Characterizations of discrete Sugeno integrals as polynomial functions over distributive lattices

We give several characterizations of discrete Sugeno integrals over bounded distributive lattices, as particular cases of lattice polynomial functions, that is, functions which can be represented in the language of bounded lattices using variables and constants. We also consider the subclass of term functions as well as the classes of symmetric polynomial functions and weighted infimum and supremum functions, and present their characterizations, accordingly. Moreover, we discuss normal form representations of these functions.