Congruences and the discrete Sugeno integrals on bounded distributive lattices

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.