There exist infinitely many ways to extend the classical propositional connectives to the set $[0,1]$, preserving their behaviors in the extremes $0$ and $1$ exactly as in the classical logic. However, it is a consensus that this issue is not sufficient, and, therefore, these extensions must also preserve some minimal logical properties of the classical connectives. The notions of $t$-norms (conjunction), $t$-conorms (disjunction), fuzzy negations and fuzzy implications taking these considerations into account. In previous works, the author, joint with other colleagues, generalizes these notions to the set $\mathbb{U}=\{[a,b]\;|\; 0\leq a\leq b\leq 1\}$ , providing canonical constructions to obtain, for example, interval-valued $t$-norms that are the best interval representations of $t$-norms. In this talk, we will make a revision of fuzzy negations,  interval-valued fuzzy negations and provide  generalizations, in a natural way, of several notions related with fuzzy negations, such as the ones of equilibrium point and negation-preserving automorphism. We show that the main properties of these notions are preserved in those generalizations.