Quasi-Lov́sz Extensions on Bounded Chains

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Abstract

We study quasi-Lovász extensions as mappings f:Cn →ℝ defined on a nonempty bounded chain C, and which can be factorized as f(x 1,...,x n) = L(φ(x1),...,φ(xn)), where L is the Lovász extension of a pseudo-Boolean function ψ:{0,1}n → ℝ and φ: C → ℝ 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 φ: C → ℝ. Furthermore, we make some remarks on possible lattice-based variants and bipolar extensions to be considered in an upcoming contribution by the authors. © Springer International Publishing Switzerland 2014.

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APA

Couceiro, M., & Marichal, J. L. (2014). Quasi-Lov́sz Extensions on Bounded Chains. In Communications in Computer and Information Science (Vol. 442 CCIS, pp. 199–205). Springer Verlag. https://doi.org/10.1007/978-3-319-08795-5_21

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