Quasi-Lovász extensions on bounded chains

Miguel Couceiro (1, 2) , Jean-Luc Marichal (3)

1 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision
2 ORPAILLEUR - Knowledge representation, reasonning
3 SMA - Service de Mathématiques Appliquées

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.

Mots clés: Aggregation function; discrete Choquet integral; Lovász extension; quasi-Lovász extension; comonotonic modularity

Domaines: Mathématiques [math]

Miguel Couceiro, Jean-Luc Marichal. Quasi-Lovász extensions on bounded chains. 15th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2014), Jul 2014, Montpellier, France. pp.199-205, ⟨10.1007/978-3-319-08795-5_21⟩. ⟨hal-01090634⟩