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arXiv · 2101.12030

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

Thadeu Milfont·Ivan Mezzomo·Benjamín Bedregal·Edmundo Mansilla·Humberto Bustince
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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.

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Thadeu Milfont, Ivan Mezzomo, Benjamín Bedregal, Edmundo Mansilla, Humberto Bustince. 2021-01-27. Aggregation functions on n-dimensional ordered vectors equipped with an admissible order and an application in multi-criteria group decision-making. https://arxiv.org/abs/2101.12030

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