References of "Marichal, Jean-Luc 50002296"
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See detailA characterization of barycentrically preassociative functions
Marichal, Jean-Luc UL; Teheux, Bruno UL

in Results in Mathematics (2016), 69(1), 245-256

We provide a characterization of the variadic functions which are barycentrically preassociative as compositions of length-preserving associative string functions with one-to-one unary maps. We also ... [more ▼]

We provide a characterization of the variadic functions which are barycentrically preassociative as compositions of length-preserving associative string functions with one-to-one unary maps. We also discuss some consequences of this characterization. [less ▲]

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See detailAgrégation des valeurs médianes et fonctions compatibles pour la comparaison
Couceiro, Miguel; Marichal, Jean-Luc UL; Teheux, Bruno UL

in Lefèvre, Erice; Hadjali, Allel (Eds.) Rencontres francophones sur la logique floue et ses applications 2015 (2015, November)

Nous caractérisons les fonctions d'agrégation qui préservent la valeur médiane dans le cas où l'opération médiane est conservative. Nous commençons par rappeler les notions d'algèbre et de demi-treillis ... [more ▼]

Nous caractérisons les fonctions d'agrégation qui préservent la valeur médiane dans le cas où l'opération médiane est conservative. Nous commençons par rappeler les notions d'algèbre et de demi-treillis médian en les introduisant à partir de la notion de valeur médiane sur les réels. Nous obtenons également une double caractérisation des algèbres médianes conservatives en termes de sous-structures interdites et de représentations par des chaînes [less ▲]

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See detailA classification of barycentrically associative polynomial functions
Marichal, Jean-Luc UL; Mathonet, Pierre; Tomaschek, Jörg

in Aequationes Mathematicae (2015), 89(5), 1281-1291

We describe the class of polynomial functions which are barycentrically associative over an infinite commutative integral domain.

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See detailMedian Preserving Aggregation Functions
Couceiro, Miguel; Marichal, Jean-Luc UL; Teheux, Bruno UL

in Baczyński, Michal; De Baets, Bernard; Mesiar, Radko (Eds.) Proceedings of the 8th Int. Summer School on Aggregation Operators (2015, July)

A median algebra is a ternary algebra that satisfies every equation satisfied by the median terms of distributive lattices. We present a characterization theorem for aggregation functions over ... [more ▼]

A median algebra is a ternary algebra that satisfies every equation satisfied by the median terms of distributive lattices. We present a characterization theorem for aggregation functions over conservative median algebras. In doing so, we give a characterization of conservative median algebras by means of forbidden substructures and by providing their representation as chains. [less ▲]

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See detailGeneralizations and variants of associativity for aggregation functions (2-hour tutorial)
Marichal, Jean-Luc UL; Teheux, Bruno UL

in Baczyński, Michal; De Baets, Bernard; Mesiar, Radko (Eds.) Proceedings of the 8th Int. Summer School on Aggregation Operators (2015, July)

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See detailGeneralizations and variants of associativity for variadic functions: a survey (invited talk)
Marichal, Jean-Luc UL

Scientific Conference (2015, June 17)

See attached PDF file

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See detailPreassociative aggregation functions
Marichal, Jean-Luc UL; Teheux, Bruno UL

in Fuzzy Sets & Systems (2015), 268

The classical property of associativity is very often considered in aggregation function theory and fuzzy logic. In this paper we provide axiomatizations of various classes of preassociative functions ... [more ▼]

The classical property of associativity is very often considered in aggregation function theory and fuzzy logic. In this paper we provide axiomatizations of various classes of preassociative functions, where preassociativity is a generalization of associativity recently introduced by the authors. These axiomatizations are based on existing characterizations of some noteworthy classes of associative operations, such as the class of Aczélian semigroups and the class of t-norms. [less ▲]

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See detailAlgorithms and formulas for conversion between system signatures and reliability functions
Marichal, Jean-Luc UL

in Journal of Applied Probability (2015), 52(2), 490-507

The concept of signature is a useful tool in the analysis of semicoherent systems with continuous and i.i.d. component lifetimes, especially for the comparison of different system designs and the ... [more ▼]

