Erich Peter Klement, Anna Kolesárová (2005)
Kybernetika
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Smallest and greatest -Lipschitz aggregation operators with given diagonal section, opposite diagonal section, and with graphs passing through a single point of the unit cube, respectively, are determined. These results are used to find smallest and greatest copulas and quasi-copulas with these properties (provided they exist).
Fabrizio Durante, José Quesada-Molina, Carlo Sempi (2006)
Kybernetika
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We characterize some bivariate semicopulas and, among them, the semicopulas satisfying a Lipschitz condition. In particular, the characterization of harmonic semicopulas allows us to introduce a new concept of depedence between two random variables. The notion of multivariate semicopula is given and two applications in the theory of fuzzy measures and stochastic processes are given.
Fabrizio Durante, Carlo Sempi (2005)
Kybernetika
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We define the notion of semicopula, a concept that has already appeared in the statistical literature and study the properties of semicopulas and the connexion of this notion with those of copula, quasi-copula, -norm.
Gaspar Mayor, Radko Mesiar, Joan Torrens (2008)
Kybernetika
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Quasi-homogeneity of copulas is introduced and studied. Quasi-homogeneous copulas are characterized by the convexity and strict monotonicity of their diagonal sections. As a by-product, a new construction method for copulas when only their diagonal section is known is given.
Elisabetta Alvoni, Pier Luigi Papini (2007)
Commentationes Mathematicae Universitatis Carolinae
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In this paper we consider a class of copulas, called quasi-concave; we compare them with other classes of copulas and we study conditions implying symmetry for them. Recently, a measure of asymmetry for copulas has been introduced and the maximum degree of asymmetry for them in this sense has been computed: see Nelsen R.B., , Statist. Papers (2007), 329–336; Klement E.P., Mesiar R., ?, Comment. Math. Univ. Carolin. (2006), 141–148. Here we compute the maximum degree of asymmetry that...