References of "Marichal, Jean-Luc 50002296"
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See detailA classification of polynomial functions satisfying the Jacobi identity over integral domains
Marichal, Jean-Luc UL; Mathonet, Pierre

in Aequationes Mathematicae (in press)

The Jacobi identity is one of the properties that are used to define the concept of Lie algebra and in this context is closely related to associativity. In this paper we provide a complete description of ... [more ▼]

The Jacobi identity is one of the properties that are used to define the concept of Lie algebra and in this context is closely related to associativity. In this paper we provide a complete description of all bivariate polynomials that satisfy the Jacobi identity over infinite integral domains. Although this description depends on the characteristic of the domain, it turns out that all these polynomials are of degree at most one in each indeterminate. [less ▲]

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See detailJoint signature of two or more systems with applications to multistate systems made up of two-state components
Marichal, Jean-Luc UL; Mathonet, Pierre; Navarro, Jorge et al

in European Journal of Operational Research (in press)

The structure signature of a system made up of n components having continuous and i.i.d. lifetimes was defined in the eighties by Samaniego as the n-tuple whose k-th coordinate is the probability that the ... [more ▼]

The structure signature of a system made up of n components having continuous and i.i.d. lifetimes was defined in the eighties by Samaniego as the n-tuple whose k-th coordinate is the probability that the k-th component failure causes the system to fail. More recently, a bivariate version of this concept was considered as follows. The joint structure signature of a pair of systems built on a common set of components having continuous and i.i.d. lifetimes is a square matrix of order n whose (k,l)-entry is the probability that the k-th failure causes the first system to fail and the l-th failure causes the second system to fail. This concept was successfully used to derive a signature-based decomposition of the joint reliability of the two systems. In the first part of this paper we provide an explicit formula to compute the joint structure signature of two or more systems and extend this formula to the general non-i.i.d. case, assuming only that the distribution of the component lifetimes has no ties. We also provide and discuss a necessary and sufficient condition on this distribution for the joint reliability of the systems to have a signature-based decomposition. In the second part of this paper we show how our results can be efficiently applied to the investigation of the reliability and signature of multistate systems made up of two-state components. The key observation is that the structure function of such a multistate system can always be additively decomposed into a sum of classical structure functions. Considering a multistate system then reduces to considering simultaneously several two-state systems. [less ▲]

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See detailRecent results on conservative and symmetric n-ary semigroups
Kiss, Gergely UL; Devillet, Jimmy UL; Marichal, Jean-Luc UL

Scientific Conference (2017, June 16)

See attached file

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See detailOn conservative and associative operations on finite chains
Devillet, Jimmy UL; Couceiro, Miguel; Marichal, Jean-Luc UL

Scientific Conference (2017, June 16)

See attached file

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See detailOn idempotent discrete uninorms
Couceiro, Miguel; Devillet, Jimmy UL; Marichal, Jean-Luc UL

in De Baets, Bernard; Torra, Vicenç; Mesiar, Radko (Eds.) Aggregation Functions in Theory and in Practice (2017, June)

In this paper we provide two axiomatizations of the class of idempotent discrete uninorms as conservative binary operations, where an operation is conservative if it always outputs one of its input values ... [more ▼]

In this paper we provide two axiomatizations of the class of idempotent discrete uninorms as conservative binary operations, where an operation is conservative if it always outputs one of its input values. More precisely we first show that the idempotent discrete uninorms are exactly those operations that are conservative, symmetric, and nondecreasing in each variable. Then we show that, in this characterization, symmetry can be replaced with both bisymmetry and existence of a neutral element. [less ▲]

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See detailOn the generalized associativity equation
Marichal, Jean-Luc UL; Teheux, Bruno UL

in Aequationes Mathematicae (2017), 91(2), 265-277

The so-called generalized associativity functional equation G(J(x,y),z) = H(x,K(y,z)) has been investigated under various assumptions, for instance when the unknown functions G, H, J, and K are real ... [more ▼]

The so-called generalized associativity functional equation G(J(x,y),z) = H(x,K(y,z)) has been investigated under various assumptions, for instance when the unknown functions G, H, J, and K are real, continuous, and strictly monotonic in each variable. In this note we investigate the following related problem: given the functions J and K, find every function F that can be written in the form F(x,y,z) = G(J(x,y),z) = H(x,K(y,z)) for some functions G and H. We show how this problem can be solved when any of the inner functions J and K has the same range as one of its sections. [less ▲]

