Pierre Mathonet

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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(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(More)
The concept of system signature was introduced by Samaniego for systems whose components have i.i.d. lifetimes. We consider its extension to the continuous dependent case and give an explicit expression for this extension as a difference of weighted means of the structure function values. We then derive a formula for the computation of the coefficients of(More)
The concept of signature was introduced by Samaniego for systems whose components have i.i.d. lifetimes. This concept proved to be useful in the analysis of theoretical behaviors of systems. In particular, it provides an interesting signature-based representation of the system reliability in terms of reliabilities of k-out-of-n systems. In the non-i.i.d.(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 functionˆf : [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(More)
The Banzhaf power index was introduced in cooperative game theory to measure the real power of players in a game. The Banzhaf interaction index was then proposed to measure the interaction degree inside coalitions of players. It was shown that the power and interaction indexes can be obtained as solutions of a standard least squares approximation problem(More)
By considering a least squares approximation of a given square integrable function f : [0, 1] n → IR by a shifted L-statistic function (a shifted linear combination of order statistics), we define an index which measures the global influence of the kth largest variable on f. We show that this influence index has appealing properties and we interpret it as(More)
For a coherent system the Barlow-Proschan importance index, defined when the component lifetimes are independent, measures the probability that the failure of a given component causes the system to fail. Iyer (1992) extended this concept to the more general case when the component lifetimes are jointly absolutely continuous but not necessarily independent.(More)
By considering a least squares approximation of a given square integrable function f ∶ [0, 1] n → R by a multilinear polynomial of a specified degree, we define an index which measures the overall interaction among variables of f. This definition extends the concept of Banzhaf interaction index introduced in cooperative game theory. Our approach is partly(More)
We consider the approximation problem of a pseudo-Boolean function by a symmetric pseudo-Boolean function in the sense of weighted least squares. We give explicit expressions for the approximation and provide interpretations and properties of its L-statistic representation. We also discuss applications of these expressions in cooperative game theory and(More)