Abstract
Ordered modular aggregation functions (OMAF in short) can be seen as symmetrized modular aggregation functions and they are characterized by comonotone modularity. As such, OMAFs generalize OWA operators. We show a one-to-one correspondence between idempotent OMAFs and copula-based integrals with respect to a symmetric capacity.
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References
Beliakov, G.: Learning Weights in the Generalized OWA Operators. Fuzzy Optimization and Decision Making 4, 119–130 (2005)
Beliakov, G., Pradera, A., Calvo, T.: Aggregation functions: a Guide for Practitioners. Springer, Heidelberg (2007)
Calvo, T., Mesiar, R.: Stability of aggregation op- erators. In: Proc of Int. Conference in Fuzzy Logic and Technology, Leicester, pp. 475–478 (2001)
Calvo, T., Kolesárová, A., Komorníková, M., Mesiar, R.: Aggregation Operators: Properties, Classes and Construction Methods. In: Calvo, T., Mayor, G., Mesiar, R. (eds.) Aggregation Operators, pp. 3–107. Physica-Verlag, Heidelberg (2002)
Grabisch, M.: Fuzzy integral in multicriteria decision making. Fuzzy Sets and Systems 69, 279–298 (1995)
Grabisch, M., Marichal, J.-L., Mesiar, R., Pap, E.: Aggregation Functions. Cambridge University Press, Cambridge (2009)
Grabisch, M.: OWA operators and nonadditive integrals. In: [16] (to appear)
Klement, E.P., Mesiar, R., Pap, E.: Measure-based aggregation operators. Fuzzy Sets and Systems 142(1), 3–14 (2004)
Merigó, J.M., Gil-Lafuente, A.M.: The induced generalized OWA operator. In: New dimensions in fuzzy logic and related technologies. Proceedings of the 5th EUSFLAT Conference, Ostrava, Czech Republic, pp. 463–470 (2007)
Murofushi, T., Sugeno, M.: Some quantities represented by the Choquet integral. Fuzzy Sets and Systems 56, 229–235 (1993)
Nelsen, R.B.: An Introduction to Copulas. Springer, New York (1999)
Torra, V.: The weighted OWA operator. Int. J. of Intelligent Systems 12, 153–166 (1997)
Yager, R.R.: On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Transactions on Systems, Man and Cybernetics 18, 183–190 (1988)
Yager, R.R., Filev, D.P.: Induced Ordered Weighted Averaging Operators. IEEE Transactions on Systems, Man and Cybernetics 29(2), 141–150 (1999)
Yager, R.R., Kacprzyk, J.: The Ordered Weighted Averaging Operators: Theory and Applications. Kluwer Academic Publishers, Boston (1997)
Yager, R.R., Kacprzyk, J., Beliakov, G.: Recent Developments in the Ordered Weighted Averaging Operators: Theory and Practice. Springer, Heidelberg (to appear)
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Mesiar, R., Mesiarová-Zemánková, A. (2010). Symmetrization of Modular Aggregation Functions. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds) Computational Intelligence for Knowledge-Based Systems Design. IPMU 2010. Lecture Notes in Computer Science(), vol 6178. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14049-5_40
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DOI: https://doi.org/10.1007/978-3-642-14049-5_40
Publisher Name: Springer, Berlin, Heidelberg
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