The concept of signature is a useful tool in the analysis of semicoherent systems with continuous and i.i.d. component lifetimes, especially for the comparison of different system designs and the computation of the system reliability. For such systems, we provide conversion formulas between the signature and the reliability function through the corresponding vector of dominations and we derive efficient algorithms for the computation of any of these concepts from the other. We also show how the signature can be easily computed from the reliability function via basic manipulations such as differentiation, coefficient extraction, and integration. [less ▲]

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See detailBarycentrically associative and preassociative functions
Marichal, Jean-Luc UL; Teheux, Bruno UL

in Acta Mathematica Hungarica (2015), 145(2), 468-488

We investigate the barycentric associativity property for functions with indefinite arities and discuss the more general property of barycentric preassociativity, a generalization of barycentric ... [more ▼]

We investigate the barycentric associativity property for functions with indefinite arities and discuss the more general property of barycentric preassociativity, a generalization of barycentric associativity which does not involve any composition of functions. We also provide a generalization of Kolmogoroff-Nagumo's characterization of the quasi-arithmetic mean functions to barycentrically preassociative functions. [less ▲]

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See detailOn modular decompositions of system signatures
Marichal, Jean-Luc UL; Mathonet, Pierre; Spizzichino, Fabio

in Journal of Multivariate Analysis (2015), 134

Considering a semicoherent system made up of $n$ components having i.i.d. continuous lifetimes, Samaniego defined its structural signature as the $n$-tuple whose $k$-th coordinate is the probability that ... [more ▼]

Considering a semicoherent system made up of $n$ components having i.i.d. continuous lifetimes, Samaniego defined its structural signature as the $n$-tuple whose $k$-th coordinate is the probability that the $k$-th component failure causes the system to fail. This $n$-tuple, which depends only on the structure of the system and not on the distribution of the component lifetimes, is a very useful tool in the theoretical analysis of coherent systems. It was shown in two independent recent papers how the structural signature of a system partitioned into two disjoint modules can be computed from the signatures of these modules. In this work we consider the general case of a system partitioned into an arbitrary number of disjoint modules organized in an arbitrary way and we provide a general formula for the signature of the system in terms of the signatures of the modules. The concept of signature was recently extended to the general case of semicoherent systems whose components may have dependent lifetimes. The same definition for the $n$-tuple gives rise to the probability signature, which may depend on both the structure of the system and the probability distribution of the component lifetimes. In this general setting, we show how under a natural condition on the distribution of the lifetimes, the probability signature of the system can be expressed in terms of the probability signatures of the modules. We finally discuss a few situations where this condition holds in the non-i.i.d. and nonexchangeable cases and provide some applications of the main results. [less ▲]

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See detailLa logique floue et ses applications
Bisgambiglia, Paul-Antoine; Guelton, Kevin; Lauber, Jimmy et al

in Revue d'Intelligence Artificielle [=RIA] (2015), 29(5), 489-619

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See detailInfluence and interaction indexes for pseudo-Boolean functions: a unified least squares approach
Marichal, Jean-Luc UL; Mathonet, Pierre UL

in Discrete Applied Mathematics (2014), 179

The Banzhaf power and interaction indexes for a pseudo-Boolean function (or a cooperative game) appear naturally as leading coefficients in the standard least squares approximation of the function by a ... [more ▼]

The Banzhaf power and interaction indexes for a pseudo-Boolean function (or a cooperative game) appear naturally as leading coefficients in the standard least squares approximation of the function by a pseudo-Boolean function of a specified degree. We first observe that this property still holds if we consider approximations by pseudo-Boolean functions depending only on specified variables. We then show that the Banzhaf influence index can also be obtained from the latter approximation problem. Considering certain weighted versions of this approximation problem, we introduce a class of weighted Banzhaf influence indexes, analyze their most important properties, and point out similarities between the weighted Banzhaf influence index and the corresponding weighted Banzhaf interaction index. We also discuss the issue of reconstructing a pseudo-Boolean function from prescribed influences and point out very different behaviors in the weighted and non-weighted cases. [less ▲]

