Weighted lattice polynomials

TL;DR

This paper introduces weighted lattice polynomial functions, extending lattice polynomials with parameters, and characterizes them through median decompositions, encompassing discrete Sugeno integrals within a unified framework.

Contribution

It defines weighted lattice polynomial functions, provides their equivalent forms in bounded distributive lattices, and characterizes them via median-based decomposition formulas.

Findings

Includes discrete Sugeno integrals as special cases

Provides equivalent forms in arbitrary bounded distributive lattices

Characterizes functions through median-based decomposition

Abstract

We define the concept of weighted lattice polynomial functions as lattice polynomial functions constructed from both variables and parameters. We provide equivalent forms of these functions in an arbitrary bounded distributive lattice. We also show that these functions include the class of discrete Sugeno integrals and that they are characterized by a median based decomposition formula.