Communication publiée dans un ouvrage (Colloques, congrès, conférences scientifiques et actes)
Preassociative aggregation functions
MARICHAL, Jean-Luc; TEHEUX, Bruno
2014 • In Laurent, Anne; Strauss, Olivier; Bouchon-Meunier, Bernadetteet al. (Eds.) 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
[en] 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.
Disciplines :
Mathématiques Méthodes quantitatives en économie & gestion
Auteur, co-auteur :
MARICHAL, Jean-Luc ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
TEHEUX, Bruno ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Langue du document :
Anglais
Titre :
Preassociative aggregation functions
Date de publication/diffusion :
22 juillet 2014
Nom de la manifestation :
15th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2014)
Organisateur de la manifestation :
Anne Laurent Oliver Strauss
Lieu de la manifestation :
Montpellier, France
Date de la manifestation :
from 15-07-2014 to 19-07-2014
Manifestation à portée :
International
Titre de l'ouvrage principal :
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
Editeur scientifique :
Laurent, Anne
Strauss, Olivier
Bouchon-Meunier, Bernadette
Yager, Ronald R.
Maison d'édition :
Springer, Heidelberg, Allemagne
ISBN/EAN :
978-3-319-08851-8
Collection et n° de collection :
Communications in Computer and Information Science, Vol. 444
Aczél, J.: Sur les opérations définies pour nombres réels. Bull. Soc. Math. France 76, 59-64 (1949)
Aczél, J.: The associativity equation re-revisited. In: Erikson, G., Zhai, Y. (eds.) Bayesian Inference and Maximum Entropy Methods in Science and Engineering, pp. 195-203, American Institute of Physics, Melville-New York (2004)
Alsina, C., Frank, M.J., Schweizer, B.: Associative functions: triangular norms and copulas. World Scientific, London (2006)
Beliakov, G., Pradera, A., Calvo, T.: Aggregation functions: a guide for practitioners. STUDFUZZ, vol. 221. Springer, Heidelberg (2007)
Calvo, T., Kolesárová, A., Komorníková, M., Mesiar, R.: Aggregation operators: properties, classes and construction methods. In: Aggregation Operators. New Trends and Applications. STUDFUZZ, vol. 97, pp. 3-104. Physica-Verlag, Heidelberg (2002)
Couceiro, M., Marichal, J.-L.: Associative polynomial functions over bounded distributive lattices. Order 28, 1-8 (2011)
Couceiro, M., Marichal, J.-L.: Aczélian n-ary semigroups. Semigroup Forum 85, 81-90 (2012)
Craigen, R., Páles, Z.: The associativity equation revisited. Aeq. Math. 37, 306-312 (1989)
Fodor, J., Roubens, M.: Fuzzy preference modelling and multicriteria decision support. In: Theory and Decision Library. Series D: System Theory, Knowledge Engineering and Problem Solving. Kluwer Academic Publisher, Dordrecht (1994)
Grabisch, M., Marichal, J.-L., Mesiar, R., Pap, E.: Aggregation functions. In: Encyclopedia of Mathematics and its Applications, vol. 127, Cambridge University Press, Cambridge (2009)
Klement, E.P., Mesiar, R. (eds.): Logical, algebraic, analytic, and probabilistic aspects of triangular norms. Elsevier Science, Amsterdam (2005)
Klement, E.P., Mesiar, R., Pap, E.: Triangular norms. In: Trends in Logic - Studia Logica Library, vol. 8. Kluwer Academic, Dordrecht (2000)
Marichal, J.-L.: Aggregation operators for multicriteria decision aid. PhD thesis, Department of Mathematics, University of Liège, Liège, Belgium (1998)
Marichal, J.-L.: On the associativity functional equation. Fuzzy Sets and Systems 114, 381-389 (2000)
Schweizer, B., Sklar, A.: Probabilistic metric spaces. North-Holland Series in Probability and Applied Mathematics. North-Holland Publishing Co., New York (1983) (New edition in: Dover Publications, New York, 2005)
Yager, R.R.: Quasi-associative operations in the combination of evidence. Kybernetes 16, 37-41 (1987)
