a lattice considering a generalized notion of sub lattices. For both methods goal (1) is completely achieved, however extension via retractions fails in preserving some properties of these fuzzy connectives.