References of "Marichal, Jean-Luc 50002296"
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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 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)

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

Scientific Conference (2014, June 24)

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See detailAssociativity, preassociativity, and string functions
Lehtonen, Erkko UL; Marichal, Jean-Luc UL; Teheux, Bruno UL

Scientific Conference (2014, June 20)

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See detailOn structure signatures and probability signatures of general decomposable systems (invited talk)
Marichal, Jean-Luc UL; Mathonet, Pierre UL; Spizzichino, Fabio

Scientific Conference (2014, June 16)

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

Scientific Conference (2014, June 16)

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See detailFonctions d'agrégation associatives et préassociatives (invited lecture)
Marichal, Jean-Luc UL

Presentation (2014, May 20)

Dans cette présentation, nous étudions la propriété d'associativité pour les fonctions d'agrégation à arités multiples et nous introduisons la propriété plus générale de préassociativité qui n'implique ... [more ▼]

Dans cette présentation, nous étudions la propriété d'associativité pour les fonctions d'agrégation à arités multiples et nous introduisons la propriété plus générale de préassociativité qui n'implique aucune composition de fonctions. Nous étudions cette nouvelle propriété et nous décrivons certaines classes de fonction préassociatives. Nous montrons aussi comment des axiomatisations de plusieurs classes de functions (comme les semi-groupes aczéliens ou les polynômes latticiels associatifs) peuvent être obtenues en affaiblissant l'associativité en la remplaçant par la préassociativité. [less ▲]

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See detailAnalyse de fiabilité des systèmes et description par des polynômes latticiels
Marichal, Jean-Luc UL

Presentation (2014, March 07)

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See detailFonctions d'agrégation pour l'aide multicritère à la décision
Marichal, Jean-Luc UL

Presentation (2014, February 21)

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See detailSubsignatures of systems
Marichal, Jean-Luc UL

in Journal of Multivariate Analysis (2014), 124

We introduce the concept of subsignature for semicoherent systems as a class of indexes that range from the system signature to the Barlow-Proschan importance index. Specifically, given a nonempty subset ... [more ▼]

We introduce the concept of subsignature for semicoherent systems as a class of indexes that range from the system signature to the Barlow-Proschan importance index. Specifically, given a nonempty subset M of the set of components of a system, we define the M-signature of the system as the |M|-tuple whose k-th coordinate is the probability that the k-th failure among the components in M causes the system to fail. We give various explicit linear expressions for this probability in terms of the structure function and the distribution of the component lifetimes. We also examine the case of exchangeable lifetimes and the special case when the lifetime are i.i.d. and M is a modular set. [less ▲]

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See detailFonctions associatives et préassociatives
Marichal, Jean-Luc UL; Teheux, Bruno UL

Scientific Conference (2013, October 18)

We investigate the associativity property for functions of multiple arities and introduce the more general property of preassociativity, an extension of associativity which does not involve any ... [more ▼]

We investigate the associativity property for functions of multiple arities and introduce the more general property of preassociativity, an extension of associativity which does not involve any composition of functions. We discuss this new property and describe certain classes of preassociative functions. We also show how axiomatizations of several function classes can be extended by relaxing associativity to preassociativity. [less ▲]

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See detailFonctions d’agrégation barycentriquement associatives
Marichal, Jean-Luc UL; Teheux, Bruno UL

in Marichal, Jean-Luc; Essounbouli, Najib; Guelton, Kevin (Eds.) Actes des 22èmes rencontres francophones sur la Logique Floue et ses Applications, 10-11 octobre 2013, Reims, France (2013, October)

We investigate the algebraic property of barycentric associativity for aggregation functions. This property, well-known in Kolmogoroff-Nagumo’s axiomatization of the quasi-arithmetic means, is often ... [more ▼]

We investigate the algebraic property of barycentric associativity for aggregation functions. This property, well-known in Kolmogoroff-Nagumo’s axiomatization of the quasi-arithmetic means, is often considered as very natural whenever the aggregation process is of an (arithmetic, geometric, harmonic...) mean type. We recall the definition of this property and propose some extensions. We also present some results, some rather surprising, related to these properties. [less ▲]

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See detailActes des 22èmes rencontres francophones sur la Logique Floue et ses Applications, 10-11 octobre 2013, Reims, France
Marichal, Jean-Luc UL; Essounbouli, Najib; Guelton, Kevin

Book published by Université de Reims Champagne-Ardenne (2013)

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See detailDiscrete integrals based on comonotonic modularity
Couceiro, Miguel; Marichal, Jean-Luc UL

in Axioms (2013), 2(3), 390-403

It is known that several discrete integrals, including the Choquet and Sugeno integrals as well as some of their generalizations, are comonotonically modular functions. Based on a recent description of ... [more ▼]

It is known that several discrete integrals, including the Choquet and Sugeno integrals as well as some of their generalizations, are comonotonically modular functions. Based on a recent description of the class of comonotonically modular functions, we axiomatically identify more general families of discrete integrals that are comonotonically modular, including signed Choquet integrals and symmetric signed Choquet integrals as well as natural extensions of Sugeno integrals. [less ▲]

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See detailComputing system signatures through reliability functions
Marichal, Jean-Luc UL; Mathonet, Pierre UL

in Statistics and Probability Letters (2013), 83(3), 710-717

It is known that the Barlow-Proschan index of a system with i.i.d. component lifetimes coincides with the Shapley value, a concept introduced earlier in cooperative game theory. Due to a result by Owen ... [more ▼]

It is known that the Barlow-Proschan index of a system with i.i.d. component lifetimes coincides with the Shapley value, a concept introduced earlier in cooperative game theory. Due to a result by Owen, this index can be computed efficiently by integrating the first derivatives of the reliability function of the system along the main diagonal of the unit hypercube. The Samaniego signature of such a system is another important index that can be computed for instance by Boland's formula, which requires the knowledge of every value of the associated structure function. We show how the signature can be computed more efficiently from the diagonal section of the reliability function via derivatives. We then apply our method to the computation of signatures for systems partitioned into disjoint modules with known signatures. [less ▲]

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See detailOn the extensions of Barlow-Proschan importance index and system signature to dependent lifetimes
Marichal, Jean-Luc UL; Mathonet, Pierre UL

in Journal of Multivariate Analysis (2013), 115

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 ... [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. Assuming only that the joint distribution of component lifetimes has no ties, we give an explicit expression for this extended index in terms of the discrete derivatives of the structure function and provide an interpretation of it as a probabilistic value, a concept introduced in game theory. This enables us to interpret Iyer's formula in this more general setting. We also discuss the analogy between this concept and that of system signature and show how it can be used to define a symmetry index for systems. [less ▲]

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

in Mesiar, Radko; Pap, Endre; Klement, Erich Peter (Eds.) 34th Linz Seminar on Fuzzy Set Theory (LINZ 2013) - Non-Classical Measures and Integrals (2013)

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See detailOn the cardinality index of fuzzy measures and the signatures of coherent systems
Mathonet, Pierre UL; Marichal, Jean-Luc UL

in Mesiar, Radko; Pap, Endre; Klement, Erich Peter (Eds.) 34th Linz Seminar on Fuzzy Set Theory (LINZ 2013) - Non-Classical Measures and Integrals (2013)

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See detailOn comonotonically modular functions
Couceiro, Miguel; Marichal, Jean-Luc UL

in Mesiar, Radko; Pap, Endre; Klement, Erich Peter (Eds.) 34th Linz Seminar on Fuzzy Set Theory (LINZ 2013) - Non-Classical Measures and Integrals (2013)

Detailed reference viewed: 42 (3 UL)