  In [arXiv 0811.3913] the authors introduced the notion of quasi-polynomial
function as being a mapping f: X^n -> X defined and valued on a bounded chain X
and which can be factorized as f(x_1,...,x_n)=p(phi(x_1),...,phi(x_n)), where p
is a polynomial function (i.e., a combination of variables and constants using
the chain operations / and) and phi is an order-preserving map. In the current
paper we study this notion in the more general setting where the underlying
domain and codomain sets are, possibly different, bounded distributive
lattices, and where the inner function is not necessarily order-preserving.
These functions appear naturally within the scope of decision making under
uncertainty since, as shown in this paper, they subsume overall preference
functionals associated with Sugeno integrals whose variables are transformed by
a given utility function. To axiomatize the class of quasi-polynomial
functions, we propose several generalizations of well-established properties in
aggregation theory, as well as show that some of the characterizations given in
[arXiv 0811.3913] still hold in this general setting. Moreover, we investigate
the so-called transformed polynomial functions (essentially, compositions of
unary mappings with polynomial functions) and show that, under certain
conditions, they reduce to quasi-polynomial functions.
