What aggregation rules can be classified as logical concepts?

TL;DR

This paper classifies aggregation rules with symmetric invariant sets that have a logical nature, using algebraic and function theory methods.

Contribution

It provides a complete classification of such aggregation rules based on their logical and algebraic properties.

Findings

Complete classification of aggregation rules with logical invariant sets

Application of universal algebra and discrete function theory

Identification of symmetric classes of invariant sets

Abstract

In this paper, we study aggregation rules with nontrivial symmetric classes of invariant sets (restricted domains), assuming that they, unlike others, have a logical nature. In the simplest case, we provide a complete classification of such rules. Our primary tools are methods of universal algebra and the theory of closed classes of discrete functions.