10 research outputs found

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

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    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    LIPIcs, Volume 261, ICALP 2023, Complete Volume

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    LIPIcs, Volume 261, ICALP 2023, Complete Volum

    Computer Science Logic 2018: CSL 2018, September 4-8, 2018, Birmingham, United Kingdom

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    Acta Cybernetica : Volume 23. Number 1.

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    Axiomatizations of quasi-Lovász extensions of pseudo-Boolean functions

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    We introduce the concept of quasi-Lov\'asz extension as being a mapping f ⁣:InRf\colon I^n\to\R defined on a nonempty real interval II containing the origin and which can be factorized as f(x1,,xn)=L(φ(x1),,φ(xn))f(x_1,\ldots,x_n)=L(\varphi(x_1),\ldots,\varphi(x_n)), where LL is the Lov\'asz extension of a pseudo-Boolean function ψ ⁣:{0,1}nR\psi\colon\{0,1\}^n\to\R (i.e., the function L ⁣:RnRL\colon\R^n\to\R whose restriction to each simplex of the standard triangulation of [0,1]n[0,1]^n is the unique affine function which agrees with ψ\psi at the vertices of this simplex) and φ ⁣:IR\varphi\colon I\to\R 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 11-place nondecreasing odd functions

    Acta Cybernetica : Volume 18. Number 1.

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