  $n$-Dimensional fuzzy sets are a fuzzy set extension where the membership
values are n-tuples of real numbers in the unit interval [0,1] increasingly
ordered, called n-dimensional intervals. The set of n-dimensional intervals is
denoted by $L_n([0,1])$. This paper aims to investigate semi-vector spaces over
a weak semifield and aggregation functions concerning an admissible order on
the set of $n$-dimensional intervals and the construction of aggregation
functions on $L_n([0,1])$ based on the operations of the semi-vector spaces. In
particular, extensions of the family of OWA and weighted average aggregation
functions are investigated. Finally, we develop a multi-criteria group
decision-making method based on n-dimensional aggregation functions with
respect to an admissible order and give an illustrative example.
