n-Dimensional Interval Uninorms

n-Dimensional fuzzy sets are an extension of fuzzy sets where the membership values are n-tuples of real numbers in the unit interval [0, 1] ordered in increasing order, called n-dimensional intervals. The set of n-dimensional intervals is denoted by L
n
([0, 1]). In the present paper, we consider the notion of uninorms and n-dimensional fuzzy sets to define n-dimensional interval uninorms and we obtain results involving the notion of the neutral element, degenerate element, representable uninorms, ⊆-monotone and monotone by parts. Finally, we prove results involving the concepts of n-dimensional interval uninorms and n-dimensional automorphisms.