Aggregation functions on n-dimensional ordered vectors equipped with an admissible order and an application in multi-criteria group decision-making

Abstract

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 Ln([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 Ln([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.