Reference : Cumulative distribution functions and moments of weighted lattice polynomials
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Cumulative distribution functions and moments of weighted lattice polynomials
Marichal, Jean-Luc mailto [University of Luxembourg > Faculty of Law, Economics and Finance > Applied Mathematics Unit (SMA)]
Seminar "Mathématiques discrètes et sciences sociales"
Jean-Pierre Barthelemy
Marc Demange
Michel Grabisch
Olivier Hudry
Bruno Leclerc
Bernard Monjardet
Centre d'Analyse et de Mathématiques Sociales (CAMS), Ecole des Hautes Etudes en Sciences Sociales, Paris
[en] In the first part of this presentation we define the concept of weighted lattice polynomials as lattice polynomials constructed from both variables and parameters. We then show that, in any bounded distributive lattice, these functions can always be written in conjunctive and disjunctive normal forms. We also show that these functions include the class of discrete Sugeno integrals and that they are characterized by a remarkable median based decomposition formula.
In the second part we give the cumulative distribution functions, the expected values, and the moments of weighted lattice polynomials when regarded as real functions. Since weighted lattice polynomial functions include Sugeno integrals, lattice polynomial functions, and order statistics, our results encompass the corresponding formulas for these particular functions. We then conclude with some applications of our results to the reliability analysis of coherent systems.
University of Luxembourg - UL
Recherches méthodologiques et mathématiques en aide à la décision et à la classification > 01/01/2005 – 12/12/2007 > BISDORFF Raymond
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