We study quasi-Lovász extensions as mappings defined on a nonempty bounded chain C, and which can be factorized as f(x 1,…,x n ) = L(ϕ(x 1),…,ϕ(x n )), where L is the Lovász extension of a pseudo-Boolean function and is an order-preserving function. We axiomatize these mappings by natural extensions to properties considered in the authors’ previous work. Our motivation is rooted in decision making under uncertainty: such quasi-Lovász extensions subsume overall preference functionals associated with discrete Choquet integrals whose variables take values on an ordinal scale C and are transformed by a given utility function . Furthermore, we make some remarks on possible lattice-based variants and bipolar extensions to be considered in an upcoming contribution by the authors.