Browse ORBi

- What it is and what it isn't
- Green Road / Gold Road?
- Ready to Publish. Now What?
- How can I support the OA movement?
- Where can I learn more?

ORBi

Pivotal decompositions of functions Marichal, Jean-Luc ; Teheux, Bruno 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 ▲] Detailed reference viewed: 200 (11 UL)Quasi-Lovász extensions on bounded chains ; Marichal, Jean-Luc 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: 130 (5 UL)Preassociative aggregation functions Marichal, Jean-Luc ; Teheux, Bruno 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 ▲] Detailed reference viewed: 131 (8 UL)Associative string functions Lehtonen, Erkko ; Marichal, Jean-Luc ; Teheux, Bruno Scientific Conference (2014, June 24) Detailed reference viewed: 219 (16 UL)Associativity, preassociativity, and string functions Lehtonen, Erkko ; Marichal, Jean-Luc ; Teheux, Bruno Scientific Conference (2014, June 20) Detailed reference viewed: 79 (9 UL)On structure signatures and probability signatures of general decomposable systems (invited talk) Marichal, Jean-Luc ; Mathonet, Pierre ; Scientific Conference (2014, June 16) Detailed reference viewed: 145 (4 UL)Preassociativity for aggregation functions Marichal, Jean-Luc ; Teheux, Bruno Scientific Conference (2014, June 16) Detailed reference viewed: 85 (5 UL)Fonctions d'agrégation associatives et préassociatives (invited lecture) Marichal, Jean-Luc 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 ▲] Detailed reference viewed: 66 (8 UL)Analyse de fiabilité des systèmes et description par des polynômes latticiels Marichal, Jean-Luc Presentation (2014, March 07) Detailed reference viewed: 70 (13 UL)Fonctions d'agrégation pour l'aide multicritère à la décision Marichal, Jean-Luc Presentation (2014, February 21) Detailed reference viewed: 156 (7 UL)Subsignatures of systems Marichal, Jean-Luc 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 ▲] Detailed reference viewed: 102 (21 UL)Fonctions associatives et préassociatives Marichal, Jean-Luc ; Teheux, Bruno 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 ▲] Detailed reference viewed: 92 (9 UL)Fonctions d’agrégation barycentriquement associatives Marichal, Jean-Luc ; Teheux, Bruno 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 ▲] Detailed reference viewed: 161 (11 UL)Actes des 22èmes rencontres francophones sur la Logique Floue et ses Applications, 10-11 octobre 2013, Reims, France Marichal, Jean-Luc ; ; Book published by Université de Reims Champagne-Ardenne (2013) Detailed reference viewed: 182 (7 UL)Discrete integrals based on comonotonic modularity ; Marichal, Jean-Luc 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 ▲] Detailed reference viewed: 137 (8 UL)Computing system signatures through reliability functions Marichal, Jean-Luc ; Mathonet, Pierre 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 ▲] Detailed reference viewed: 234 (24 UL)On the extensions of Barlow-Proschan importance index and system signature to dependent lifetimes Marichal, Jean-Luc ; Mathonet, Pierre 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 ▲] Detailed reference viewed: 208 (15 UL)Pivotal decompositions of aggregation functions Marichal, Jean-Luc ; Teheux, Bruno 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: 61 (14 UL)On the cardinality index of fuzzy measures and the signatures of coherent systems Mathonet, Pierre ; Marichal, Jean-Luc 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: 84 (4 UL)On comonotonically modular functions ; Marichal, Jean-Luc 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) |
||