2011
DOI: 10.1007/s00010-011-0091-0
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Axiomatizations of quasi-Lovász extensions of pseudo-Boolean functions

Abstract: We introduce the concept of quasi-Lovász extension as being a mapping f : I n → R defined on a nonempty real interval I containing the origin and which can be factorized as f (x 1 , . . . , xn) = L(ϕ(x 1 ), . . . , ϕ(xn)), where L is the Lovász extension of a pseudo-Boolean function ψ : {0, 1} n → R (i.e., the function L : R n → R whose restriction to each simplex of the standard triangulation of [0, 1] n is the unique affine function which agrees with ψ at the vertices of this simplex) and ϕ : I → R is a nond… Show more

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Cited by 8 publications
(11 citation statements)
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“…The following two results are variants of Lemma 2 and Proposition 3 in [4]. and their proofs follow in complete analogy.…”
Section: Axiomatizations Of Quasi-lovász Extensionsmentioning
confidence: 93%
See 1 more Smart Citation
“…The following two results are variants of Lemma 2 and Proposition 3 in [4]. and their proofs follow in complete analogy.…”
Section: Axiomatizations Of Quasi-lovász Extensionsmentioning
confidence: 93%
“…A generalization of the notion of Lovász extension of a pseudo-Boolean function was introduced in [4] and called "quasi-Lovász extension". In this paper we extend this notion to the following concept.…”
Section: Quasi-lovász Extensions On Bounded Chainsmentioning
confidence: 99%
“…In the discrete case, a characterization using comonotonic modularity was obtained by Couceiro and Marichal [46,47]. The Sugeno integral was characterized in the discrete case by de Campos and Bolaños [44].…”
Section: Theoremmentioning
confidence: 98%
“…Situation (ii) in Theorem 1 implies that criteria i and k are independent (see (9)). The condition that…”
Section: Theorem 1 Let X I ∈ X I and ε > 0 Then One Of The Followingmentioning
confidence: 99%
“…In this setting, there is no commensurateness issue since all attributes and thus all value functions are identical. In [9], the Choquet integral is axiomatized as an aggregation function in the context of decision under uncertainty. In [10], the neutral element of a bipolar scale is determined under the knowledge that the decision maker satisfies a special decision strategy called conditional relative importance between criteria.…”
Section: Introductionmentioning
confidence: 99%