Meaningful aggregation functions mapping ordinal scales into an ordinal scale: a state of the art

TL;DR

This paper reviews the current state of meaningful aggregation functions that map ordinal scales into an ordinal scale, focusing on three main classes and highlighting lattice polynomial functions as prominent examples.

Contribution

It provides a comprehensive overview of the main classes of meaningful aggregation functions for ordinal scales, emphasizing the role of lattice polynomial functions.

Findings

Lattice polynomial functions are the most prominent meaningful aggregation functions.

Three main classes of functions are identified: order invariant, comparison meaningful on a single scale, and on independent scales.

The paper offers a state-of-the-art overview of the topic.

Abstract

We present an overview of the meaningful aggregation functions mapping ordinal scales into an ordinal scale. Three main classes are discussed, namely order invariant functions, comparison meaningful functions on a single ordinal scale, and comparison meaningful functions on independent ordinal scales. It appears that the most prominent meaningful aggregation functions are lattice polynomial functions, that is, functions built only on projections and minimum and maximum operations.