Abstract
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.
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References
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)
Bacchelli, B.: Representation of continuous associative functions. Stochastica 10, 13–28 (1986)
Beliakov, G., Pradera, A., Calvo, T.: Aggregation functions: a guide for practitioners. STUDFUZZ, vol. 221. Springer, Heidelberg (2007)
Calvo, T., Kolesárová, A., KomornÃková, 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)
Ling, C.H.: Representation of associative functions. Publ. Math. Debrecen 12, 189–212 (1965)
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)
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Marichal, JL., Teheux, B. (2014). Preassociative Aggregation Functions. In: Laurent, A., Strauss, O., Bouchon-Meunier, B., Yager, R.R. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2014. Communications in Computer and Information Science, vol 444. Springer, Cham. https://doi.org/10.1007/978-3-319-08852-5_34
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DOI: https://doi.org/10.1007/978-3-319-08852-5_34
Publisher Name: Springer, Cham
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