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See detailAssociative string functions
Lehtonen, Erkko; Marichal, Jean-Luc UL; Teheux, Bruno UL

in Asian-European Journal of Mathematics (2014), 7(4), 145005918

We introduce the concept of associativity for string functions, where a string function is a unary operation on the set of strings over a given alphabet. We discuss this new property and describe certain ... [more ▼]

We introduce the concept of associativity for string functions, where a string function is a unary operation on the set of strings over a given alphabet. We discuss this new property and describe certain classes of associative string functions. We also characterize the recently introduced preassociative functions as compositions of associative string functions with injective unary maps. Finally, we provide descriptions of the classes of associative and preassociative functions which depend only on the length of the input. [less ▲]

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See detailOn the use of power indexes in reliability theory (invited lecture)
Marichal, Jean-Luc UL

Scientific Conference (2014, November 07)

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See detailComputing subsignatures of systems with exchangeable component lifetimes
Marichal, Jean-Luc UL

in Statistics & Probability Letters (2014), 94

The subsignatures of a system with continuous and exchangeable component lifetimes form a class of indexes ranging from the Samaniego signature to the Barlow-Proschan importance index. These indexes can ... [more ▼]

The subsignatures of a system with continuous and exchangeable component lifetimes form a class of indexes ranging from the Samaniego signature to the Barlow-Proschan importance index. These indexes can be computed through explicit linear expressions involving the values of the structure function of the system. We show how the subsignatures can be computed more efficiently from the reliability function of the system via identifications of variables, differentiations, and integrations. [less ▲]

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See detailAssociative and preassociative functions
Marichal, Jean-Luc UL; Teheux, Bruno UL

in Semigroup Forum (2014), 89(2), 431-442

We investigate the associativity property for functions of multiple arities and introduce and discuss the more general property of preassociativity, a generalization of associativity which does not ... [more ▼]

We investigate the associativity property for functions of multiple arities and introduce and discuss the more general property of preassociativity, a generalization of associativity which does not involve any composition of functions. [less ▲]

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See detailPivotal decompositions of functions
Marichal, Jean-Luc UL; Teheux, Bruno UL

in Discrete Applied Mathematics (2014), 174

We extend the well-known Shannon decomposition of Boolean functions to more general classes of functions. Such decompositions, which we call pivotal decompositions, express the fact that every unary ... [more ▼]

We extend the well-known Shannon decomposition of Boolean functions to more general classes of functions. Such decompositions, which we call pivotal decompositions, express the fact that every unary section of a function only depends upon its values at two given elements. Pivotal decompositions appear to hold for various function classes, such as the class of lattice polynomial functions or the class of multilinear polynomial functions. We also define function classes characterized by pivotal decompositions and function classes characterized by their unary members and investigate links between these two concepts. [less ▲]

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See detailPreassociative aggregation functions
Marichal, Jean-Luc UL; Teheux, Bruno UL

in Laurent, Anne; Strauss, Olivier; Bouchon-Meunier, Bernadette (Eds.) et al 15th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2014, Montpellier, France, July 15-19, 2014. Proceedings, Part III (2014, July 22)

We investigate the associativity property for varying-arity aggregation functions and introduce the more general property of preassociativity, a natural extension of associativity. We discuss this new ... [more ▼]

We investigate the associativity property for varying-arity aggregation functions and introduce the more general property of preassociativity, a natural extension of associativity. We discuss this new property and describe certain classes of preassociative functions. [less ▲]

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See detailQuasi-Lovász extensions on bounded chains
Couceiro, Miguel; Marichal, Jean-Luc UL

in Laurent, Anne; Strauss, Olivier; Bouchon-Meunier, Bernadette (Eds.) et al 15th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2014, Montpellier, France, July 15-19, 2014. Proceedings, Part I (2014, July 22)

Detailed reference viewed: 84 (1 UL)