Weighted lattice polynomials (Q1011717)

By allowing some variables to be fixed as parameters, the author generalizes lattice polynomial functions to so-called weighted lattice polynomial functions. Equivalent disjunctive or conjunctive normal forms are given in bounded distributive lattices (with chains as a special case). It is shown that these functions include the class of discrete Sugeno integrals, extensively used in aggregation function theory and in fuzzy set theory. Finally, a median-based system of functional equations that completely characterizes the weighted lattice polynomial functions is given.