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

Scientific Conference (2016, November 08)

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See detailRelaxations of associativity and preassociativity for variadic functions
Couceiro, Miguel; Marichal, Jean-Luc UL; Teheux, Bruno UL

in Fuzzy Sets & Systems (2016), 299

In this paper we consider two properties of variadic functions, namely associativity and preassociativity, that are pertaining to several data and language processing tasks. We propose parameterized ... [more ▼]

In this paper we consider two properties of variadic functions, namely associativity and preassociativity, that are pertaining to several data and language processing tasks. We propose parameterized relaxations of these properties and provide their descriptions in terms of factorization results. We also give an example where these parameterized notions give rise to natural hierarchies of functions and indicate their potential use in measuring the degrees of associativeness and preassociativeness. We illustrate these results by several examples and constructions and discuss some open problems that lead to further directions of research. [less ▲]

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See detailA characterisation of associative idempotent nondecreasing functions with neutral elements
Kiss, Gergely UL; Laczkovich, Miklós; Marichal, Jean-Luc UL et al

Scientific Conference (2016, June)

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See detailStructure functions and minimal path sets
Marichal, Jean-Luc UL

in IEEE Transactions on Reliability (2016), 65(2), 763-768

In this short note we give and discuss a general multilinear expression of the structure function of an arbitrary semicoherent system in terms of its minimal path and cut sets. We also examine the link ... [more ▼]

In this short note we give and discuss a general multilinear expression of the structure function of an arbitrary semicoherent system in terms of its minimal path and cut sets. We also examine the link between the number of minimal path and cut sets consisting of one or two components and the concept of structure signature of the system. [less ▲]

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

in Journal of Mathematical Analysis and Applications (2016), 437(1), 181-193

We study the property of strong barycentric associativity, a stronger version of barycentric associativity for functions with indefinite arities. We introduce and discuss the more general property of ... [more ▼]

We study the property of strong barycentric associativity, a stronger version of barycentric associativity for functions with indefinite arities. We introduce and discuss the more general property of strong barycentric preassociativity, a generalization of strong 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 strongly barycentrically preassociative functions. [less ▲]

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See detailConservative median algebras and semilattices
Couceiro, Miguel; Marichal, Jean-Luc UL; Teheux, Bruno UL

in Order : A Journal on the Theory of Ordered Sets and its Applications (2016), 33(1), 121-132

We characterize conservative median algebras and semilattices by means of forbidden substructures and by providing their representation as chains. Moreover, using a dual equivalence between median ... [more ▼]

We characterize conservative median algebras and semilattices by means of forbidden substructures and by providing their representation as chains. Moreover, using a dual equivalence between median algebras and certain topological structures, we obtain descriptions of the median-preserving mappings between products of finitely many chains. [less ▲]

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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 detailAn extension of the concept of distance as functions of several variables
Kiss, Gergely UL; Marichal, Jean-Luc UL; Teheux, Bruno UL

in De Baets, Bernard; Mesiar, Radko; Saminger-Platz, Susanne (Eds.) et al 36th Linz Seminar on Fuzzy Set Theory (LINZ 2016) - Functional Equations and Inequalities (2016, February)

Extensions of the concept of distance to more than two elements have been recently proposed in the literature to measure to which extent the elements of a set are spread out. Such extensions may be ... [more ▼]

Extensions of the concept of distance to more than two elements have been recently proposed in the literature to measure to which extent the elements of a set are spread out. Such extensions may be particularly useful to define dispersion measures for instance in statistics or data analysis. In this note we provide and discuss an extension of the concept of distance, called n-distance, as functions of n variables. The key feature of this extension is a natural generalization of the triangle inequality. We also provide some examples of n-distances that involve geometric and graph theoretic constructions. [less ▲]

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See detailThe mathematics behind the property of associativity
Marichal, Jean-Luc UL; Teheux, Bruno UL

in De Baets, Bernard; Mesiar, Radko; Saminger-Platz, Susanne (Eds.) et al 36th Linz Seminar on Fuzzy Set Theory (LINZ 2016) - Functional Equations and Inequalities (2016, February)

The well-known equation of associativity for binary operations may be naturally generalized to variadic operations. In this talk, we illustrate different approaches that can be considered to study this ... [more ▼]

The well-known equation of associativity for binary operations may be naturally generalized to variadic operations. In this talk, we illustrate different approaches that can be considered to study this extension of associativity, as well as some of its generalizations and variants, including barycentric associativity and preassociativity. [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 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 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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