Aggregation functions as lax morphisms of quantales

TL;DR

This paper generalizes aggregation functions within the framework of quantales, showing they are lax morphisms, and unifies various known results in metric and fuzzy metric aggregation.

Contribution

It introduces a global framework by characterizing aggregation functions as lax morphisms of quantales, linking them to existing mathematical structures.

Findings

Aggregation functions are exactly lax morphisms of quantales.

The framework unifies results in metric and fuzzy metric aggregation.

Provides a new perspective for studying aggregation functions mathematically.

Abstract

We will generalize the concept of aggregation function for mathematical structures as a certain function between quantales. In fact, these functions turn to be exactly the lax morphism of quantales. This provides a global framework for the study of aggregation functions. As a consequence of our theory, we are able to deduce several known results about the aggregation of metrics and fuzzy metrics.