  n-Dimensional fuzzy sets is a fuzzy set extension where the membership values
are n-tuples of real numbers in the unit interval [0,1] orderly increased,
called n-dimensional intervals. The set of n-dimensional intervals is denoted
by Ln([0,1]). This paper aims to investigate a special extension from [0,1] -
n-representable fuzzy negations on Ln([0,1]), summarizing the class of such
functions which are continuous and monotone by part. The main properties of
(strong) fuzzy negations on [0,1] are preserved by representable (strong) fuzzy
negation on Ln([0,1]), mainly related to the analysis of degenerate elements
and equilibrium points. The conjugate obtained by action of an n-dimensional
automorphism on an $n$-dimensional fuzzy negation provides a method to obtain
other n-dimensional fuzzy negation, in which properties such as
representability, continuity and monotonicity on Ln([0,1]) are preserved.
