Abstract
We recall first graded classes of copula - based integrals and their specific form when a finite universe X is considered. Subsequently, copula - based generalizations of OWA operators are introduced, as copula - based integrals with respect to symmetric capacities. As a particular class of our new operators, recently introduced OMA operators are obtained. Several particular examples are introduced and discussed to clarify our approach.
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References
Beliakov, G.: Learning weights in the generalized OWA operators. Fuzzy Optimization and Decision Making 4(2), 119–130 (2005)
Choquet, G.: Theory of capacities. Ann. Inst. Fourier, 131–295 (1953/1954)
Dubois, D., Prade, H.: A review of fuzzy set aggregation connectives. Inform. Sci. 36, 85–121 (1985)
Even, Y., Lehrer, E.: Decomposition-Integral: Unifying Choquet and the Concave Integrals. Economic Theory, 1–26 (2013) (article in Press)
Grabisch, M.: Fuzzy integral in multicriteria decision making. Fuzzy Sets and Systems 69(3), 279–298 (1995)
Grabisch, M., Marichal, J.L., Mesiar, R., Pap, E.: Aggregation Functions. Cambridge University Press, New York (2009)
Joe, H.: Multivariate Models and Dependence Concepts. Monographs on Statics and Applied Probability, vol. 73. Chapman & Hall, London (1997)
Klement, E.P., Mesiar, R., Pap, E.: A universal integral as common frame for Choquet and Sugeno integral. IEEE Transactions on Fuzzy Systems 18, 178–187 (2010)
Klement, E.P., Mesiar, R., Pap, E.: Measure-based aggregation operators. Fuzzy Sets and Systems 142(1), 3–14 (2004)
Klement, E.P., Mesiar, R., Spizzichino, F., Stupňanová, A.: Universal integrals based on copulas. Submitted to Fuzzy Optimization and Decision Making
Mesiar, R., Mesiarová-Zemánková, A.: The ordered modular averages. IEEE Transactions on Fuzzy Systems 19(1), 42–50 (2011)
Mesiar, R., Stupňanová, A.: Decomposition integrals. International Journal of Approximate Reasoning 54, 1252–1259 (2013)
Murofushi, T., Sugeno, M.: Some quantities represented by the Choquet integral. Fuzzy Sets and Systems 56(2), 229–235 (1993)
Nelsen, R.B.: An Introduction to Copulas, 2nd edn. Springer, New York (2006)
Schmeidler, D.: Integral representation without additivity. Proc. Amer. Math. 97(2), 255–270 (1986)
Shilkret, N.: Maxitive measure and integration. Indag. Math. 33, 109–116 (1971)
Sklar, A.: Fonctions de répartition à n dimensions et leurs marges. Publ. Inst. Statist. Univ. Paris 8, 229–231 (1959)
Sugeno, M.: Theory of fuzzy integrals and its applications. PhD thesis, Tokyo Institute of Technology (1974)
Torra, V.: The weighted OWA operator. International Journal of Intelligent Systems 12(2), 153–166 (1997)
Yager, R.R.: On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Trans. Systems Man Cybernet. 18(1), 183–190 (1988)
Yager, R.R., Filev, D.P.: Induced Ordered Weighted Averaging operators. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 29(2), 141–150 (1999)
Yager, R.R., Kacprzyk, J. (eds.): The Ordered Weighted Averanging Operators. Kluwer Academic Publishers, USA (1999)
Yager, R.R., Kacprzyk, J., Beliakov, G. (eds.): Recent Developments in the Ordered Weighted Averaging Operators: Theory and Practice. STUDFUZZ. Springer, Berlin (2011)
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Mesiar, R., Stupňanová, A. (2014). Copula - Based Generalizations of OWA Operators. 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_29
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DOI: https://doi.org/10.1007/978-3-319-08852-5_29
Publisher Name: Springer, Cham
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