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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: 84 (1 UL)Relation graphs and partial clones on a 2-element set. Schölzel, Karsten ; ; et al in Multiple-Valued Logic (ISMVL), 2014 IEEE 44rd International Symposium on (2014) In a recent paper, the authors show that the sublattice of partial clones that preserve the relation $\{(0,0),(0,1),(1,0)\}$ is of continuum cardinality on $\2$. In this paper we give an alternative proof ... [more ▼] In a recent paper, the authors show that the sublattice of partial clones that preserve the relation $\{(0,0),(0,1),(1,0)\}$ is of continuum cardinality on $\2$. In this paper we give an alternative proof to this result by making use of a representation of relations derived from $\{(0,0),(0,1),(1,0)\}$ in terms of certain types of graphs. As a by-product, this tool brings some light into the understanding of the structure of this uncountable sublattice of strong partial clones. [less ▲] Detailed reference viewed: 71 (3 UL)An Arrow-like theorem over median algebras ; Teheux, Bruno Poster (2014) We present an Arrow-like theorem for aggregation functions over convervative median algebras. In doing so, we give a characterization of conservative median algebras by means of forbidden substructures ... [more ▼] We present an Arrow-like theorem for aggregation functions over convervative 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 ▲] Detailed reference viewed: 78 (6 UL)Sur des classes de fonctions à seuil caractérisables par des contraintes relationnelles ; Lehtonen, Erkko ; Schölzel, Karsten 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) Motivated by modal semantics induced by majority games, we consider the class of threshold functions. It was shown by L. Hellerstein that this class is characterizable by relational constraints (or ... [more ▼] Motivated by modal semantics induced by majority games, we consider the class of threshold functions. It was shown by L. Hellerstein that this class is characterizable by relational constraints (or equivalently, by functional equations), but that there is no characterization by means of finitely many constraints. In this paper, we present a complete classification of classes of threshold functions induced by Boolean clones, into whether they are characterizable by finitely many relational constraints. Moreover we provide sets of constraints characterizing each of such classes. [less ▲] Detailed reference viewed: 123 (1 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: 107 (5 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: 24 (2 UL)A complete classification of equational classes of threshold functions included in clones ; Lehtonen, Erkko ; Schölzel, Karsten E-print/Working paper (2013) The class of threshold functions is known to be characterizable by functional equations or, equivalently, by pairs of relations, which are called relational constraints. It was shown by Hellerstein that ... [more ▼] The class of threshold functions is known to be characterizable by functional equations or, equivalently, by pairs of relations, which are called relational constraints. It was shown by Hellerstein that this class cannot be characterized by a finite number of such objects. In this paper, we investigate classes of threshold functions which arise as intersections of the class of all threshold functions with clones of Boolean functions, and provide a complete classification of such intersections in respect to whether they have finite characterizations. Moreover, we provide a characterizing set of relational constraints for each class of threshold functions arising in this way. [less ▲] Detailed reference viewed: 76 (3 UL)Set-reconstructibility of Post classes ; Lehtonen, Erkko ; Schölzel, Karsten E-print/Working paper (2013) The clones of Boolean functions are classified in regard to set-reconstructibility via a strong dichotomy result: the clones containing only affine functions, conjunctions, disjunctions or constant ... [more ▼] The clones of Boolean functions are classified in regard to set-reconstructibility via a strong dichotomy result: the clones containing only affine functions, conjunctions, disjunctions or constant functions are set-reconstructible, whereas the remaing clones are not weakly reconstructible. [less ▲] Detailed reference viewed: 67 (3 UL)Quasi-extensions de Lovász et leur version symétrique ; Marichal, Jean-Luc in Rencontres francophones sur la logique floue et ses applications 2012 (2012, November 15) We present a study of the class of quasi-Lovász extensions (i.e. functions which are a composition of a Lovász extension with a nondecreasing function vanishing at the origin) as well as that of their ... [more ▼] We present a study of the class of quasi-Lovász extensions (i.e. functions which are a composition of a Lovász extension with a nondecreasing function vanishing at the origin) as well as that of their symmetric variants. These functions appear naturally within the scope of decision making under uncertainty since they subsume overall preference functionals associated with discrete Choquet integrals and symmetric discrete Choquet integrals, respectively, whose variables are transformed by a given utility function. [less ▲] Detailed reference viewed: 37 (0 UL)Using Choquet integral in Machine Learning: what can MCDA bring? ; ; et al in DA2PL' 2012 - from Multiple Criteria Decision Aid to Preference Learning (2012) In this paper we discuss the Choquet integral model in the realm of Preference Learning, and point out advantages of learning simultaneously partial utility functions and capacities rather than ... [more ▼] In this paper we discuss the Choquet integral model in the realm of Preference Learning, and point out advantages of learning simultaneously partial utility functions and capacities rather than sequentially, i.e., first utility functions and then capacities or vice-versa. Moreover, we present possible interpretations of the Choquet integral model in Preference Learning based on Shapley values and interaction indices. [less ▲] Detailed reference viewed: 160 (0 UL)On three properties of the discrete Choquet integral ; Marichal, Jean-Luc in Dubois, Didier; Grabisch, Michel; Mesiar, Radko (Eds.) et al 32nd Linz Seminar on Fuzzy Set Theory (LINZ 2011) - Decision Theory: Qualitative and Quantitative Approaches (2011) Three important properties in aggregation theory are investigated, namely horizontal min-additivity, horizontal max-additivity, and comonotonic additivity, which are defined by certain relaxations of the ... [more ▼] Three important properties in aggregation theory are investigated, namely horizontal min-additivity, horizontal max-additivity, and comonotonic additivity, which are defined by certain relaxations of the Cauchy functional equation in several variables. We show that these properties are equivalent and we completely describe the functions characterized by them. By adding some regularity conditions, these functions coincide with the Lovász extensions vanishing at the origin, which subsume the discrete Choquet integrals. [less ▲] Detailed reference viewed: 36 (0 UL) |
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