References of "Mathonet, Pierre 40000450"
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See detailMeasuring the interactions among variables of functions over the unit hypercube
Marichal, Jean-Luc UL; Mathonet, Pierre UL

Scientific Conference (2010, January)

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See detailWeighted Banzhaf interaction indexes and weighted least squares
Marichal, Jean-Luc UL; Mathonet, Pierre UL

Scientific Conference (2010, January)

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See detailApproximations of Lovász extensions and their induced interaction index
Marichal, Jean-Luc UL; Mathonet, Pierre UL

in Discrete Applied Mathematics (2008), 156(1), 11-24

The Lovász extension of a pseudo-Boolean function f : {0,1}^n --> R is defined on each simplex of the standard triangulation of [0,1]^n as the unique affine function \hat f : [0,1]^n --> R that ... [more ▼]

The Lovász extension of a pseudo-Boolean function f : {0,1}^n --> R is defined on each simplex of the standard triangulation of [0,1]^n as the unique affine function \hat f : [0,1]^n --> R that interpolates f at the n+1 vertices of the simplex. Its degree is that of the unique multilinear polynomial that expresses f. In this paper we investigate the least squares approximation problem of an arbitrary Lovász extension \hat f by Lovász extensions of (at most) a specified degree. We derive explicit expressions of these approximations. The corresponding approximation problem for pseudo-Boolean functions was investigated by Hammer and Holzman and then solved explicitly by Grabisch, Marichal, and Roubens, giving rise to an alternative definition of Banzhaf interaction index. Similarly we introduce a new interaction index from approximations of \hat f and we present some of its properties. It turns out that its corresponding power index identifies with the power index introduced by Grabisch and Labreuche. [less ▲]

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See detailDecomposition of symmetric tensor fields in the presence of a flat contact projective structure
Frégier, Yaël; Mathonet, Pierre UL; Poncin, Norbert UL

in Journal of Nonlinear Mathematical Physics (2008), 15(2), 252--269

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See detailNatural dualities for varieties generated by a set of subalgebras of a semi-primal algebra
Mathonet, Pierre UL; Niederkorn, Philippe; Teheux, Bruno UL

in Algebra and Discrete Mathematics (2007), (1), 67--85

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See detailEquivariant symbol calculus for differential operators acting on forms
Boniver, Fabien; Hansoul, Sarah; Mathonet, Pierre UL et al

in Letters in Mathematical Physics (2002), 62(3), 219-232

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See detailOn comparison meaningfulness of aggregation functions
Marichal, Jean-Luc UL; Mathonet, Pierre UL

in Journal of Mathematical Psychology (2001), 45(2), 213-223

This paper will give a description of all continuous functions which are comparison meaningful in the sense of measurement theory.

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See detailCharacterization of some aggregation functions stable for positive linear transformations
Marichal, Jean-Luc UL; Mathonet, Pierre UL; Tousset, Eric

in Fuzzy Sets & Systems (1999), 102(2), 293-314

This paper deals with the characterization of some classes of aggregation functions often used in multicriteria decision making problems. The common properties involved in these characterizations are ... [more ▼]

This paper deals with the characterization of some classes of aggregation functions often used in multicriteria decision making problems. The common properties involved in these characterizations are "increasing monotonicity" and "stability for positive linear transformations". Additional algebraic properties related to associativity allow to completely specify the functions. [less ▲]

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See detailA characterization of the ordered weighted averaging functions based on the ordered bisymmetry property
Marichal, Jean-Luc UL; Mathonet, Pierre UL

in IEEE Transactions on Fuzzy Systems (1999), 7(1), 93-96

This paper deals with a characterization of a class of aggregation operators. This class concerns operators which are symmetric, increasing, stable for the same positive linear transformations and present ... [more ▼]

This paper deals with a characterization of a class of aggregation operators. This class concerns operators which are symmetric, increasing, stable for the same positive linear transformations and present a property close to the bisymmetry property: the ordered bisymmetry property. It is proved that the class investigated contains exactly the ordered weighted averaging operators (OWA) introduced by Yager in 1988. [less ▲]

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See detailCharacterization of some aggregation functions stable for positive linear transformations
Marichal, Jean-Luc UL; Mathonet, Pierre UL; Tousset, Eric

Scientific Conference (1997, January)

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See detailCharacterization of some aggregation functions stable for positive linear transformations
Marichal, Jean-Luc UL; Mathonet, Pierre UL; Tousset, Eric

in Proc. 44th Meeting of the Eur. Working Group "Multiple Criteria Decision Aiding" (MCDA 44), Brussels, Belgium, Oct. 3-4, 1996 (1996, October)

This paper deals with the characterization of some classes of aggregation functions often used in multicriteria decision making problems. The common properties involved in these characterizations are ... [more ▼]

This paper deals with the characterization of some classes of aggregation functions often used in multicriteria decision making problems. The common properties involved in these characterizations are “increasing monotonicity” and “stability for positive linear transformations”. Additional algebraic properties related to associativity allow to completely specify the functions. [less ▲]

Detailed reference viewed: 82 (0 UL)