Congruences and the discrete Sugeno integrals on bounded distributive lattices

TL;DR

This paper explores compatible aggregation functions on bounded distributive lattices, providing new proofs and characterizations of discrete Sugeno integrals, enhancing understanding of their algebraic structure and applications.

Contribution

It offers a new proof of Grätzer's result and introduces a novel characterization of discrete Sugeno integrals on bounded distributive lattices.

Findings

New proof of Grätzer's theorem

Characterization of discrete Sugeno integrals

Insights into compatible aggregation functions

Abstract

We study compatible aggregation functions on a general bounded distributive lattice $L$, where the compatibility is related to the congruences on $L$. As a by-product, a new proof of an earlier result of G. Gr\"atzer is obtained. Moreover, our results yield a new characterization of discrete Sugeno integrals on bounded distributive lattices.