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

TL;DR

This paper explores aggregation functions on n-dimensional ordered vectors within semi-vector spaces, extending OWA and weighted averages, and applies these to multi-criteria group decision-making.

Contribution

It introduces a new framework for aggregation functions on n-dimensional intervals using semi-vector spaces and applies it to decision-making.

Findings

Extended OWA and weighted average functions for n-dimensional intervals.

Developed a multi-criteria decision-making method based on these aggregation functions.

Provided an illustrative example demonstrating the application.

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 $L_n([0,1])$. 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.