Characterizations of discrete Sugeno integrals as polynomial functions over distributive lattices

TL;DR

This paper characterizes discrete Sugeno integrals over bounded distributive lattices as lattice polynomial functions, exploring subclasses like symmetric and weighted functions, and discusses their normal form representations.

Contribution

It provides new characterizations of Sugeno integrals as polynomial functions and details their subclasses and normal forms.

Findings

Sugeno integrals characterized as lattice polynomial functions

Subclasses like symmetric and weighted functions characterized

Normal form representations discussed

Abstract

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 minimum and maximum functions, and present their characterizations, accordingly. Moreover, we discuss normal form representations of these functions.