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.

n维模糊集是模糊集的扩展，其中隶属度值是单位区间内实数的n元组$[0,1]$越来越有序，称为n维区间。一组n维区间表示为${升}_n([0,1])$. 本文旨在研究弱半场上的半向量空间和关于n维区间集上的可容许阶的聚合函数，以及聚合函数的构造${升}_n([0,1])$基于半向量空间的运算。特别是，研究了 OWA 家族的扩展和加权平均聚合函数。最后，我们开发了一种基于n维聚合函数的多准则群决策方法，并给出了一个示例。