Abstract
A copula-based method to integrate a real vector-valued function, obtaining a single real number, is discussed. Special attention is paid to the case when the underlying universe is finite. The integral considered here is shown to be an extension of [0,1]-valued copula-based universal integrals.
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References
Choquet, G.: Theory of capacities. Ann. Inst. Fourier (Grenoble) 5, 131–295 (1954)
Imaoka, H.: On a subjective evaluation model by a generalized fuzzy integral. Internat. J. Uncertain. Fuzziness Knowledge-Based Systems 5, 517–529 (1997)
Klement, E.P., Mesiar, R., Pap, E.: Measure-based aggregation operators. Fuzzy Sets and Systems 142, 3–14 (2004)
Klement, E.P., Mesiar, R., Pap, E.: A universal integral as common frame for Choquet and Sugeno integral. IEEE Trans. Fuzzy Systems 18, 178–187 (2010)
Nelsen, R.B.: An Introduction to Copulas, 2nd edn. Lecture Notes in Statistics, vol. 139. Springer, New York (2006)
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)
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Klement, E.P., Mesiar, R. (2012). Copula-Based Integration of Vector-Valued Functions. In: Greco, S., Bouchon-Meunier, B., Coletti, G., Fedrizzi, M., Matarazzo, B., Yager, R.R. (eds) Advances in Computational Intelligence. IPMU 2012. Communications in Computer and Information Science, vol 300. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31724-8_59
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DOI: https://doi.org/10.1007/978-3-642-31724-8_59
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31723-1
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