10 research outputs found
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
Axiomatizations of quasi-Lovász extensions of pseudo-Boolean functions
We introduce the concept of quasi-Lov\'asz extension as being a mapping defined on a nonempty real interval containing the origin and which can be factorized as , where is the Lov\'asz extension of a pseudo-Boolean function (i.e., the function whose restriction to each simplex of the standard triangulation of is the unique affine function which agrees with at the vertices of this simplex) and is a nondecreasing function vanishing at the origin. These functions appear naturally within the scope of decision making under uncertainty since they subsume overall preference functionals associated with discrete Choquet integrals whose variables are transformed by a given utility function. To axiomatize the class of quasi-Lov\'asz extensions, we propose generalizations of properties used to characterize the Lov\'asz extensions, including a comonotonic version of modularity and a natural relaxation of homogeneity. A variant of the latter property enables us to axiomatize also the class of symmetric quasi-Lov\'asz extensions, which are compositions of symmetric Lov\'asz extensions with -place nondecreasing odd functions